La Trobe Statistics and Stochastic Seminar
Speaker: Dr Andrea Collevecchio, Monash University
Time & Date: 12:00pm Thursday 5 September 2019
Venue: Room 310, Physical Sciences 2, La Trobe University, Melbourne Campus.
Pure Nash Equilibria is formally defined as a profile of actions (one for each player) such that, given the choice of the other players, no player has an incentive to make a different choice, i.e., deviations from equilibrium are not profitable for any player. Although quite simple and powerful, this concept has the drawback that not every game admits pure equilibria. John Nash’s major contribution was to introduce the more general concept of mixed equilibria and to show that in a game with a finite number of players and actions the existence of mixed equilibria is guaranteed.
We prove that games with N players, two possible actions for each player and random payoffs, have many Pure Nash Equilibria; we show a way to find them, as well as describe the limiting distribution of their number and their “geometry”. We will also discuss generalizations to the various models explored. This result is valid under the assumptions of independent, identically distributed payoffs with atoms. It relies on the connections of game theory and statistical mechanics.
The talk is elementary, so no previous knowledge of game theory and statistical mechanics is required. Some very basic knowledge of probability would help, such as independence and central limit theorem.
Based on joint works with Ben Amiet, Marco Scarsini.