Representing von Neumann-Morgenstern Games in the Situation Calculus

work by Oliver Schulte and Jim Delgrande, presented by Glendon Holst (SFU)

Von Neumann-Morgenstern Games (VM Games) are a powerful representational schema for multiplayer games, subsuming single agent MDPs. They are often used in Economics, Decision Theory, Operations Research, and Political Science. While representationally expressive, they are often unwieldy in practice, so we prefer a logical formalism instead. Situation Calculus is a well studied, widely used, computational formalism, with many nice properties, suitable to representing VM Games. In this talk we provide an introduction to VM Games and the Situation Calculus, and demonstrate how to axiomatize VM Game Forms in the Situation Calculus. This axiomatization is shown to be categorical (basically, complete and sound). Additionally we show how to capture continuous payoff (utility) functions in the Situation Calculus using the Baire topology.

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