Wojciech Jamroga, Clausthal University of Technology

Juergen Dix, Clausthal University of Technology

**Abstract:**

This article is about defining a suitable logic for expressing
classical game theoretical notions. We define an extension of
alternating-time temporal logic (ATL) that enables us to express
various rationality assumptions of intelligent agents. Our proposal,
the logic ATLP (*ATL with plausibility*) allows us to specify
sets of rational strategy profiles in the object language, and
reason about agents' play if only these strategy profiles were
allowed. For example, we may assume the agents to play only Nash
equilibria, Pareto-optimal profiles or undominated strategies, and
ask about the resulting behaviour (and outcomes) under such an
assumption. The logic also gives rise to generalized versions of
classical solution concepts through characterizing patterns of
payoffs by suitably parameterized formulae of ATLP. We investigate
the complexity of model checking ATLP for several classes of
formulae: It ranges from Delta3 to PSPACE in the general case
and from Delta3 to Delta4 for the most interesting
subclasses, and roughly corresponds to solving extensive games with
imperfect information.

**Keywords:** game theory, modal and temporal logic, reasoning about
agents, rationality.

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Computational Intelligence Group @ Clausthal University of Technology | Last modified 2010-01-08 |