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
Summary
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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