From Computing Sets of Optima, Pareto Sets, and Sets of Nash Equilibria to General Decision-Related Set Computations

Vladik Kreinovich (University of Texas at El Paso, USA)

Bartlomiej Jacek Kubica (Warsaw University of Technology, Poland)

Abstract: Several algorithms have been proposed to compute sets of optima, Pareto sets, and sets of Nash equilibria. In this paper, we present a general algorithm for decision-related set computations that includes all these algorithms as particular cases.

To make our algorithm understandable to people working in optimization and in game theory, we also provide motivations and explanations for our formalizations of the corresponding problems and for the related notions of computable mathematics.

Keywords: Nash equilibria, Pareto sets, computing sets, sets of optima

Categories: F.2.1, F.4, G.1.m