Abstract
We endogenize the precision parameter lambda of logit quantal response equilibrium (LQRE) (McKelvey and Palfrey, 1995). In the first stage of an endogenous quantal response equilibrium (EQRE), each player chooses precision optimally subject to costs, given correct beliefs over other players’ (second-stage) actions. In the second stage, players’ actions form a heterogeneous LQRE given the first-stage choices of precision. EQRE satisfies a modified version of the regularity axioms (Goeree et al., 2005), nests LQRE as a limiting case for a sequence of cost functions, and admits analogues of classic results for LQRE such as those for equilibrium selection. For generalized matching pennies, the sets of EQRE and LQRE (i.e. indexed by their respective parameters) are curves in the unit square that cross at finite points that we give explicitly, and hence the models’ predictions are generically distinct. We apply EQRE to experimental data.
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