Larry Samuelson Publications

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent’s signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents’ observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily agents. Does it follow that the agents will commonly learn its value, i.e., that the true value of the parameter will become (approximate) common-knowledge? We show that the answer is affirmative when each agent’s signal space is finite and show by example that common learning can fail when observations come from a countably infinite signal space.

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily agents. Does it follow that the agents will commonly learn its value, i.e., that the true value of the parameter will become (approximate) common-knowledge? We show that the answer is affirmative when each agent’s signal space is finite and show by example that common learning can fail when observations come from a countably infinite signal space.

Keywords: Common learning, Common belief, Private signals, Private beliefs

JEL Classification: D82, D83

Evolutionary game theory is one of the most active and rapidly growing areas of research in economics. Unlike traditional game theory models, which assume that all players are fully rational and have complete knowledge of details of the game, evolutionary models assume that people choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. In games that are repeated many times, low-payoff strategies tend to be weeded out, and an equilibrium may emerge.

arry Samuelson has been one of the main contributors to the evolutionary game theory literature. In Evolutionary Games and Equilibrium Selection, he examines the interplay between evolutionary game theory and the equilibrium selection problem in noncooperative games. After providing an overview of the basic issues of game theory and a presentation of the basic models, the book addresses evolutionary stability, the dynamics of sample paths, the ultimatum game, drift, noise, backward and forward induction, and strict Nash equilibria.