Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning. Copyright The Econometric Society 2002.

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning.

If individuals care about their status, defined as their rank in the distribution of consumption of one “positional” good, then the consumer's problem is strategic as her utility depends on the consumption choices of others. In the symmetric Nash equilibrium, each individual spends an inefficiently high amount on the status good. Using techniques from auction theory, we analyze the effects of exogenous changes in the distribution of income. In a richer society, almost all individuals spend more on conspicuous consumption, and individual utility is lower at each income level. In a more equal society, the poor are worse off.

We study the efficiency of premarital investments when parents care about their child’s marriage prospects, in a large frictionless marriage market with nontransferable utility. Stochastic returns to investment ensure that equilibrium is unique. We find that, generically, investments exceed the Pareto-efficient level, unless the sexes are symmetric in all respects. Girls will invest more than boys if their quality shocks are less variable than shocks for boys or if they are the abundant sex. The unique equilibrium in our continuum agent model is the limit of the equilibria of finite models, as the number of agents tends to infinity.

We report a continuous-time experiment studying the Burdett-Judd model, whose unique Nash equilibrium (NE) features dispersed prices. Adaptive dynamics predict that the NE is stable for one of our parameter sets and unstable for another. The empirical price distribution is close to the NE distribution for the stable parameter set, but for the unstable parameter set it skews toward higher prices in its NE support interval. We offer an empirical definition of price cycles in terms of changes over time in robust measures of central tendency and dispersion, by which the data exhibit persistent cycles in both treatments but larger cycles for the unstable parameters. Results are roughly similar for professional and student sellers and for limited-information treatments.