By far the most common specification for QRE is logit equilibrium (LQRE). In a logit equilibrium, player's strategies are chosen according to the probability distribution:
is the probability of player i choosing strategy j. is the expected utility to player i of choosing strategy j given other players are playing according to the probability distribution .
Of particular interest in the logit model is the non-negative parameter λ (sometimes written as 1/μ). λ can be thought of as the rationality parameter. As λ→0, players become "completely irrational", and play each strategy with equal probability. As λ→∞, players become "perfectly rational", and play approaches a Nash equilibrium.
Read more about this topic: Quantal Response Equilibrium
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