Convergence occurs in war and bargaining models as uninformed rivals discover their opponent's type by fighting and making calibrated offers that only the weaker party would accept. Fighting ends with the compromise that reveals the other side's type. This article shows that, if the protagonists are free to fight and bargain in the time continuum, they no longer make increasing concessions in an attempt to end the war promptly and on fair terms. Instead, the rivals stand firm on extreme bargaining positions, fighting it out in the hope that the other side will give in, until much of the war has been fought. Despite ongoing resolution of uncertainty by virtue of time passing, the rivals choose not to try to narrow their differences by negotiating.
(Online publication November 08 2011)
* Department of Mathematics, San Francisco State University (email: Langlois@math.sfsu.edu); and McDonough School of Business, Georgetown University, respectively. The order of the authors’ names is not indicative of their respective contributions, which they consider equal. They thank anonymous reviewers for extensive and insightful feedback.