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
Famous quotes containing the word equilibrium:
“There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.”
—Ralph Waldo Emerson (1803–1882)