In a canonical model of military conflict, victory and defeat depend stochastically on the difference of resources deployed by the conflict parties. The present paper offers a comprehensive analysis of that model. The unique Nash equilibrium reflects either (i) peace, (ii) submission, (iii)...

This essay reviews new histories of the role of game theory and rational decision-making in shaping the social sciences, economics among them, in the post war period. The recent books "The World the Game Theorists Made" by Paul Erickson and "How Reason Almost Lost Its Mind" by Paul Erickson,...

Conventionally, game theory predicts that the joint mixed strategy of players in a noncooperative game will satisfy some equilibrium concept. Relative probabilities of the joint strategies satisfying the concept are unspecified, and all strategies not satisfying it are assigned probability zero....

This paper presents a generalized Stackelberg model of market leaderhip with noisy observation. The current prevailing Stackelberg model and Cournot market are two extreme cases of this generalized Stackelberg model. As the follower relies less on the inaccurate noisy observation and more on...

Perfect Bayesian equilibrium is not a subset of Nash equilibrium. Perfect Bayesian equilibrium requires players to have beliefs that are consistent with the equilibrium strategies of other players. Nash equilibrium does not explicitly specify the beliefs of the players. However, the default...

This paper uses Bayesian equilibrium by iterative conjectures approach to solve a noisy sequential game, that is, a sequential game with inaccurate observation clouded by noise. Bayesian equilibrium by iterative conjectures requires players to form conjectures about the strategies of the other...

This paper studies a new refinement for Perfect Bayesian equilibrium, Bayesian equilibrium by iterative conjectures (BEIC). BEIC requires players to make predictions, starting from first order uninformative predictive distribution functions (or conjectures) and keep updating with statistical...

In the Ultimatum Game (UG) one player, named “proposer”, has to decide how to allocate a certain amount of money between herself and a “responder”. If the offer is greater than or equal to the responder’s minimum acceptable offer (MAO), then the money is split as proposed, otherwise,...

This paper constructs a novel equilibrium in the chopstick auction of Szentes and Rosenthal (Games and Economic Behavior, 2003a, 2003b). In contrast to the existing solution, the identified equilibrium strategy allows a simple and intuitive characterization. Moreover, its best-response set has...

Sets closed under rational behavior were introduced by Basu and Weibull (1991) as subsets of the strategy space that contain all best replies to all strategy profiles in the set. We here consider a more restrictive notion of closure under rational behavior: a subset of the strategy space is...