Computing approximate bayes-nash equilibria in tree-games of incomplete information
We provide efficient algorithms for finding approximate Bayes-Nash equilibria (BNE) in graphical, specifically tree, games of incomplete information. In such games an agent's payoff depends on its private type as well as on the actions of the agents in its local neighborhood in the graph. We consider two classes of such games: (1) arbitrary tree-games with discrete types, and (2) tree-games with continuous types but with constraints on the effect of type on payoffs. For each class we present a message passing on the game-tree algorithm that computes an ε-BNE in time polynomial in the number of agents and the approximation parameter 1\ε.