Consider a large population of individuals that are repeatedly randomly matched to play a cyclic 2x2 game such as Matching Pennies with fixed roles assigned in the game. Some learn by sampling previous play of a finite number of other individuals in the same role. We analyze population dynamics...

We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a...

The paper studies equilibrium selection in supermodular games based on a class of perfect foresight dynamics, introduced by Matsui and Matsuyama (JET 1995) and further developed by Hofbauer and Sorger (JET 1999, IGTR 2002) and Oyama (JET 2002). A normal form game is played repeatedly in a large...

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous- time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible...

We call a correspondence, defined on the set of mixed strategy proles, a generalized best reply correspondence if it (1) has a product structure, (2) is upper hemi-continuous, (3) always includes a best reply to any mixed strategy prole, and (4) is convex- and closed-valued. For each generalized...

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has (1) a product structure, is (2) upper semi-continuous, (3) always includes a best reply to any mixed strategy profile, and is (4) convex- and closed-valued. For each...

This paper provides an in-depth study of the (most) refined best reply correspondence introduced by Balkenborg, Hofbauer, and Kuzmics (2012). An example demonstrates that this correspondence can be very different from the standard best reply correspondence. In two-player games, however, the...