Negotiating Peace with Your Enemy: The Problem of Costly Concessions

Why do some parties fail to settle conflict, even after long periods of fighting? Bargaining theory ex-plains this through imperfect information, commitment problems, war entrepreneurs, and indivisible stakes. Integrating insights from social psychology into bargaining theory, this article proposes an additional bargaining obstacle. Conflict party members not only care about their in-group’s welfare, but also want to avoid rewarding their opponent through concessions. A mutually acceptable agreement always contains concessions, yet when concessions are unpopular with key constituents, they are costly for leaders to make. This may result in a situation where leaders would prefer to settle but still decide to continue the war. Modifying a standard bargaining setup to account for this dilemma, the article demonstrates the difficulties of settling a conflict when out-group preferences are salient. It shows how events that increase the saliency of out-group preferences, such as major ceasefire vio-lations, lead to a drop in public support for negotiations. The problem of costly concessions renders the search for a mutually acceptable agreement a delicate balancing act, particularly if constituents are isolated from the costs of war and political competitors mobilize around unpopular concessions.

The majority of ongoing armed conflicts today started before the turn of the century (see Allansson, Melander, and Themnér 2017). Such long-running conflicts cause enormous human suffering and are highly destructive. They lead to internal displacement and migration, destroy a country's key infrastructure, and divert resources away from productive activities and investment in public health and education (Collier et al. 2003). The instability caused by these conflicts has spillover effects on neighboring countries and can often destabilize an entire region. A key characteristic of such protracted conflicts is their apparent resistance to any negotiated settlement (Crocker, Hampson, and Aall 2004). Leaders of parties to such conflicts refuse to enter into negotiations, stall progress in talks, escalate violence at critical moments or make hardline statements that render productive negotiations all but impossible. This poses a key puzzle: why do conflict parties fail to negotiate a conflict settlement, even when they know that war is costly?
Bargaining theorists primarily attribute bargaining failures to information problems: because parties have an interest in exaggerating their own capabilities and resolve, they do not trust each other's information, which may lead to a situation where one or both parties overestimate their relative strength. In these situations, they may believe that they can achieve more through continued fighting than through settlement (see Schelling 1960;Lax and Sebenius 1986;Fearon 1995;Powell 1999;Walter 2009). After long periods of fighting, their assessments of the expected military outcome should converge, revealing a range of mutually preferable agreements (Wagner 2000;Slantchev 2003;Powell 2004;Werner and Yuen 2005;Walter 2009). But even when both sides would prefer a negotiated agreement, they may fail to reach settlement, if they cannot credibly commit to implementing a peace agreement (Fearon 1995;Powell 1999;Reiter 2009;Walter 1997Walter , 2009). Other common explanations for protracted conflicts include the indivisibility of stakes (Pillar 1983, 24-26) and the presence of war entrepreneurs (Collier, Hoeffler, and Söderbom 2004). Scholars from the sociopsychological peace and conflict studies focus on a very different set of factors, such as social identity and hatred, to explain protracted conflicts (e.g., Galtung 2004Galtung , 2009Kelman 2007;Kriesberg 2003Kriesberg , 2005. These explanations often present a competing logic, leading to contradicting expectations about conditions that foster conflict settlement (see Greig and Diehl 2005, 624-29). This article forms part of an emerging effort to close the gap between these two bodies of work (see Hafner-Burton et al. 2017).
Disaggregating conflict parties and integrating social preferences into the parsimonious choice model first proposed by Fearon (1995), the article proposes an understudied bargaining obstacle to conflict settlement. It focuses on intrastate conflicts, although the general dynamics may also apply to other forms of violent, political conflicts. The article builds on the simple idea that negotiating in war is different from ordinary bargaining situations: conflict party members not only care about their own benefits but also want to avoid rewarding the negative behavior of their opponent. This may lead to a situation where individuals prefer continued fighting over an agreement that contains important concessions to an enemy, even if they would profit from such an agreement. Leaders have their own personal assessment of a bargaining situation and are also constrained by constituent support. A negotiated agreement, by definition, contains concessions, yet when concessions are unpopular with key constituents, they are costly for leaders to make. This renders the search for a mutually acceptable agreement a delicate balancing act. It may even result in a situation where leaders would prefer to enter into a peace deal with an opponent but still decide to continue the war. I call this the problem of costly concessions.
The analysis shows how for conflict party leaders, negotiated conflict settlement is politically unfeasible if key constituents have strong hatred for the opponent and are largely isolated from the costs of war. Political competitors who mobilize around the issue of concessions may further entrench the problem. The problem of costly concessions highlights the need to distinguish between conflict prevention and conflict resolution and puts into question the assumption that, over time, fighting always reveals a bargaining range. This implies that the transition from war to peace is more difficult than bargaining theorists often presume. For while fighting reveals information, it also fuels or entrenches mutual hatred and by extension creates or engrains the problem of costly concessions. This can lead to a vicious cycle and to protracted conflict.
The article follows the logic of analytic narratives, combining the use of a formal choice model with a qualitative case study (see Bates et al. 2000). It proceeds as follows. The first section discusses how bargaining theory fails to account for social preferences, in particular the wish to punish a sworn enemy. The second section integrates social preferences into a standard bargaining model and discusses the implications at an individual level and for policy support. The third section outlines the implications of costly concessions for leadership decisions and how leaders may seek to overcome this bargaining obstacle. The fourth section illustrates the problem of costly concessions on the basis of the 2012-2016 peace negotiations between the government of Colombia and the FARC. The concluding section discusses the implications of the costly concession problem on our understanding of the transition from war to negotiated peace.

Bargaining Theory and Social Preferences
In the broad literature on armed conflicts, the bargaining theory of war works at the most abstract level. It does not explain the roots of conflicts, i.e., why there are contested issues between conflict parties in the first place. It seeks rather to identify why, when conflict exists, some actors go to war while others resolve the conflict through peaceful means.

Two Types of Bargaining Problems
At the heart of the bargaining problem is the lack of a compromise solution or the perceived lack thereof. A negotiated settlement requires parties to find a mutually acceptable agreement, necessitating the consent of both sides. As long as at least one of the conflict parties believes that what it can achieve outside of negotiation is better than the agreement that is currently on the table, even after accounting for the costs of war, then continuing war is rational behavior. But could the other side then not simply offer a better deal, one that makes a rational actor choose to stop fighting? Ex post, wars are always inefficient, as the final arrangement could have been negotiated without the costs of war. Conflict parties thus have an incentive to negotiate an agreement that leaves them Downloaded from https://academic.oup.com/jogss/advance-article/doi/10.1093/jogss/ogaa054/6124710 by guest on 09 February 2021 better off than fighting (Schelling 1960;Raiffa 1982, 14-15;Lax and Sebenius 1986;Fearon 1995;Walter 2009).
A key rationalist explanation why they may fail to do so is imperfect and asymmetric information. Parties have an incentive to misrepresent information about their fighting capabilities and their resolve in order to extract concessions from the other side. This may lead to a situation where parties cannot find an agreement that is mutually acceptable, even if in the presence of perfect information such an agreement would exist (Schelling 1960;Lax and Sebenius 1986;Fearon 1995;Powell 1999). Over the course of a violent conflict, conflict parties reveal information about their capabilities and resolve, and expectations about the expected outcome of fighting converge (Wagner 2000;Filson and Werner 2002;Powell 2004;Walter 2009). But even when a range of mutually acceptable agreements appears, conflict parties may fail to settle, if they have time-inconsistent incentives (Fearon 1995;Reiter 2003;Walter 1997). This is particularly a problem in intrastate conflicts, where the non-state actor is usually required to demobilize and disarm as part of conflict settlement, to return the monopoly on the use of force to the state. This leaves them vulnerable to defection by the state actor, and the state actor in turn may fail to credibly commit to the implementation of the agreement post-disarmament (Walter 1997(Walter , 2009). The salience of the credible commitment problem further varies among different types of intrastate conflicts, with "sons of the soil" conflicts being particularly resistant to negotiated settlements (see Fearon 2004).
We may thus broadly distinguish between bargaining problems that relate to a lack of a bargaining range, in particular the problem of imperfect information (see e.g., Schelling 1960;Lax and Sebenius 1986;Fearon 1995;Powell 1999;Werner and Yuen 2005;Findley 2013) and those related to enforcement problems, i.e., the inability to trust or commit to future implementation (see, e.g., Fearon 1995;Walter 1997;Powell 1999;Fortna 2003Fortna , 2004Reiter 2009). The two types of bargaining problems are fundamentally different yet interlinked. Recent scholarship made great progress in theorizing how they affect conflict parties' incentives to settle and how the two types of problems interact with each other. Using sophisticated game theoretical models, the aim of these scholars is to predict and explain specific war outcomes, including when conflict parties accept conflict settlement through a negotiated deal (e.g., Leventoglu and Slantchev 2007;Wolford, Reiter, and Carrubba 2011;Fearon 2013). The aim of this article is more basic: it seeks to theorize an additional obstacle to conflict settlement, focusing on when parties do not settle. Enforceability issues arguably only become salient once a bar-gaining range exists, as parties with no incentive to settle are not primarily concerned with how to make an eventual settlement enforceable (see Walter 2009). This article therefore focuses on bargaining problems related to the bargaining range, setting enforcement problems temporarily aside. The concluding section discusses how the bargaining problem introduced in this article relates but is different from the problem of credible commitment.

Intergroup Competition
Most bargaining models represent conflict parties as abstract, rational entities. 1 These entities care only about their own welfare. If they care about gains of the other side, they essentially do so because relative gains by the opponent may affect one's own welfare in the future (see Snidal 1991). 2 Such self-centered preferences imply that wars are just like ordinary bargaining situations and that-strategic considerations about future interactions aside-conflict parties evaluate an agreement irrespective of whom they are negotiating with.
Scholars studying the relationships between social identity, group dynamics, and hatred would reject such a suggestion as nonsensical. A central question to these scholars is how social identity shapes conflict, and vice versa. Even without conflict, humans tend to pursue a sense of belonging through the creation of social groups: in-group, to which we belong, and out-groups, from which we distinguish ourselves (see Tajfel and Turner 1979;Kriesberg 2003;Kelman 2007). Such categorizations provide us with a way to identify ourselves in social terms and to define our place in society (Tajfel and Turner 1979, 40). Because most of us strive to create or maintain a positive social identity, we tend to distinguish or differentiate our in-group from the outgroup in favourable terms (Tajfel and Turner 1979, 40). Intergroup competition expands the perceived distance between the in-and out-group: it increases the social 1 Examples of exceptions are Acharya and Grillo (2015) or Crisman-Cox (2020), who combine rational and behavioral actors; or Little and Zeitzoff (2017), who integrate evolutionary preferences into their bargaining model. 2 An exception to this is Kydd (2019), who integrates other regarding preferences into his formal bargaining analysis. He demonstrates that such preferences may stand in the way of a full agreement, but, with certain utility functions, parties may find a partial agreement that leaves them better off than no deal. In contrast to Kydd, this article unpacks unitary actors, assessing the impact of social preferences in the context of constituent constraints.
Downloaded from https://academic.oup.com/jogss/advance-article/doi/10.1093/jogss/ogaa054/6124710 by guest on 09 February 2021 identification of individuals with their own group and leads them to view and treat members of the other group as members of that group, rather than as individuals (Cikara, Botvinick, and Fiske 2011, 306;Rosenberg and Wolfsfeld 1977, 85;Tajfel and Turner 1979, 33-36). War is an extreme form of intergroup competition, where individuals tend to have strong social identification with their in-group and strong hatred for the out-group (Kelman 2007). While conflict party members may already negatively identify with the other side before the onset of war, hatred will likely intensify when fighting breaks out (Galtung 2004;Glasl 1982). For individuals tend to see violent acts by their own groups as necessitated by the opponent's behavior, while viewing violent acts by the opponent as intentional and malicious (and thus necessitating counter-attacks) (Kelman 2007, 97;Rubin 1991, 222). Leaders who engage in war have an incentive for further polarization, as hatred for an out-group mobilizes political support, creates cohesion and unity, and helps legitimize a violent course of action (Hodges 2015;Kelman 2007, 66, 82-85;2007;Kriesberg 2005). Hatred may thus exist before the onset of war, but it will likely intensify and become entrenched as war breaks out and fighting persists.

Social Preferences
Such dynamics affect how individuals assess the benefits of conflict settlement. Individual members of a conflict party will likely assess the outcome of negotiations for both their in-and out-group (Cikara, Botvinick, and Fiske 2011, 2;Mackie, Smith, andRay 2008, 1871). Behavioral economists sometimes use the term social preferences to describe such other-regarding preferences (Fong 2001, 226). The underlying argument is that individuals "care deeply that other people get what they deserve" (Fong 2001, 226). This may go in either direction: individual choices may be based, among others, "on a positive or negative concern for the welfare of others" (Fehr and Camerer 2007, 419). Given their strong identification with the in-group and the strong hatred for an outgroup, conflict party members will likely have positive concern for the welfare of their own group and negative concern for the welfare of the other.
The assumption that social preferences shape individual assessments of preferred outcome has been confirmed in numerous experimental studies by behavior economists (e.g., Bearden 2001;Fehr and Schmidt 1999;Rabin 1993). It is also consistent with findings from neuroscience. Neuroimaging shows that both fair behavior and punishment of unfair behavior triggers reward centers of our brain (Quervain et al. 2004;Tabibnia and Lieberman 2007). Membership of a group that is responsible for such behavior seems sufficient to trigger such responses: research has shown that neural responses of individuals with a strong social identification feel pleasure and pain when members of their own group make gains or losses, but feel pleasure when members of an enemy out-group suffers and pain when it thrives (Cikara, Botvinick, and Fiske 2011). This offers support for the assumption that individuals evaluate gains positively for members of their own group, and negatively for members of a group that is perceived as the enemy (and vice versa for losses).

Saliency of Out-group Preferences
A history of violent conflict makes it likely that hatred and strong intergroup competition prevail in most intrastate conflicts, and that social preferences not only include in-group preferences but also (negative) concern for the welfare of the out-group (see, e.g., Galtung 2004Galtung , 2009Kriesberg 2003). Yet how strongly individuals care about punishing (or avoiding reward for) an out-group may vary from conflict to conflict, among individuals in the same conflict context, and over time. Dispositional factors (such as a person's values or beliefs) and situational factors (i.e., the external environment) will likely shape how strongly an individual cares about the opponent's versus their own group's welfare. Of particular interest to this analysis are situational factors, as they allow to assess or predict how shifts in dynamics that tend to increase or decrease the saliency of individual preferences for punishment will affect the overall support for or against a negotiated settlement.
Two important such factors are the types and levels of conflict violence and elite framing of the conflict. Ongoing hostilities entrench hatred and ensure that the saliency of out-group preferences remains high (see Galtung 2004Galtung , 2009Kelman 2007;Kriesberg 2003;Zartman 2001). Positive changes in conflict behavior, such as continued compliance with a ceasefire, may incrementally decrease the saliency of out-group preferences over time. This does not suggest that ceasefires undo the hatred resulting from years or decades of fighting, but that over time, out-group preferences may become less salient in affecting an individual's overall assessment of a situation when hostilities have substantially decreased for a sufficient period of time (see Sticher 2020). A major ceasefire violation, by contrast, will immediately increase the saliency of out-group preferences, particularly if such a violation is perceived as a sign of bad faith (Åkebo 2013, 201-3). Elite cues may also decrease or increase the saliency of out-group preferences. Leaders may start using more reconciliatory narratives or Downloaded from https://academic.oup.com/jogss/advance-article/doi/10.1093/jogss/ogaa054/6124710 by guest on 09 February 2021 purposefully use language that dehumanizes or demonizes the opponent (see Hodges 2015;Kelman 2007;Kriesberg 2005). Similarly, they may specifically highlight or deemphasize concessions to an opponent (Matanock and Garbiras-Díaz 2018; Matanock and García-Sánchez 2017; Sticher 2019), which will likely increase or decrease the saliency of out-group preferences. This is particularly important in contexts were the public has relatively little information about the actual content of an agreement (Matanock and Garbiras-Díaz 2018).

Support for a Negotiated Settlement
With the exception of those who profit from the instability that war brings, everyone wants peace-but not necessarily at all costs. 3 Integrating the above insights into bargaining theory allows discussing preferred policy options from the perspective of individual members of conflict parties, showing how hatred, ongoing hostilities, and war narratives negate space for a negotiated settlement. This section starts by introducing a standard setup in bargaining theory, before revising its assumptions to discuss policy support from the perspective of individual conflict party members and constituent groups.

The Standard Setup
A formal choice model, first proposed by Fearon (1995), has become a standard setup to analyze bargaining range problems (Lake 2011, 10). The setup has been criticized for some of its assumptions (e.g., Wagner 2000) and is illsuited to identify when and under what conditions conflict parties settle. It does, however, allow for a clear and concise analysis if the primary aim is to identify obstacles to a negotiated settlement, as is the case for this article.
The setup depicts a conflict between two unitary actors (in Fearon's example, two states) that fight over issues represented by a continuum from 0 to 1. Party A prefers an agreement close to 1, while party B prefers an outcome close to 0. For illustrative purposes, Fearon presents this as a territorial dispute, where 1 represents the border A claims and 0 represents the border B claims. However, the continuum can be thought of more abstractly as representing, at any specific moment in time, the issues over which the parties have competing positions. Before the onset of war, these are the contested issues that caused the conflict, such as opposing demands 3 Note that this article is based on the assumption that conflict parties use violence to achieve a wider (often political) goal and are not interested in violence per se (see Slantchev 2003, 623).
regarding territories, governance structures, economic policies, etc. Over time, the contested issues may change and the range of issues expands. In particular, conflict behavior (that results from unresolved issues) may lead to new contested issues, such as demands for justice for crimes committed during the course of the conflict. The standard setup works with probabilities to assess the expected outcome of the war, i.e., how the contested issues are addressed, should the parties fight to the bitter end. The probability of party A winning the war is p ∈ [0, 1], and both parties have positive costs of war c i , i = A, B. Fearon shows how under perfect information and positive costs of war, and as long as conflict parties are not risk-seeking, there is always a range of agreements that both parties would prefer to fighting. For risk-neutral actors, this bargaining range equals the combined costs of war, because the parties do not suffer these costs if they agree on a settlement rather than continuing the fighting. It is located between the two parties' nonagreement options, i.e., between what they each expect to achieve through continued fighting (see figure 1). These points are calculated for party A by subtracting its costs of war from its probability of winning (p − c A ), and for party B by adding its costs of war to the probability of it losing the war (p + c B ), because as noted above, A wants to be as close as possible to 1 and B to 0.
Under imperfect information, the two actors may have different assessments of the expected outcome of the war. Concretely, one or both sides may overestimate their strength relative to the other side's strength (p A > p B , with p i standing for actor i's assessment of the probability of A winning the war). As a result, their assessments of the nonagreement options diverge. Because A only prefers an agreement x if it is located to the right of what it believes is its nonagreement option (x > p A − c A ), and B only if it is to the left (x < p B + c B ), their ranges of acceptable agreement may no longer overlap. If this is the case, the bargaining range disappears.

Support for Peace Negotiations
This model is commonly used to explain why conflict parties may choose war over negotiated settlement (e.g., Fearon 1995;Powell 1999;Werner and Yuen 2005;Lake 2011). It depicts conflict parties as abstract, unitary actors that only care about their own benefits. Integrating social preferences allows unpacking the unitary actors and discusses the expected benefits of conflict settlement from the perspective of individual conflict party members. In line with the argument above, we may assume that individual members of a conflict party share the same outcome preference as their leader (1 in the case of party A and 0 for B). They will support a leader's decision to negotiate if the expected outcome of negotiations (x) lies inside their range of acceptable agreements, given their individual assessment of the relative strength (p) and the costs of continued armed conflict (c i ). As long as they only care about the welfare of their in-group, individual members of party A disagree with peace talks if: and member of conflict party B if This changes once they have negative concerns for the opponent's welfare-which the theory above suggests.
Because of a history of violent conflict and high intergroup competition, individuals will likely attribute positive utility to punishment and negative utility to rewards of the opponent. In the context of negotiations, concessions toward an enemy may be seen as rewards, as they increase the opponent's welfare compared to continued armed conflict. This suggests that individual members of a conflict party will likely attribute negative utility to concessions made to the other side.
The positive utility of punishment may be accounted for directly in the costs of war, i.e., as a negative component of the costs of conflict, as they only arise when war is raging. In other words, if an individual derives a benefit from hurting an opponent militarily, then this may lower the perceived costs of war. If the war stops, both the costs of war and the benefits of punishment fall away. However, the negative utility of concessions cannot be accounted for in the same way, as concessions are only made in the context of a negotiated settlement, i.e., when the war stops. We thus need to account separately for the negative utility of concessions in the utility functions.
The negative utility attributed to concessions is determined by both the scope of concessions and the saliency of out-group preferences. Not every individual cares the same way about making concessions to an enemy, and preferences may change over time. The saliency of out-group preferences is here represented by a variable, β i ∈ [0, ∞], which indicates how strongly an individual wants to avoid concessions to an opponent at a specific moment in time. Technically speaking, β i is the perceived "exchange rate" at which an individual is willing to trade welfare of their own group for a reduction in the welfare of the out-group. If β i equals 0, an individual only cares about in-group welfare; between 0 and 1, they seek to avoid concessions but more strongly care about in-group gains; and at 1, they care equally about the two. Above 1, they care predominantly about avoiding concessions to the enemy.
Integrating such preferences into the bargaining setup changes expectations about the policy support for negotiations. Under perfect information, members of party A will now reject an agreement if 4 and members of party B if Because any mutually acceptable agreement contains concessions, the minimally acceptable agreement will shift toward an actor's preferred outcome (see figure 2). 5 Individuals who attribute negative utility to concessions thus need to be offered a better deal to prefer it over continued fighting than those who care only about the welfare of their in-group.
To render this shift more intuitive, let us look at the point slightly to the right of party A's nonagreement option (p-c A ) in figure 2. In line with the standard model assumptions, individuals who only care about in-group welfare would prefer such an agreement over continued 4 See appendix, equations (10) to (13). 5 See appendix, equations (10) to (13). fighting, even if the gains were minimal. 6 But while such an agreement may provide minimal benefits to conflict party A, it entails massive concessions to party B: nearly all the surplus from the bargaining process would fall into the hands of the opponent. To members of conflict party A who attribute negative utility to concessions (β i > 0), such a deal may seem far worse than continued fighting. Social preferences work in concert with other bargaining parameters to determine individual support for negotiations. In the modified standard setup, these parameters include individual assessments of the costs of war and the relative strengths of the conflict parties. Naturally, individuals will not quantify these parameters and then calculate their support. Rather, the parameters shape their intuitive assessments, determining whether a conflict settlement seems a better option than continued fighting or the other way around.
Generally, individuals with a strong focus on avoiding concessions (high β i ) are less likely to prefer a negotiated agreement than individuals who care strongly about their own group's welfare and are not so worried about the opponent's gains. This does not mean that individuals with highly salient out-group preferences want war to continue. But they may reject negotiations or an agreement because they feel that it contains too many concessions, even when such concessions are necessary to stop the war. All else equal, individuals who feel strongly affected by war (high c i ) will more likely accept a negotiated agreement than those who are largely insulated from war (low c i ). But even under high costs of war, individuals may reject a negotiated agreement if their preferences for punishment are highly salient.

6
This does not suggest that they would automatically accept such an agreement: they may (rightly) feel that their group could achieve a better deal through continued fighting.
Individuals who strongly overestimate their own party's relative fighting capability and resolve (p A > p) are also less likely to support negotiations and an eventual peace deal. In the modified setup, the negative effect of imperfect information gets amplified by the effect it has on the perception of concessions. By overestimating their nonagreement option, individuals also overestimate the scope of concessions a proposed deal entails. They may believe that a proposal by their leader contains considerable concessions, even when the offer lies below the other side's effective nonagreement option. Accordingly, they reject such a deal, while the opponent takes the offer as an insult.

Constituent Support for a Negotiated Settlement
At an aggregate level, individual assessments of a bargaining situation shape constituent support for negotiations or a settlement. We can expect that support to find a negotiated settlement will be higher when respondents are asked about peace talks in general, compared to when they are asked about a specific agreement that entails concrete concessions to an enemy. We may also expect support to be lower in the context of elite competition, if political challengers seek to increase the saliency of out-group preferences to challenge or undermine the policy decision of a pro-settlement government. Changes in situational factors that affect the saliency of outgroup preferences-such as major ceasefire violationsmay lead to shifts in constituent support. Figures 3 and 4 visually illustrate the expected relationship between the saliency of out-group preferences and public support for peace talks. As a simplification, it is here assumed that individuals of a specific constituent group share the same expectations about the outcome of talks (x). The dots represent individual assessments by members of conflict party A about a minimally acceptable agreement The location of these dots varies, because the saliency of out-group preferences may vary and individuals may have different expectations about the continued costs of war and the relative strength. For those individuals whose minimally acceptable agreement is lower than the expected outcome of talks (MMA i < x), negotiations seem attractive. Figure 3 depicts the situation during a successful ceasefire and figure 4 in the aftermath of a major ceasefire violation. As the saliency of out-group preferences increases after a major ceasefire violation, individual assessments of the minimally acceptable agreement tend to shift to the right. Some individuals who have previously supported peace talks now no longer see the benefits of negotiated settlement, and support for talks drops. 8

Impact on Peace Negotiations
So far, the theoretical framework focused on how social preferences shape individual and constituent support for a negotiated settlement. But what are the implications of these dynamics for peace negotiations?

Constituent Constraints
Social preferences affect strategic decision-making processes of conflict party leaders in two distinct ways. First,

7
See equation (3). 8 This assumes that the effect of potentially new information about the relative strength and costs of continued conflict do not offset the effect of the saliency of outgroup preferences. See Sticher (2020) for a comprehensive discussion of the effects of ceasefires on the expected costs of conflict and information provision.
they directly shape leaders' personal assessments of a conflict situation, making it more or less likely that they view the benefits of a negotiated agreement. Second, they shape policy support of various constituent groups, rendering a negotiated agreement opportune or politically unfeasible.

Individual Assessment
Individual assessments of conflict party leaders shape their views on whether continued war is justified a negotiated solution to the conflict would be preferable. Leaders with strong personal hatred of the opponent are more likely to attribute high negative utility to concessions and are thus less likely to see the benefits of a negotiated settlement. This suggests that they are more reluctant to enter into serious negotiations. A strong focus on out-group welfare by a conflict party leader thus becomes a potential obstacle to peace negotiations. Such an obstacle may be overcome in multiple ways: battlefield dynamics may change leaders' social preferences and their assessment of the bargaining situation, making it more likely that they seek to enter into negotiations when they gain additional information about the parties' relative strengths or when they start focusing more strongly on in-group rather than out-group welfare. Leaders may also be replaced by someone with a stronger focus on in-group welfare and a more realistic understanding of dynamics on the battlefield, making it more likely for negotiations to start.

Constituent Support
However, even if leaders personally prefer to pursue conflict settlement, they cannot decide in a political void. They need to ensure that their preferred course of action Downloaded from https://academic.oup.com/jogss/advance-article/doi/10.1093/jogss/ogaa054/6124710 by guest on 09 February 2021 is acceptable to key constituents, as any peace deal that lacks such support is not politically feasible (Haass 1988;Keller and Yang 2008;Mintz 2004).

Constituent Type
Which groups of individuals are most influential in constraining a leader's decision-making process, and why? The relevance of different constituent groups varies across state and non-state actor and across regime type. In democratic states, citizens can vote on leadership change. In anticipation of the voting process, leaders take public opinion into account. The opinion of swing voters and members of a leader's own political party may count more than the opinion of traditional opposition voters.
Leaders in authoritarian regimes may not be voted out of office, but they risk being forcefully removed by the military leadership if the latter do not agree with key decisions. Such forcible removal from office has more serious consequences than regular end of tenure (Chiozza and Goemans 2011, 5), which makes authoritarian leaders particularly sensitive to military influence. Ordinary citizens may also have some limited influence, as a leader who is strongly unpopular risks being overthrown.
Leaders of armed non-state actors share some similarities with authoritarian regimes. Regional or branch commanders play a particularly influential role, but leaders also consider the mood of soldiers on the ground (or even citizens living in rebel areas), as potential challengers within their own organization may seize on the unpopularity of a leader. If key constituent groups or influential commanders disagree with important policy decisions, such as negotiating a conflict settlement, this may result in the forceful removal of the leader or the formation of splinter groups. Both have grave consequences not only for the leader, but also for the peace process. Accordingly, leaders will try to anticipate and avoid decisions that are unpopular with these groups.

Sensitivity toward Constituents
Aside from type of actor and regime, a leader's assessment of how much support and by whom is necessary to move forward with a policy decision depends on situational and dispositional factors (Keller and Yang 2008, 689-90). Situational factors include common practices or legal requirements for ratification of a peace agreement. Governments are particularly sensitive toward public opinion if they are legally required to hold a popular referendum or have committed themselves to such a process (see Amaral 2018;Putnam 1988, 437-39). If a peace agreement has to be approved by a legislative body, then leaders will need to anticipate the support of members of this body. Other situational factors include the state of the economy: leaders are more sensitive in times of eco-nomic decline than when the economy prospers. Generally, popular leaders are less sensitive to constituent support for a specific policy decision than leaders who already face criticism. Tenure, i.e., how much longer they can expect to be in office, is another factor for consideration (Chiozza and Goemans 2004). For non-state actors, leaders are more strongly constrained by constituent preferences if their organization is fragmented, i.e., lacks clear formal and informal rules and consists of several factions, with power dispersed across these factions (see Bakke, Cunningham, and Seymour 2012).
Dispositional factors include the risk leaders are willing to take and their underlying motivation (Keller and Yang 2008, 689-90). Some are motivated primarily by staying in power, while others may be "motivated by a task, a mission, or an ideology" (Keller and Yang 2008, 690). But even if leaders do not seek to retain their leadership position, those with a peace agenda have an interest in ensuring sufficient constituent buy-in to avoid that the next leader simply overturns the agreement and restarts the conflict.
In some situations, unpopular concessions can be a bargaining tool: if leaders can credibly demonstrate that they are constrained by their constituents, the other side may consider additional concessions to reach a deal (see Putnam 1988;Schelling 1960). However, there is an important trade-off: if concessions are unpopular on both sides, this will likely lead to a situation where no agreement is acceptable to the constituents of either side, and by extension not acceptable to the leaders themselves. And even when a bargaining range exists, it may be much smaller than without accounting for social preferences, making it more challenging to find a mutually acceptable agreement.
In the appendix, constituent constraints on leadership decisions are formalized for democratic state actors, showing how both the sensitivity of leaders and the saliency of social preferences shape the bargaining space. The analysis demonstrates that, even under perfect information, finding a negotiated agreement becomes impossible once leaders on both sides care more about avoiding costly concessions than about achieving absolute gains. The same is true if one leader cares at least mildly about and the other is obsessed with avoiding concessions.

Overcoming Costly Concessions
Naturally, leaders do not calculate support through some elaborate calculation; instead, they use heuristics to gauge whether a policy decision to engage in, stay in, or conclude negotiations enjoys a minimum of required support from key constituents. Leaders may actively communicate progress in talks or leak interim agreements to gauge the reaction of the public, the media, or specific constituent groups. Opinion polls, consultations with key opinion makers, and editorial comments in mainstream media are other examples of ways to help leaders determine whether negotiations or an eventual agreement have sufficient constituent support. If they do not, leaders face one of three options: they may stall the negotiation process, return to fighting, or engage in initiatives to actively change the constraints posed by their constituents.
A possible way for pro-settlement leaders to overcome the costly concessions problem is by decreasing their sensitivity toward constituent preferences. If formal ratification is the main problem and the political system allows it, leaders may change the ratification mechanism. More generally, leaders may try to increase their general appeal or seek to secure a possible future outside the political arena. This may help them achieve conflict settlement, even if it is politically not opportune. However, a lack of support from key constituents can lead to problems in the implementation phase, or to successors rejecting the deal, with the risk of a return to violent conflict in the future (Paffenholz 2015;Putnam 1988, 436). Lowering constituent constraints does, therefore, not replace the need to create constituent support, but it can offer the opportunity to postpone this difficult task to the postagreement phase.
A second strategy to overcome the problem of costly concessions is related to perceptions of concessions and how they are assessed by constituents. Leaders with a peace agenda may emphasize the benefits of peace, deemphasize concessions, and highlight positive changes in the opponent's behavior to decrease the saliency of out-group preferences. However, internal challengers may seek to counter such portrayal, highlighting actions by the opponent that increase the saliency of out-group preferences (Sticher 2019). They may also highlight anything that can be seen as a concession to the enemy, to discredit the conflict party leader and portray her as sympathetic to the other side (Assouline and Trager 2017;Kelman 2007, 89;Matanock and Garbiras-Díaz 2018). This heightens the risk of the leader being sidelined or potentially even assassinated by hardliners (see Stedman 1997).
A third strategy is to seek to change conflict dynamics that maintain or increase the saliency of out-group preferences. Conflict party leaders may seek to deescalate battlefield dynamics and create some calm. They may negotiate a bilateral ceasefire or, if this is not possible, seek other ways of deescalating the conflict (see Clayton et al. 2019). Such changes in conflict behavior can potentially create space for the narrative strategy outlined above, but leaders need to be careful not to undermine conflict ripeness (see Sticher 2020).
In sum, there are three complementary strategies leaders may pursue to overcome the problem of costly concessions, but all come with their own challenges, rendering the process of finding a peace deal that is acceptable to both the opponent and constituent groups as a delicate balancing act.

Illustration in the Colombian Case
The 2012-2016 peace talks between the Government of Colombia and the FARC serve as an illustrative example of how the problem of costly concessions makes it challenging to negotiate a peace agreement with a sworn enemy. 9 The case study focuses on the Colombian government perspective, as the problem of costly concessions is particularly salient for democratic state actors. President Santos promised to submit an eventual peace agreement to a popular referendum, rendering the need for public support particularly high. While not a necessary condition, this makes it a likely case to find evidence should the framework be valid. Because the parties eventually reached a peace agreement, the case serves to illustrate not only the problem of costly concessions, but also how leaders may overcome it.

Background
The Colombian government had engaged in talks with the FARC under various administrations, including major initiatives in the early 1980s, the early 1990s and around the turn of the century, to seek to end the armed conflict with the largest guerilla group in the country. Each abandoned process was followed by a return to open warfare. Under President Uribe, with military and financial support from the United States, the government considerably weakened but never fully defeated the FARC. Uribe's 9 The analysis focuses on negotiation dynamics between the Government of Colombia and the FARC and does not discuss the role of third-party actors in influencing the bargaining space (see, e.g., Beardsley 2008 for an example of the latter). While there were no mediators in the Colombian case, third-party actors did play an important role in hosting and facilitating the process and helped conflict parties overcome critical junctions during the negotiations (IFIT 2018, 10;Jaramillo 2017, 4-5).
The involvement happened primarily behind the scenes and did not directly influence constituent constraints and public support, which is the focus of the empirical discussion. A survey experiment showed that simply mentioning that the FARC had endorsed a specific provisionincreased political representation of conflict-affected areas-significantly reduced the number of those willing to accept the provision (García-Sánchez, Montalvo, and Seligson 2015, 86;Matanock and Garbiras-Díaz 2018). The respondents came from conflict-affected areas and would have profited from the provision (Matanock and Garbiras-Díaz 2018). While this finding does not establish any causality, it is in line with the theoretical expectation that individuals attributed negative utility to gains made by the FARC.
As a consequence of unpopular concessions, the government struggled to maintain support for the talks while making the necessary concessions that would keep the FARC engaged in the process. Finding agreement in the areas of political participation and transitional justice were two major sticking points during the talks. The government recognized that while justice without jail time was a hard sell to the public (Segura and Mechoulan 2017, 18), the FARC leadership would not accept a deal that sends its members to jail (Semple and Casey 2016b).
Similarly, political participation by the FARC was highly unpopular, but a key demand for it to accept disarmament and demobilization (ICG 2017). In other words, the government saw these concessions as highly undesirable yet necessary to reach a peace deal.
Political opposition -under the lead of former president Uribe-rallied around the issue of concessions to challenge President Santos over his decision to negotiate with the FARC. In the critical phase of the 2014 reelection campaign, when Santos was particularly sensitive toward voter preferences, his main challenger mobilized votes primarily through his opposition to the peace talks. He continuously highlighted unpopular concessions to justify his stance on the talks, using "Peace without Impunity" as a campaign slogan. Santos was reelected in the runoff round, but his defeat in the first round suggests that he, and by extension the peace negotiations, were vulnerable to mobilization around unpopular concessions.
Concessions also played an important role in the No campaign of the plebiscite. While the pro-settlement government focused on the benefits of peace, the Uribe camp specifically highlighted components of the talks that could be seen as concessions, framing them as "rewards" to the FARC (Matanock and Garbiras-Díaz 2018; Matanock and García-Sánchez 2017; Sticher 2019). Uribe and his supporters specifically emphasized concessions in the most controversial areas, highlighting that FARC members would not go to jail and that they would be able to participate in elections.
While unpopular concessions alone do not explain the outcome of the plebiscite, 10 they do explain why many casted a no. Many felt that the agreement was too generous toward the FARC and rewarded instead of punishing them (see, e.g., ICG 2016; Segura and Mechoulan 2017, 2, 18;Semple and Casey 2016a). A BBC analysis listed the lack of jail time for FARC crimes committed during the conflict, financial stipends for demobilized FARC members, and guaranteed seats in the Colombian Congress for upcoming elections as key reasons mentioned by voters who rejected the referendum (BBC 2016). We would 10 Explanations for the narrow and unexpected result include a low voter turnout, particularly in regions that were supportive of the deal. While the No campaign managed to better mobilize turnout (ICG 2017, 7), turnout was also affected by a hurricane in coastal areas, which tended to support the peace deal (Casey 2016b). Some church leaders also mobilized against the peace deal, arguing that it contained unacceptable language about gender and sexual orientation (Casey 2016a;Segura and Mechoulan 2017, 30-31).
not expect such arguments to play a decisive role on individual decision-making if voters only cared about ingroup welfare. If they only cared about in-group welfare, their primary concern would be whether the deal, compared to no deal, brings any benefits, considering the risk of a return to violent conflict in the absence of a deal. 11 The No vote was particularly high in urban areas that were not strongly affected by the conflict (Arjona 2016), supporting the argument that unpopular concessions influence a decision more strongly for those who are largely isolated from the costs of war.

Change in Ratification Mechanism
The Colombian case also demonstrates how leaders may overcome the problem of costly concessions through a change in the ratification mechanisms, and the potential risk of doing so. In the aftermath of the plebiscite, after a short period of uncertainty, the government moved to negotiate first with the opposition and then with the FARC, against a backdrop of civil society mobilization and strong international encouragement for continued engagement. The renegotiated peace deal included many amendments demanded by the opposition, but left some key issues unchanged (see ICG 2017, i). Santos changed the ratification process, and thus the constraints he faced by the electorate, submitting a modified deal to Congress instead of resubmitting it to a plebiscite. Despite continued rejection by the opposition, Congress ratified the revised deal, paving the way to end a more than halfcentury-old conflict. A number of factors facilitated this move. The propeace movement quickly mobilized and there was strong international support to continue the peace process. Santos saw the peace deal as his main legacy (e.g., Weymouth 2014). He was in his second and final term and therefore less sensitive toward public opinion than when he was running for reelection. By changing the ratification mechanism rather than seeking to broaden 11 There are alternative explanations for why constituents have listed concessions as the reason to vote no. Perhaps most importantly, constituents may have felt that concessions to the FARC would signal to other groups that fighting pays off (see Walter 2009, 250-51 for a similar argument related to the resolve of governments). The two explanations are not mutually exclusive. Indeed, social preferences for punishment have likely played a key role in the evolution of human cooperation, by safeguarding against the long-term repercussions of rewarding undesirable behavior (see, e.g., Fehr and Gächter 2002;Quervain et al. 2004).
the public support before a renewed plebiscite, Santos was able to move forward with the peace deal and overcome the problem of costly concessions. However, this left the challenge of reaching a national accord on the implementation of the peace deal to the post-agreement phase (Bouvier 2016;Segura and Mechoulan 2017, 1). It also meant that the implementation was left vulnerable to leadership changes, as the opposition continued to reject the legitimacy of the new deal (ICG 2017).

Battlefield Dynamics and Public Support
In addition to the more general dynamics at play, the above theory offers concrete propositions with regard to how shifts on the battlefield will likely affect popular support for an agreement. A particularity of the Colombian peace negotiations was that until the very end of the process, parties negotiated in the absence of a bilateral ceasefire. From the beginning of the talks, the government was adamant that it would continue its military offensive until a settlement was reached (see discussions in Cortés and Millán Hernández 2019;IFIT 2018). Nevertheless, there were important shifts in the conflict behavior on both sides over the course of the negotiation process. In the early years of negotiations, hostilities continued unabated, with the exception of a few temporally limited unilateral FARC ceasefires. In December 2014, following the short suspension of the talks in the aftermath of a kidnapping incident, the FARC declared an indefinite unilateral ceasefire. The government partly replicated the arrangement by announcing a cessation of air strikes in March 2015. The arrangements held until mid-April 12 when-under contested circumstances-the FARC killed eleven soldiers in an attack (see ICG 2015a). The government announced that it would immediately resume air strikes. The FARC initially maintained its ceasefire, but suspended it after twenty-six of its members were killed by government offensives in late May 2015. This led to a return of open hostilities on both sides (ICG 2015b, 3-4). Figure 5 shows the development of public support for peace talks throughout the public phase of the negotiations. 13 Many factors have likely shaped public support for peace talks. With the available data, it is 12 The cessation of air strikes was originally announced for a month, but extended before the ceasefire violation that led to the resumption of air strikes. 13 Respondents were asked what they saw as the best option to solve the guerilla problem-to insist on dialogue until a peace agreement is reached or to try to defeat the guerilla militarily. The question was included in the survey already before the peace talks with the Downloaded from https://academic.oup.com/jogss/advance-article/doi/10.1093/jogss/ogaa054/6124710 by guest on 09 February 2021 Figure 5. Development of support for peace talks during the public phase of talks. Source: Gallup (2016, 103).
not possible to control for all of them to statistically assess the effect of battlefield dynamics on support for the talks. 14 FARC were announced. The broad formulation of the question offers a (partial) explanation why at the time of the plebiscite, the percentage of those reportedly supporting dialogue was much higher than the percentage of those who voted for the concrete peace agreement.
In the No campaign, the Uribe camp argued that negotiations were the right approach, but that the agreement made too many concessions to the FARC. Also note that the question referred to the guerilla in general, without singling out the FARC. Given that the FARC was the largest guerilla movement in the country, and that the FARC peace talks received high public attention, many will likely have responded with the FARC talks in mind. However, developments related to talks with the smaller guerilla organization ELN may also have influenced some respondents. The government and the ELN held exploratory talks in 2014. In March 2016, they announced formal peace talks for May 2016, but these were later postponed and only started in 2017. 14 One feasible way to control for other factors would be through a quasi-experimental setup, in which individual level data immediately before and after an event are compared (see Nussio, Bove, and Steele 2019, for an example of such a study design). Unfortunately, the annual However, the trends in support for peace talks broadly align with major shifts that took place in the battlefield, offering some tentative support for the plausibility of the argument. Figure 6 zooms in on the period in which these major shifts occurred, namely between late 2014 and late 2015, depicting levels of support for peace talks together with the battle-related deaths that occurred on the government side. In December 2014, the FARC announced its first indefinite unilateral ceasefire. In February 2015, when there was solid compliance with the FARC unilateral ceasefire, support for peace talks was relatively high. Between February 2015 and April 2015, when the only major ceasefire violation by the FARC took place, support decreased from 69 percent to 52 percent, the largest drop in public support during the entire public phase of the talks. The downward trend continued till June 2015, as hostilities between the parties escalated and the FARC announced the end of the ceasefire. This was the only point in time where support for a military approach was higher than support for peace talks-though only by a percentage point. 15 data collection of the LAPOP survey-which is available at individual level and measures support for the talks and concessions-was completed shortly before the April 15, 2015 ceasefire violation. 15 Note that the reported error margin for the GALLUP polling is 4 percent (GALLUP 2016, 103). The government and the FARC never suspended the talks during this crucial period, demonstrating a high commitment to find a negotiated settlement. They even made important progress, reaching agreement on a truth commission after a year of negotiating without much concrete achievement. Yet despite this positive development at the negotiation table, the talks were on the brink of collapse. With public support at a low and political patience running out, observers noted that "it would take only a spark to suspend the process or trigger its breakdown" (ICG 2015b, 1). And even without a major incident, continued violence would have provided a very challenging environment for the government to rally support in a popular referendum (ICG 2015b, 18).
In this context, in early July 2015, the FARC announced a one-month unilateral ceasefire. Shortly after, the parties agreed on measures to de-escalate the conflict and speed up the talks ("Joint Communique #55: Expedite in Havana and De-Escalate in Colombia" 2015). The government resumed its suspension of air strikes and the FARC announced to maintain the unilateral ceasefire beyond the initially announced time period. The talks regained public support (from 45 percent in June to 54 percent in August 2015).
In short, trends in public support for the peace talks between December 2014 and August 2015 align with the largest shifts in conflict behavior during the public phase of the talks, with the saliency of out-group pref-erences offering a plausible explanation for the link between the two. Outrage about the FARC attack in the midst of a ceasefire will likely have increased the relative importance of the feeling that the FARC behavior should be punished, rather than awarded through a settlement that benefits them. From established bargaining theory, we would explain either no influence (if the ceasefire violation revealed no new information) or a shift in the opposite direction, if the violation revealed new information about the fighting capability or resolve of the FARC (see, e.g., Fearon 1995;Powell 1999).
Events at the negotiation table do not offer a plausible alternative to explain the trends in development of support, in particular the large drop in support between February and April 2015. In this time period, the only notable agreement that was reached was to conduct a de-mining pilot project (Colombia Reports 2016). This was primarily a confidence-building measure and not seen as a concession to the FARC. A lack in progress at the negotiation table may have affected public opinion, but it seems more likely that this impasse would be reflected by a continuous decline in support, rather than the sharp drop we see between February and April. There are also other events not linked to the peace process that likely influenced the polling, but "national outrage and indignation" over the FARC attack appeared to be the most important factor (Bouvier 2015, 1).
Downloaded from https://academic.oup.com/jogss/advance-article/doi/10.1093/jogss/ogaa054/6124710 by guest on 09 February 2021 A possible alternative explanation is that the shift in public support relates to the problem of credible commitment. The public may have had higher confidence in FARC willingness and ability to abide by an eventual agreement when it complied with the ceasefire, and lost confidence after the ceasefire violation. 16 When considering the merits of this alternative explanation, it is important to note that the opposition under the lead of former president Uribe did not reject negotiations in general, but mobilized against the conditions under which such negotiations took place. In the lead up to the referendum, Uribe called for renegotiation of the content rather than questioning FARC willingness to abide by an agreement in general. He consistently claimed that components of the agreement would reward the FARC instead of punishing them (e.g., Uribe 2016; see Sticher 2019 for a list of examples). This suggests that on the state side, unpopular concessions arguably played a more important role in affecting popular support for the peace agreement than the problem of credible commitment. 17

Discussion
The formal analysis and the Colombian case study demonstrate the difficulties of negotiating a settlement in violent conflicts. Scholars have long highlighted the challenges posed by those who thrive on the instability of war (see Collier et al. 2003). But war can be a preferable option even for leaders who see the benefits of peace, as they have to consider the political ramifications of making concessions to a sworn enemy. Negotiating peace is challenging if constituents blame the opponent for the painful experiences of the conflict-particularly if key constituents are largely isolated from the costs of war and opposition within a conflict party mobilizes around unpopular concessions.
This challenges some common assumptions of bargaining theory, in particular the expectation that fighting always reveals a bargaining range over time. Fighting helps convey and reveal information and eventually solves the problem of imperfect information. But at 16 This is a relatively broad interpretation of the credible commitment problem: in intrastate war literature, the problem of credible commitment is commonly formulated with a focus on non-state actors, as they cannot return to fighting once they are disarmed and demobilized (Walter 1997;). 17 By contrast, on the FARC side, the problem of credible commitment was likely salient during much of the negotiations, fueled not least in part by the experience of the Patriotic Union party in the late 1980s (see ICG 2014).
the same time, ongoing hostilities lead to salient outgroup preferences that may render conflict settlement politically inopportune. This demonstrates how one bargaining problem (imperfect information) may result in conflict behavior (fighting) that in turn may create, accentuate, or entrench other bargaining problems, such as the problem of costly concessions. Appreciating such dynamics contributes to our understanding of why conflicts become intractable. The potential negative impact of fighting on the bargaining range points to the importance of finding alternative ways of information provision, including through the use of ceasefires (seeÅkebo 2016; Sticher and Vuković forthcoming) or through third parties (see Beardsley et al. 2006;Kydd 2003). More generally, the findings suggest that a change in conflict behavior may often be necessary for parties to move toward a negotiated settlement. There is a common perception that the perceived costs of war need to be high to render a conflict ripe for settlement. However, the concept of "mutually hurting stalemates"-as originally conceived-relates to a ripe moment to start negotiations rather than ripeness to fully settle a conflict (Zartman 2001; see also . The problem of costly concessions suggests that, while it may be necessary for warring parties to experience some mutually hurting stalemate to enter into negotiations, a ceasefire or other forms of violence reduction during negotiations may often be necessary to enable leaders to move toward a final settlement (see Sticher and Vuković forthcoming). At the same time, the analysis points to the risks of a premature ceasefire, as major ceasefire violations may lead to a drop in public support and render the search for a mutually acceptable agreement difficult or impossible.
The problems of credible commitment and costly concessions share some commonalities: both problems tend to aggravate when fighting intensifies and both may result in a situation where leaders refuse an agreement that promises benefits for their own parties. But the two problems are distinct and can exist independently from each other. Concessions may be costly for leaders to make even if enforceability of an agreement or future competition are not a key concern. This is particularly relevant for state actors: in intrastate conflicts, state actors can usually keep their fighting capabilities as part of a negotiated settlement, rendering them less vulnerable to defection than a non-state actor. In contrast, they have to consider domestic audiences, who tend to strongly oppose concessions-not only because they detract from their in-group's welfare, but because they are seen as unjustly rewarding the behavior of the opponent. The case study illustrates how the Colombian government struggled to make concessions to the FARC, including with regard to issues that are not linked to future warfare.
This article focuses on conflict parties, but the findings have important implications for third parties. Established bargaining theory implies three key roles for third-party actors that seek to promote conflict settlement: providing information, increasing the expected future costs of war, and helping conflict parties overcome the problem of credible commitment (Beardsley et al. 2006;Kydd 2003Kydd , 2010Savun 2008;Walter 1997). However, this article demonstrates the perils of focusing third-party assistance solely at the leadership level, at which these interventions are usually targeted. Constituents shape their leader's decisions, even if they are not present at the negotiation table. Without a change in their support, negotiating a deal may be too costly politically for their leaders. Third parties interested in promoting conflict settlement should therefore consider support for initiatives on multiple levels, including "softer" engagements that seek to change the conflict narrative and humanize the opponent.
Finally, the problem of costly concessions highlights the importance of conflict prevention. The impact of battlefield dynamics on social preferences suggests that to settle a conflict, more information is needed after the onset of war. And as this article demonstrates, negotiating conflict settlement with a sworn enemy may be politically unfeasible even under the assumption of perfect information. Investing resources in third-party engagement is therefore most effective before war breaks out.
A's absolute gains from agreement x are therefore: while B's absolute gains are

Integrating Gains Preferences
The negative utility of concessions is determined by the importance an actor attaches to avoiding concessions (β i ) and the scope of those concessions (u −i (x) −u −i (na)). This means that once we account for the negative utility of concessions, the old utility functions of A and B become interrelated, expressed here through the new utility functionũ i (x). Under perfect information, the utility of an agreement x for a member of A is now and for a member of B The utility of nonagreement remains unchanged, as continued fighting does not entail any concessions. Accordingly, under perfect information, members of A will only support an agreement if or that is, if the absolute gains of an agreement are larger than the negative utility of making concessions. In the same vein, members of B will only support an agreement if Minimally Acceptable Agreement (Individual Perspective) The utility of the minimally acceptable agreement u i (x i ) equals the utility of nonagreementũ i (na), i.e., for A:x and for B: In equations (11) and (13), a higher β i yields a higher x A for members of A (who prefer 1) and a lowerx B for members of B (who prefer 0), as long as the costs of war of the opponent are positive.

Conditions for a Bargaining Range (Leader Perspective)
Under the assumptions outlined above, and building on equations (8) and (9), we know that leader A will only consider an agreement x if and leader B if Equation (14) may also be expressed as and equation (15) as This means that the leaders on both sides only accept an agreement if their own gains relative to the other side's gains are larger than the negative weight they attribute to concessions (s i β i ). Because it also implies that agreement under perfect information will only be possible if If equation (19) is not true, then a continuation of war is the natural outcome.