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Noisy Directional Learning and the Logit Equilibrium
Author(s) -
Anderson Simon P.,
Goeree Jacob K.,
Holt Charles A.
Publication year - 2004
Publication title -
the scandinavian journal of economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.725
H-Index - 64
eISSN - 1467-9442
pISSN - 0347-0520
DOI - 10.1111/j.0347-0520.2004.00378.x
Subject(s) - generalization , logit , mathematical economics , stochastic game , economics , nash equilibrium , class (philosophy) , econometrics , mathematics , computer science , mathematical analysis , artificial intelligence
We specify a dynamic model in which agents adjust their decisions toward higher payoffs, subject to normal error. This process generates a probability distribution of players’ decisions that evolves over time according to the Fokker–Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studied games. In equilibrium, the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs. This “logit equilibrium” forms a stochastic generalization of the Nash equilibrium and provides a possible explanation of anomalous laboratory data.