Finding a Nash Equilibrium by Asynchronous Backtracking

Graphical Games are a succinct representation of multi agent interactions in which each participant interacts with a limited number of other agents. The model resembles Distributed Constraint Optimization Problems (DCOPs) including agents, variables, and values (strategies). However, unlike distributed constraints, local interactions of Graphical Games take the form of small strategic games and the agents are expected to seek a Nash Equilibrium rather than a cooperative minimal cost joint assignment. The present paper models graphical games as a Distributed Constraint Satisfaction Problem with unique k-ary constraints in which each agent is only aware of its part in the constraint. A proof that a satisfying solution to the resulting problem is an -Nash equilibrium is provided and an Asynchronous Backtracking algorithm is proposed for solving this distributed problem. The algorithm’s completeness is proved and its performance is evaluated.