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

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.