How the Number of Strategies Impacts the Likelihood of Equilibria in Random Graphical Games

Anisse Ismaili (1) , Evripidis Bampis (2) , Nicolas Maudet (3) , Patrice Perny (1)

1 DECISION
2 RO - Recherche Opérationnelle
3 SMA - Systèmes Multi-Agents

This paper studies the likelihood of the existence of a pure Nash equilibrium (PNE) in random payoff graphical games. Here, players are represented by vertices, they choose a strategy in finite discrete sets of strategies, and the scope of a player’s utility function is only local. In this setting, the probability of existence of a PNE has been deeply studied for various graphical structures when the number of players tends to infinity, but only in the two strategies-per-player case: this paper extends these studies to an arbitrary number of strategies-per-player. We prove theoretically how more strategies-per-player makes the distribution of the number of equilibria get closer to a Poisson distribution. We apply these results to various graph structures and conclude with numerical experiments.

Domaines: Informatique [cs]

Anisse Ismaili, Evripidis Bampis, Nicolas Maudet, Patrice Perny. How the Number of Strategies Impacts the Likelihood of Equilibria in Random Graphical Games. 13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014, May 2014, Paris, France. pp.285-292. ⟨hal-01216644⟩