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Rational Teams : Logical Aspects of Multi-Agent Systems

Aldewereld H., Van der Hoek W., Meyer J.-J.

Fundamenta Informaticae

2004

Vol. 63, nr 2,3

159--183

This paper describes a possible extension to the logical framework KARO to make it able to handle multiple agents. The KARO framework, which was initially developed by van der Hoek, van Linder and Meyer, makes use of epistemic and dynamic logics to express rational agents. These agents are capable of reasoning about their own actions and, somewhat limited, about the actions of other agents. This paper intends to extend the KARO system such that one is also able to reason about cooperation between agents.

A Modal Characterization of Nash Equilibrium

Harrenstein P., Van der Hoek W., Meyer J.-J., Witteveen C.

Fundamenta Informaticae

2003

Vol. 57, nr 2-4

281--321

Multi-agent systems comprise entities whose individual decision making behavior may depend on one another's. Game-theory provides apposite concepts to reason in a mathematically precise fashion about such interactive and interdependent situations. This paper concerns a logical analysis of the game-theoretical notions of Nash equilibrium and its subgame perfect variety as they apply to a particular class of extensive games of perfect information. Extensive games are defined as a special type of labelled graph and we argue that modal languages can be employed in their description. We propose a logic for a multi-modal language and prove its completeness with respect to a class of frames that correspond with a particular class of extensive games. In this multi-modal language (subgame perfect) Nash equilibria can be characterized. Finally, we show how this approach can formally be refined by using Propositional Dynamic Logic ( PDL), though we leave completeness as an open question.