Adaptive Nash Strategies for Repeated Games Resulting in Pareto Solutions

摘要

Adaptive game theory has roots in both repeated games and adaptive control. Radner has recently published a number of papers on repeated games. The essential message is that a Nash equilibrium exists for such a dynamic game which, as time evolves, converges to a Pareto solution of the corresponding static game (if it would be played once instead of repeatedly). The reason of this possibility is the ability to perform threats; which in its turn is possible by applying strategies which include history. In the current paper it is assumed that the decisionmakers know a noisy version of each others' past decisions, but have only partial knowledge about the payoff function of the other players (or more generally, about the system which describes the evolution of the decision process). Based on this knowledge the authors decide about the current move. Conditions and an algorithm will be given under which such a scheme will converge. (Copyright (c) 1986 by Department of Mathematics and Informatics, Delft, The Netherlands.)