When fully informed states make good the threat of war: Rational escalation and the failure of bargaining

British Journal of Political Science

Volumn 36, Issue 4, 2006, Pages 645-669

  Langlois, Catherine C ^a   Langlois, Jean Pierre P ^b  

^a GEORGETOWN UNIVERSITY   (United States)

^b SAN FRANCISCO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747881563     PISSN: 00071234     EISSN: 14692112     Source Type: Journal    
DOI: 10.1017/S0007123406000342     Document Type: Article

References (79)

1. We therefore look at an asymmetric deterrence situation which allows us to incorporate the simplest possible escalation ladder into our model. Moreover, as Zagare and Kilgour point out, such 'one-sided deterrence relationships have obvious empirical and theoretical import': Frank Zagare and Marc Kilgour, Perfect Deterrence (Cambridge: Cambridge Studies in International Relations, Cambridge University Press, 2000), p. 135.
2. James D. Fearon, 'Rationalist Explanations for War,' International Organization, 49 (1995), 379-414;
3. Robert Powell, Nuclear Deterrence Theory: The Search for Credibility (New York:Cambridge University Press, 1990). As we discuss below, these authors do explain costly conflict in equilibrium despite full information if the payers are engaged in a stochastic game. The inefficient outcome is then attributed to commitment problems.
4. See, for example, Robert Powell, 'The Inefficient Use of Power: Costly Conflict with Complete Information', American Political Science Review, 98 (2004), 231-41;
5. James D. Fearon, 'Why Do Some Civil Wars Last So Long?' Journal of Peace Research, 41 (2004), 275-302.
6. Robert Powell, In the Shadow of Power (Princeton, N.J.: Princeton University Press, 1999).
7. Fearon, 'Why Do Some Civil Wars Last So Long?'
8. Daren Acemoglu and James Robinson, 'A Theory of Political Transitions', American Economic Review, 91 (2001), 938-63.
9. Powell, 'The Inefficient Use of Power'.
10. Related work examines the incentive to run up inefficient levels of public debt (Alberto Alesina and Guido Tabellini, 'A Positive Theory of Fiscal Deficits and Government Debt', Review of Economic Studies, 57 (1990), 403-14;
11. Thorsten Persson and Lars Svensson, 'Why Stubborn Conservatives Would Run a Deficit: Policy with Time-Inconsistent Preferences', Quarterly Journal of Economics, 104 (1989), 325-45) or to create inefficient administrative procedures
12. (Rui de Figueiredo, 'Electoral Competition, Political Uncertainty, and Policy Insulation', American Political Science Review, 96 (2002), 321-35).
13. Carl von Clausewitz, On War, edited and translated by Michael Howard and Peter Paret (Princeton, N.J.: Princeton University Press, 1984), p. 605.
14. Paul R. Pillar, Negotiating Peace: War Termination as a Bargaining Process, (Princeton, N.J.: Princeton University Press, 1983);
15. R. Harrison Wagner, 'Bargaining and War', American Journal of Political Science, 44 (2000), 469-84.
16. Wagner, 'Bargaining and War', p. 480.
17. Pillar, Negotiating Peace, p. 59.
18. Darren Filson and Suzanne Werner, 'A Bargaining Model of War and Peace: Anticipating the Onset, Duration and Outcome of War', American Journal of Political Science, 46 (2002), 819-38, p. 819.
19. There is avast literature on war and bargaining that appeals to uncertainty and we do not review it here. For example, Powell models rivals that have asymmetric information on each other's preferences (Robert Powell, 'Bargaining in the Shadow of Power', Games and Economic Behavior, 15(1996), 255-89;
20. and Powell, In the Shadow of Power). The more recent literature examines the learning that occurs as a result of fighting and bargaining. In Filson and Werner one of the rivals is uncertain about the other's type and bargains accordingly.
21. The response to negotiations as well as the outcome of battle informs about the likelihood that the rival is strong or weak (see Filson and Werner, 'A Bargaining Model of War and Peace'.
22. and Darren Filson and Suzanne Werner, 'Bargaining and Fighting: The Impact of Regime Type on War Onset, Duration and Outcome', American Journal of Political Science, 48 (2004), 296-313).
23. In a related vein, Smith and Stam model states that have inconsistent beliefs about the likelihood of winning the next battle (or fort) and these beliefs converge as the rivals fight battle after battle (Alastair Smith and Allan Stam, 'Bargaining and the Nature of War', Journal of Conflict Resolution, 48 (2004), 783-813).
24. Scott D. Bennett, 'Integrating and Testing Models of Rivalry Duration', American Journal of Political Science, 42 (1998), 1200-32
25. Fearon, 'Rationalist Explanations for War', p. 380.
26. Fearon, 'Rationalist Explanations for War';
27. Powell, Nuclear Deterrence Theory.
28. James D. Fearon, 'Bargaining, Enforcement and International Cooperation', International Organization, 52 (1998), 269-305.
29. Fearon, 'Bargaining, Enforcement and International Cooperation'.
30. Branislav L. Slantchev, 'The Power to Hurt: Costly Conflict with Completely Informed States', American Political Science Review, 97 (2003), 123-35.
31. Ariel Rubinstein, 'Perfect Equilibrium in a Bargaining Game', Econometrica, 50 (1982), 97-110;
32. Lutz-Alexander Busch and Quan Wen, 'Perfect Equilibria in a Negotiation Model', Econometrica, 63 (1995), 545-65.
33. Slantchev, 'The Power to Hurt'.
34. Zagare and Kilgour, Perfect Deterrence.
35. Demanding x = 0 is substantially equivalent to not challenging in the first place and indeed results in an offer y = 0 and an immediate exit by the challenger in the equilibria we obtain.
36. Backdown does not mean that the challenger drops her demand altogether. It merely means that she shies away from immediate military action while her current demand stands. Whatever y the defender may offer at the next visit to BD, the challenger can repeat or modify her demand at her next visit to BC. The model can undoubtedly be complicated to allow more options and decision turns for the two sides. Our modelling choices were driven by a need for simplicity while allowing for repeated choices in the three main phases of the game (bargaining, crisis and war). The model variations that the authors investigated did not affect the qualitative results.
37. α where α ∈ [0,1] represents the rivals' degree of risk aversion. The lower α, the more risk averse the players. We briefly explore the impact of risk aversion on model outcomes when we develop our numerical examples (see fn. 40) and provide formulae for strategic probabilities in equilibrium in fn. 35.
38. Payoffs indicated in Figure 1 are per period payoffs. The challenger's payoff is listed first.
39. IV= tω with a reinterpretation of parameter t. In the current interpretation we assume t + u + v = 1 but we can instead let t + u + v < 1 with the difference being lost in the fighting. The future would then be more discounted after any war turn. This would discount costs more after a war episode, meaning that each side's capacity to inflict war costs in the future is reduced by fighting. Such a modification would leave formulae for probabilities in 6a-e unchanged, although a lower t would affect the probability values and the necessary conditions (s and r decrease, and condition c + d > tω/(1 - ω) is less stringent).
40. See Drew Fudenberg and Jean Tirole, Game Theory (Cambridge, Mass.: The MIT Press, 1995), chap. 5.
41. Technically, that history must lead to a subgame that is self-contained in terms of decision and information structure. This is always the case in our game structure. Also note that the prior history need not result from equilibrium play in a SPE.
42. Slantchev, 'The Power to Hurt'.
43. n). This is because, given an agreed bargain (x, 1 - x), each rival must find it in his or her interest to follow the plan, and incur the costs associated with the war episodes, in order to get the agreed share of the prize. For the same reason, pure equilibria cannot generate outcomes in which the rivals fight wars that end up costing more than the coveted asset is worth.
44. Slantchev, 'The Power to Hurt'.
45. See Fudenberg and Tirole, Game Theory, chap. 13, for an analysis of Markov Perfect equilibria. Although a MPE has a simple structure it retains all properties of SPEs, in particular that no deviation of any kind can be profitable. An elementary proof of this claim for our particular game structure is available from the authors upon request.
46. Details of this generalization are available from the authors upon request.
47. Theorem 2 in the Appendix specifies out of equilibrium behaviour as required for a SPE (Reinhart Selten, 'Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Games', International Journal of Game Theory, 4 (1975), 25-55).
48. α - Κ. Overall, when the rivals are risk averse, it takes a lower counter-offer from the defender for the challenger to accept it for certain. The risk-averse challenger tends to be more cautious and this shows up in the impact of risk aversion on model outcomes (see fn. 40).
49. Details of this generalization are available from the authors upon request.
50. A probability of war is also frequently the equilibrium outcome of incomplete information games that describe bargaining in the shadow of conflict. For example, Banks describes an asymmetric information game for which the probability of war in equilibrium increases with the informed player's payoff from war (Jeffrey S. Banks, 'Equilibrium Behavior in Crisis Bargaining Games', American Journal of Political Science, 34 (1990), 599-614). Our mixed equilibria also predict a probability of war, but in contrast to Banks, we specify the escalation process by which war occurs and it is the escalation process itself that generates the war probability in equilibrium. Banks, instead, assumes an a priori theoretical relationship between player choices and the probability of war.
51. Thomas C. Schelling, The Strategy of Conflict (Cambridge, Mass.: Harvard University Press, 1960, 18th printing 2002), p. 182.
52. D = 3 cut across the range of battle costs that the model admits.
53. D = 3 and ω = 0.95 as in Table 1, if the protagonists pick bargaining position x = 1, y = 0, then as α decreases to 0.8, probability s that Challenger reiterates her demand at BC drops to 73.1 per cent while she would have done so with 84.2 per cent probability had she been risk neutral. Overall, as risk aversion increases, the challenger accepts the defender's counter-offer with increasing probability, war is avoided with increasing probability, and the expected length of the crisis is reduced. A full numerical exploration of the impact of risk aversion, is available from the authors upon request.
54. Interestingly, allowing for decisive battle wins does not encourage fighting. Numerical simulations, available from the authors upon request, show that the impact of a decisive win in battle is limited to relatively small changes in the calibration of outcomes. Nevertheless, the fact that deterrence succeeds with higher probability when wars can be won outright is noteworthy, as it confirms our central finding: perfectly informed rivals wield deterrent threats to gain or maintain possession of the contested asset, and make good on these threats by engaging in costly warfare. The possibility of winning outright emboldens challenger and defender once war is the next possible step, and this encourages the challenger to accept the defender's counteroffer before escalation. Powell points out that a war as 'costly lottery' assumption may not be neutral (Robert Powell, 'Bargaining Theory and International Conflict', Annual Review of Political Science, 5 (2002), 1-30).
55. In fact, Wagner argues that the assumption is distorting and 'can only lead to misleading conclusions' (Wagner, 'Bargaining and War', p. 469). Our analysis suggests that the 'costly lottery' assumption reinforces incentives that are present when wars merely impose costs.
56. Robert K. Brigham, 'Vietnamese-American Peace Negotiations: The Failed 1965 Initiatives', Journal of American-East Asian Relations, 4 (1995), 377-94.
57. Gereth Porter, A Peace Denied: The United States, Vietnam and the Paris Agreement (Bloomington: Indiana University Press, 1985);
58. Gabriel Kolko, Anatomy of a War: Vietnam, the United States and the Modern Historical Experience (New York: Pantheon Books, 1985).
59. Stanley Karnov, Vietnam, A History (New York: Penguin Books, 1983), p. 549.
60. Thomas Princen, 'Beagle Channel Negotiations' (PewCase401, Institute for the Study of Diplomacy. School of Foreign Service, Georgetown University, 1995).
61. Paul Huth, Standing Your Ground: Territorial Dispute and International Conflict (Ann Arbor: University of Michigan Press, 1996), p. 197.
62. Huth, Standing Your Ground, p. 146.
63. David J. Singer, 'The Appeasement Option: Past and Future', in Melvin Small and Otto Feinstein, eds, Appeasing Fascism: Articles from the Wayne State University Conference on Munich After Fifty Years (Lanham, Md.: University Press of America, 1991).
64. Paul Kennedy, The Rise and Fall of the Great Powers (New York: Random House, 1987).
65. Kennedy, The Rise and Fall of the Great Powers, p. 85.
66. Having consulted Chistopher Mooney, Monte Carlo Simulation (Thousand Oaks, Calif.: Quantitative Applications in the Social Sciences Series, Paper 116, Sage, 1997).
67. 1. The remaining paths were sorted into four groups: paths for which both parties receive strictly negative payoffs; paths for which the players received positive payoffs; paths for which one or the other receives a strictly negative payoff. Frequencies for each of the five events were calculated. This process was repeated 1,000 times generating a distribution for the frequencies of each event. In all cases, with 95 per cent confidence, we were not able to reject the null hypothesis of a normal distribution (Jarque Bera statistic < 5.99). We were therefore able to construct 95 per cent confidence interval estimates of the likelihoods of each of the five events by adding and subtracting 1.96 standard deviations to each of the means.
68. We add the means in the < 0 column for the challenger and the < 0 row for defender.
69. 1), which leaves her with utility 0.
70. The possibility of winning the asset in battle does not significantly reduce the downside risk for either party. Estimates of the likelihood of various payoff events when battles can be won decisively are available from the authors upon request.
71. Robert Jervis, 'Rational Deterrence: Theory and Practice', World Politics, 41 (1989), 183-207, p. 184.
72. Huth, Standing Your Ground.
73. Dilip Hiro, The Longest War; The Iran-Iraq Military Conflict (New York: Routledge, Clapman and Hall, 1991), p. 1.
74. Huth, Standing Your Ground, p. 220.
75. These might be different from the initial ones. To substantiate a claim of perfect equilibrium one must allow any prior development, not just prior moves conforming to equilibrium behaviour. So, whether optimal or not, prior offers x and y may have been made.
76. s and r are 0 when y = tx -Κ and p reduces to 1 when ψ = 0. Otherwise, all are in (0, 1).
77. The Markov chain actually includes states I' and II', and its full transition matrix should formally involve two additional rows and columns. But I' and II' are absorbing states with fixed probabilities u and v of being reached and fixed outcomes. All calculations relevant to the decisions x and y and the move probabilities can therefore be limited to this 4×4 matrix for simplicity.
78. This includes the case where y>t -Κ.
79. These arguments are standard in Markov chains and can be found in James Norris, Markov Chains (Cambridge: Cambridge University Press, 1997), p. 12).