Representing von Neumann-Morgenstern Games in the Situation Calculus

Sequential von Neumann-Morgernstern (VM) games are a very general formalism for representing multi-agent interactions and planning problems in a variety of types of environments. We show that sequential VM games with countably many actions and continuous utility functions have a sound and complete axiomatization in the situation calculus. This axiomatization allows us to represent game-theoretic reasoning and solution concepts such as Nash equilibrium. We discuss the application of various concepts from VM game theory to the theory of planning and multi-agent interactions, such as representing concurrent actions and using the Baire topology to define continuous payoff functions.

• Type: Journal
• Year: 2004
• Where: AMAI
• Authors: Oliver Schulte, James P. Delgrande
• Keywords: AMAI 2004, Artificial Intelligence, Multi-agent Interactions, Sequential Vm Games, Vm Game