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Strategic Interaction and Interstate Crises: A Bayesian Quantal Response Estimator for Incomplete Information Games

  • Justin Esarey (a1), Bumba Mukherjee (a2) and Will H. Moore (a3)


Private information characteristics like resolve and audience costs are powerful influences over strategic international behavior, especially crisis bargaining. As a consequence, states face asymmetric information when interacting with one another and will presumably try to learn about each others' private characteristics by observing each others' behavior. A satisfying statistical treatment would account for the existence of asymmetric information and model the learning process. This study develops a formal and statistical framework for incomplete information games that we term the Bayesian Quantal Response Equilibrium Model (BQRE model). Our BQRE model offers three advantages over existing work: it directly incorporates asymmetric information into the statistical model's structure, estimates the influence of private information characteristics on behavior, and mimics the temporal learning process that we believe takes place in international politics.


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Author's note: For their assistance with the Phoenix cluster at Florida State University (FSU) we wish to thank Jim Wilgenbusch and Jeff MacDonald of the Computational and Information Science Technology Department. The Department of Political Science at FSU graciously provided us with access to Quantify, its shared parallel computing resource. We also wish to thank Ken Schultz, David Siegel, Curt Signorino, Jeff Staton, our anonymous reviewers, and the participants and attendees of our 2007 APSA conference panel and 2007 Political Methodology conference poster session for their helpful comments and suggestions.



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Aldrich, John, and Alt, James. 2003. Introduction to the special issue. Political Analysis 11: 309–15.
Bas, Muhammet, Signorino, Curtis, and Walker, Robert. 2007. Statistical backwards induction: A simple method for estimating strategic models. Political Analysis doi:10.1093/pan/mpm029.
Carrubba, Clifford J., Yuen, Amy, and Zorn, Christopher. 2007. In defense of comparative statics: Specifying empirical tests of models of strategic interaction. Political Analysis 15: 465–82.
Fearon, James. 1994a. Domestic political audiences and the escalation of international disputes. American Political Science Review 88: 577–92.
Fearon, James. 1994b. Signaling versus the balance of power and interests: An empirical test of a crisis bargaining model. Journal of Conflict Resolution 38: 236–70.
Fearon, James D. 1995. Rationalist explanations for war. International Organization 49: 379414.
Fey, Mark, and Ramsay, Kristopher. 2006. The common priors assumption: A comment on bargaining and the nature of war. Journal of Conflict Resolution 50: 607–13.
Gelpi, Christopher F., and Griesdorf, Michael. 2001. Winners or losers? Democracies in international crisis, 1918-94. American Political Science Review 95: 633–47.
Granato, Jim, and Scioli, Frank. 2004. Puzzles, proverbs and omega matrices: The Scientific and Social Significance and Empirical Implications of Theoretical Models (EITM). Perspectives on Politics 2: 313–23.
Greene, William. 2003. Econometric Analysis. 5th ed. New York: Prentice Hall.
Hsiao, Cheng. 2003. Analysis of panel data. 2nd ed. New York: Cambridge University Press.
Keohane, Robert O. 1984. After hegemony. Princeton, NJ: Princeton University Press.
Lewis, Jeffrey B., and Schultz, Kenneth A. 2003. Revealing preferences: Empirical estimation of a crisis bargaining game with incomplete information. Political Analysis 11: 345–67.
Martin, Andrew, and Quinn, Kevin. 2006. MCMCpack.
McKelvey, Richard, and Palfrey, Thomas. 1995. Quantal response equilibria in normal form games. Games and Economic Behavior 10: 638.
McKelvey, Richard, and Palfrey, Thomas. 1998. Quantal response equilibria in extensive form games. Experimental Economics 1(1): 941.
Morrow, James D. 1989. Capabilities, uncertainty, and resolve: A limited information model of crisis bargaining. American Journal of Political Science 33: 941–72.
Morrow, James D. 1999. The strategic setting of choices: Signaling, commitment, and negotiations in international politics. In Strategic choice and international relations, ed. Lake, D. A. and Powell, R. 77114. Princeton, NJ: Princeton University Press.
Palfrey, Thomas R. 2007. McKelvey and quantal response equilibrium. In Positive changes in political science: The legacy of richard d. mckelvey's most influential writings, ed. Alt, James, Aldrich, John, and Lupia, Arthur. Ann Arbor, MI: University of Michigan Press.
Partell, Peter J., and Palmer, Glenn. 1999. Audience costs and interstate crises: An empirical assessment of Fearon's model of dispute outcomes. International Studies Quarterly 43: 389405.
Powell, Robert R. 2004. Bargaining and learning while fighting. American Journal of Political Science 48: 344–61.
Reed, William. 2003. Information, power and war. American Political Science Review 97: 633–41.
Reiter, Dan, and Stam, Allan C. III. 1998. Democracy, war initiation, and victory. American Political Science Review 92: 377–90.
Reiter, Dan, and Stam, Allan C. III. 2002. Democracies at war, Princeton, NJ: Princeton University Press.
Rossini, Anthony, Tierney, Luke, and Li, Na. 2003. Simple parallel statistical computing in R. UW Biostatistics Working Paper Series. Working paper 193.
Russett, Bruce M., and Oneal, John R. 1999. The classic liberals were right: Democracy, interdependence, and conflict, 1950-1985. International Studies Quarterly 41: 267–94.
Russett, Bruce M., and Oneal, John R. 2001. Triangulating peace: Democracy, interdependence, and international organizations. New York: Norton.
Sartori, Anne E., and Meirowitz, Adam. 2006. Secrecy and war: The origins of private information. Unpublished manuscript, Princeton University.
Schelling, Thomas C. 1966. Arms and influence. New Haven, CT: Yale University Press.
Schultz, Kenneth. 1999. Do democratic institutions constrain or inform? Contrasting two institutional perspectives on democracy and war. International Organization 53: 233–66.
Sekhon, Jasjeet S., and Mebane, Walter R. Jr. 1998. Genetic optimization using derivatives. Political Analysis 7: 187210.
Sevcikova, Hana, and Rossini, Tony. 2004. Package rlecuyer. (accessed September 14, 2006).
Signorino, Curtis S. 1999. Strategic interaction and the statistical analysis of international conflict. American Political Science Review 99: 279–97.
Signorino, Curtis S. 2003. Structure and uncertainty in discrete choice models. Political Analysis 11: 316–44.
Signorino, Curtis S. 2007. On formal theory and statistical methods: A response to Carrubba, Yuen, and Zorn. Political Analysis 15: 483501.
Signorino, Curtis S., and Yilmaz, Kuzey. 2003. Strategic misspecification in regression models. American Journal of Political Science 47: 551–66.
Slantchev, Branislav. 2003. The power to hurt: Costly conflict with completely informed states. American Political Science Review 47: 123–35.
Smith, Alastair. 1999. Testing theories of strategic choice: The example of crisis escalation. American Journal of Political Science 43: 1254–83.
Smith, Alastair, and Stam, Allan. 2004. Bargaining and the nature of war. Journal of Conflict Resolution 48: 783813.
Snyder, Glenn, and Deising, Paul. 1977. Conflict among nations. Princeton, NJ: Princeton University Press.
Wand, Jonathan. 2006. Comparing models of strategic choice: The role of uncertainty and signaling. Political Analysis 14: 101–20.
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Strategic Interaction and Interstate Crises: A Bayesian Quantal Response Estimator for Incomplete Information Games

  • Justin Esarey (a1), Bumba Mukherjee (a2) and Will H. Moore (a3)


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