Modeling Strategic Beliefs with Outsmarting Belief Systems
We propose a model that formalizes the beliefs of agents in strategic environments and restricts their possible behaviors, without the typical epistemic assumptions used in game theory. We formalize the beliefs of an agent using outsmarting belief systems (OBS) and then propose the notion of belief stability to explain why some OBSs, in particular some that should occur in equilibrium, are more sensitive to perturbations than others. Also, we propose the concept of belief complexity as a criteria to restrict the possible OBSs. This allows us to formalize the notion of strategic communication as belief engineering, in which agents act in order to have other agents believe some low-complexity OBS. These concepts provide a new approach to understand why some equilibrium and non-equilibrium strategies are seen in practice, with applications to the centipede game.
KeywordsNash Equilibrium Common Knowledge Kolmogorov Complexity Epistemic Belief Nash Equilibrium Strategy
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