Dynamic Decision-Making in Logic Programming and Game Theory

Abstract. We present a framework for decision making with circumstance-dependent preferences and decisions. This formalism, called Ordered Choice Logic Programming, allows decisions that comprise multiple alternatives, which become available only when a choice between them is forced. The skeptical semantics is based on answer sets for which we provide a fixpoint characterization and a bottom-up algorithm. OCLPs can be used to represent and extend game theory concepts. We demonstrate that OCLPs allow an elegant translation of finite extensive games with perfect information such that the c-answer sets correspond to the Nash equilibria of the game. These equilibria are not player-deterministic, in the sense that a single player, given the other players ’ actions, could rationally leave an equilibrium state by changing her action profile. Therefor cautious Nash equilibria are introduced as the answer sets of the transformed game.