Monotone ratio orderings are refinements of first order stochastic dominance that allow monotone comparative statics results in games of incomplete information. We develop analogous refinements for second order stochastic dominance based on the monotonicity of the cumulative probability ratio...

This paper analyses comparative statics for first price auctions and all pay auctions with independent private values. In all pay auctions, bidders with low values will respond to a stochastically higher (in the sense of likelihood ratio dominance) distribution of types by playing less...

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...