Credibility and Commitment in Crisis Bargaining∗

Although scholars of international security share a skepticism for the extent to which agreements can be externally enforced, much existing game-theoretic work involves strong forms of commitment. Building on the canonical model of crisis bargaining we study the role of two forms of commitment in bargaining—the ability to commit to a settlement and the ability to commit to end negotiations and initiate war fighting. We show that, contrary to expectations, allowing a proposer to retract their offer after learning of its acceptance does not lead to greater demands. Instead, a rational actor can be best off honoring the accepted agreement in crisis bargaining, even though the act of accepting an offer changes the proposer’s beliefs about the probability that an offer is acceptable. On the other hand, allowing a proposer to continue bargaining in lieu of fighting does change the dynamics of bargaining, although this effect diminishes as players become more patient. Finally, when there is not commitment to offers or fighting after a rejected proposal, the behavior is the same as that found in the model with only renegotiation of agreements and thus mirrors the behavior in the model in which both forms of commitment are present. ∗We thank Avi Acharya, Alex Hirsch, Matias Iaryczower, David Myatt, and Francesco Squintani for useful discussions on this topic. We appreciation helpful comments at the University Wisconsin, Yale, SUNYBinghamton, University of Warwick, the London School of Economics, and the University of Rochester.