In game theory, players choose actions to achieve a payoff - a measure of the attractiveness of an outcome of the game - that depends on all the players' choices. In a quantal response equilibrium, players observe payoffs disturbed by noise and thus make errors when trying to choose an optimal action in response to a given state of other players' choices. The state of all players' choices is consistent with this decision rule. This talk is about quantal response equilibria with heterogeneous agents. I consider a distribution of distributions of payoff shocks, modeled as a functional defined over distribution functions. Given heterogeneity defined by a particular functional, a representative agent would have the average quantal response function. I show existence of a representative agent as long as this average is an
admissible quantal response function. However, this representative agent does not have a representative distribution of payoff shocks, nor any IID distribution in large enough games. I consider a specific case of heterogeneous logit responders and find that a mis-specified homogenous logit parameter will have downward bias.
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