The return function: A new computable perspective on Bayesian-Nash equilibria

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In this paper, we suggest a new approach called the return function to deal with the determination of Bayesian-Nash equilibria in games of incomplete information. Whereas in the traditional approach players reply to each others' strategies, here each player replies to his own return function. In short, given a player's choice of action and the other players' strategies, the return function of that given player is the probability distribution of the outcome. Interestingly, we show that the dynamics of best-reply strategies, which are hard to compute in practice, are mapped to an observable and easy-to-compute dynamics of return functions. We propose a new algorithm for computing Bayesian-Nash equilibria, and illustrate its implementation on a cake-cutting problem. Finally, we prove the convergence of the dynamics of return functions to the Bayesian-Nash equilibrium under fairly general topological assumptions.

, 28 pages

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European Journal of Operational Research, 279(2), 471–485, 2019 BibTeX reference