Kinetic theory for the emergence of complex behavior in social and economic systems

The N-player War of Attrition in the Limit of Infinitely Many Players

Bernt Wennberg

Chalmers University, Göteborg, Sweden


(this is joint work with Peter Helgesson, who is the main author) The “War of Attrition” is a game-theoretic model formulated by John Maynard Smith to describe the evolution of some non-violent animal behavior. The original form of the model involves two players competing for a single prize. The rules are simple: the player that is prepared to wait the longest time wins; however, there is a cost associated with the participation, proportional to the duration of the game. Maynard Smith showed that no pure strategy can be an ESS (Evolutionary Stable State, a strictly stronger condition than that of Nash equilibrium), and that the unique mixed strategy is an exponential waiting time. The War of Attrition has been generalized to several players e.g. by J. Haigh and C. Cannings. In this talk I will first discuss the original two-player model, and the concept of ESS. Then I’ll describe some possible generalizations to several players, and our own main results, concerning the limit to infinitely many players.