Abstract

We introduce consistency of beliefs in the space of hierarchies of conditional beliefs (Battigalli and Siniscalchi) and use it to provide epistemic conditions for equilibria in finite multi-stage games with observed actions.

Highlights

  • Battigalli and Sinischalchi [1] constructed the space of hierarchies of conditional beliefs and used it to provide epistemic foundations for solution concepts in dynamic games

  • We show that consistency of beliefs and extensive form rationality provide epistemic foundations for correlated subgame perfect equilibrium, and these two conditions, plus a notion of constancy of conjectures, provide epistemic foundations for subgame perfect equilibrium (SPE)

  • For simplicity we deal only with finite multi-stage games with with observed actions, so sequential rationality is well captured by subgame perfection; the analysis can be generalized to include incomplete information and/or more complex information structures, where sequential equilibrium is the relevant equilibrium concept to capture sequential rationality

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Summary

Introduction

Battigalli and Sinischalchi [1] constructed the space of hierarchies of conditional beliefs and used it to provide epistemic foundations for solution concepts in dynamic games. We provide an analogous analysis for multi-stage games with observable actions, in the corresponding space of hierarchies of conditional beliefs. Let Si (h) be player i’s set of strategies consistent with history h ∈ H.

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