Search for maximum points of a vector criterion based on decomposition properties

Abstract

A multiplayer dynamic noncooperative game is considered, in which the players make decisions by maximizing individual utility functions. In each round of the game, information exchange is performed by means of a mechanism similar to the Walras auction. The notion of market equilibrium is introduced, which combines the properties of a Nash equilibrium and Pareto maximum. A theorem on the existence of such an equilibrium is proved. An algorithm for searching for a market equilibrium is proposed, which shifts a Nash competitive equilibrium to a Pareto cooperative maximum. The algorithm is interpreted in the form of a repeated auction, in which the auctioneer has no information about the utility functions of the players. The players, in turn, have no information about the utility functions of other participants. In each round of the stepwise auction, individual interest rates are proposed to the players, based on which they maximize their utility functions. Then, the players give their best replies to the auctioneer. The auctioneer’s strategies of forming interest rates that provide conditions for reaching a market equilibrium are considered. From the game-theoretical point of view, the repeated auction describes the learning process in a noncooperative repeated game under uncertainty.