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

Licentiate thesis, 2013

The topic of this thesis is a selected problem in game theory, namely the N-player War of Attrition. The War of Attrition is a well established game theoretic model that was first introduced in the 2-player case by John Maynard Smith. Although the original idea was to describe certain animal behaviour in, for instance, territorial competition the interest in the model increased and has found interesting applications also in economic theory. Following the results of Maynard Smith, John Haigh and Chris Cannings generalised the War of Attrition to allow for more than 2 players. Their work resulted in two separate models, in this thesis called the dynamic- and the static model, both reducing to the 2-player case when N=2. In the paper we study the asymptotic behavior of the N-player models as the number of players tend to infinity. By a thorough analysis of the dynamic model we find a connection to the more difficult static one in the infinite regime. This connection is then confirmed by approaching the limit of infinitely many players also in the static model. Finally, by using the limit results as a source of inspiration for the finite case, we manage to prove new results concerning existence and non-existence of an equilibrium strategy in the N-player static case.