Asymmetric information and third-party intervention in civil wars

Abstract

I study a two-period model of conflict with two combatants and a third party who is an ally of one of the combatants. The third party is fully informed about the type of her ally but not about the type of her ally’s enemy. In a signaling game, I find that if the third party is unable to give a sufficiently high assistance to her ally, then there exists a unique separating equilibrium in which the third party’s expected intervention causes her ally’s enemy to exert more effort than in the absence of third-party intervention; this worsens the conflict.

Keywords:

• Perfect Bayesian equilibrium
• Conflict
• Intuitive criterion
• Signaling
• Third-party intervention

JEL Codes:

• D72
• D74

Acknowledgments

I thank the editor and two anonymous referees for helpful comments. I also thank Rene Kirkegaard, Asha Sadanand, Dana Sisak, Ruqu Wang, and Jun Zhang for very helpful comments on an earlier version of this paper. My thanks are also due to Olivier Bos, Bram Cadsby, and Osman Ouattara. This paper is a substantially revised version of a paper that was previously titled ‘Third party intervention in conflicts and the indirect Samaritan’s dilemma,’ circulated as CESifo working paper #2711, and presented at the Royal Military College (Canada), the 2011 CESifo ESP conference in Munich, and the 2011 workshop on contests and tournaments at the Technical University of Berlin.

Notes

1 See Blattman and Miguel (2010) and Collier and Hoeffler (2007) for surveys of the literature on intrastate conflicts and Amegashie (2010) for a discussion of third-party intervention in conflicts.

2 See also Balch-Lindsay et al. (2008). These papers used the duration of conflict to evaluate third-party interventions. Hence, third-party intervention worsens a conflict if it extends the duration of the conflict. In this paper, I use the effect of third-party intervention on the aggregate effort by the warring faction to evaluate the third party’s intervention. This is reasonable because there is likely to be a positive correlation between the duration of conflict and the magnitude of the social costs in terms of the loss of life and property. In the related case of mediation, as opposed to military intervention, Regan and Stam (2000) undertook an empirical analysis of third-party intervention in conflicts and found that mediation in the earlier stages of a conflict are more effective and that late mediations worsen conflicts. Dixon (1996) found that mediation efforts and third-party activities to open or maintain lines of communication are the most effective to resolving conflicts.

3 In a 31 May 2006 op-ed in the New York Times, Alan Kuperman claimed that intervention in Darfur was emboldening the rebels to fight on because the rebels who benefited from intervention rejected a proposed agreement. A similar argument has been made by some scholars with respect to the Kosovo crisis (see Grigorian, 2005). However, others do not think that the moral hazard argument is satisfactory (e.g. Crawford, 2005; Grigorian, 2005).

4 There is a wide literature on third-party intervention which uses the Fearon (1994, 1995) crisis-bargaining model. Favretto (2009) uses a model of incomplete information in the framework of Fearon’s (1994, 1995) crisis-bargaining model. In contrast to the present model, she assumes exogenous probabilities of success for the warring factions. Using a crisis-bargaining model with no signaling, Werner (2000) considers a model of incomplete information to determine a third party’s incentives to intervene in a conflict. She finds that an attacker can manipulate the stakes of war by making it low enough that, for a third party, the benefits of intervention do not justify the costs (see also Yuen, 2009). In my model, no one can manipulate the stakes of the conflict. And in Werner (2000), the threat of intervention does not worsen the conflict.

5 Notice that this argument is different from the argument in Elbadawi and Sambanis (2000) and Akcinaroglu and Radziszewski (2005) for using expected intervention as an explanatory variable in a regression. Unlike these authors, I am not arguing that expected intervention should be used as an instrumental variable in order to deal with the endogeneity of actual intervention. I am arguing that expected intervention and actual intervention may be distinct explanatory variables in a regression that seek to explain the intensity of conflict. Still, their finding suggests that expected intervention could have a negative effect on conflicts.

6 In a seminal two-player crisis-bargaining model in the shadow of conflict, Fearon (1994, 1995) used costly signaling as an explanation of war. In these models, the threat of conflict, not necessarily actual conflict, is used to make credible demands in crisis bargaining. In my model, conflict is inevitable and I do not allow bargaining between the third party and his ally on one hand and the ally’s enemy on the other. Crisis bargaining models are typically used to explain the conditions under which conflict will occur and the role of private information is at the heart of this literature (see Walter, 2009, for a review). I am interested in the conditions under which third-party intervention will escalate an ongoing conflict. Also, signaling in crisis bargaining models is different from signaling in the classical sense.

7 This means that I could demonstrate my result in a one-period model with more stages. However, the two-period model below is more convenient for exposition.

8 In the model, signaling occurs in period 1. Imagine that there is an exogenous third-party military assistance in period 1 but no intervention in period 2. That is, the third party has decided to exogenously withdraw from the conflict in period 2. Call this the no-intervention case. In this case, there will be no signaling in period 1. The equilibrium of the game in period 1 when the third party has incomplete information is the same as the equilibrium when the third party has complete information. Now suppose in period 2, the third party decides to withdraw or stay in the conflict based on the outcome of the conflict in period 1. Then, the analysis in the paper goes through.

9 The assumption that faction B’s valuation in period 2 is the same as his valuation in period 1 is crucial. If nature were to move again in period 2, there will be no need for signaling in period 1.

10 In addition to the reasons given below, note that in the influential alternating-offers bargaining game pioneered by Ariel Rubinstein, the timing of moves between the two bargainers is not the same in each period.

11 For a paper that examines revenge in conflicts, see Amegashie and Runkel (2012).

12 Chang et al. (2007) and Chang and Sanders (2009) used a very standard model of sequential contests. Their contribution was the introduction of third-party intervention into the Tullock contest-type models of Grossman and Kim (1995), Gershenson and Grossman (2000), Leininger (1993), and Morgan (2003). See Konrad (2009) for a review of sequential contests. Assuming complete information and simultaneous moves, this model of conflict has also been used to analyze third-party intervention by Amegashie and Kutsoati (2007) who endogenized a third party’s choice of her ally while Carment and Rowlands (1998), Rowlands and Carment (2006), and Siqueira (2003) took the third party’s ally as given and examined the effect of third party’s intervention on conflicts. Furthermore, there is a small literature on signaling in conflicts and contests. However, this literature considers only two players. It does not consider a third party or third-party intervention and so its focus is entirely different from this paper.

13 The parameters of my numerical example are such that this feature of the model is preserved. If V ⩾ 2W_k for all k, then there is no conflict even if the third party does not intervene, k = H, L. In this case, third-party intervention is not necessary, which is not a desirable feature of a model of third-party intervention. In this equilibrium, faction A is sufficiently armed (including the number of soldiers) leading faction B to acquiesce resulting in no conflict. See Grossman and Kim (1995) and Gershenson and Grossman (2000) for a discussion of this equilibrium. This equilibrium is not possible if factions A and B move simultaneously.

14 This means that the third party’s military assistance does not exceed what is required to deter the weak type of faction B. It implies that the strong type of faction B is not deterred in spite of the third party’s assistance. I construct an example that satisfies this condition.

15 This can easily be seen by putting (8) into (11).

16 Of course, if the strong type of faction B’s investment  ⩾ V, then faction A will choose a zero effort in period 1. The reader should be able to verify that this does not affect any of the analyses. However, in the subsequent numerical example, I choose parameters to ensure that faction A’s equilibrium effort in period 1 is positive.

17 In other cases, the requirement to keep civilian causalities at a minimum means that a third party and her ally cannot deploy their full and combined military might.

18 For example, if θ = 0.5, this condition is 8(W_H)²−SV² > 0.

19 See appendix B for a proof that there is no pooling equilibrium. However, proving the nonexistence of a pooling equilibrium is not crucial. Focusing on separating equilibria is sufficient for my purposes because my goal is to construct an equilibrium in which third-party intervention may worsen a conflict. Therefore, what matters is to show that such an equilibrium exists. But, the nonexistence of a pooling equilibrium strengthens the results because it gives a stronger comparative static prediction.

20 See also Hertzendorf and Overgaard (2001) and Daughety and Reinganum (2007) where two incumbent firms, with possibly different costs, send signals to consumers. A difference between all these papers and mine is that the two informed parties move simultaneously while in my case they move sequentially.

21 Notice that in considering deviations by faction B, I allow faction A to respond to the deviations. If the third party were not in the game, it would not matter whether I allow faction A to respond or if faction A sticks to his subgame perfect equilibrium investment. In either case, faction B will still choose his subgame perfect equilibrium investment. In this model, because deviations by faction B affect the third party’s beliefs, which may be different from his equilibrium beliefs, allowing faction A to respond to deviations by faction B may result in a different choice by faction B than what he will choose if faction A stuck to his equilibrium choice. And since deviations are not observed in equilibrium, we are, of course, asking the following (hypothetical) question: ‘if faction B could deviate from equilibrium, will he, mindful of the fact that faction A chooses his investment after observing his (i.e. B) investment, choose an investment that is different from the equilibrium investment?’ For consistency, we have to assume that if faction B deviates, he deviates as a first mover whose actions are observed by faction A. In contrast, being a second mover, faction A does not have to worry about faction B responding to his (i.e. A) deviations.

22 The numerical example below satisfies this condition with strict inequality. This was verified by plotting on the domain [0, ].

23 In this case, the intuitive criterion actually does not tell us what to do. However, the reasoning used here is in the spirit of the D1 condition in Cho and Kreps (1987). The D1 condition requires that we put the entire weight on the type that is willing to deviate for a wider range of inferences by the receiver (i.e. uninformed party). In my case, while a decrease (deviation) that the strong type of faction B finds profitable is also profitable to the weak type, the converse is not true. That is, there are some decreases in investment that the weak type finds profitable but are not profitable to the strong type. Hence, it is reasonable for the third party to set μ = 0 in (A.1) for investments smaller than . This is why this kind of reasoning is in the spirit of the D1 condition of Cho and Kreps (1987).

24 In this case, the inequalities in (A.8) are applicable with the inequality for the weak type being a weak inequality.