H. Peyton Young

The Evolution of Conventions

The author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality. The game is repeated many times by different players. Each player chooses an optimal reply based on incomplete information about what other players have done in the past. Occasionally they make mistakes. When the likelihood of mistakes is very small, typically one coordination equilibrium will be played almost all of the time over the long run. This stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed Markov processes. Copyright 1993 by The Econometric Society.

Individual strategy and social structure : an evolutionary theory of institutions

Suggests a reorientation of game theory in which players are not hyper-rational and knowledge is incomplete; postulates a simple adaptive learning process; and applies this framework to the study of social and economic institutions. Discusses learning; dynamic and stochastic stability; adaptive learning in small games; variations on the learning process; local interaction; equilibrium and disequilibrium selection in general games; bargaining; and contracts. Young is Scott and Barbara Black Professor of Economics at Johns Hopkins University. Bibliography; index.

Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games

We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are “payoff-based” processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network.

Learning by trial and error

A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is conditional on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium.

How Likely is Contagion in Financial Networks

Interconnections among financial institutions create potential channels for contagion and amplification of shocks to the financial system. We estimate the extent to which interconnections increase expected losses, with minimal information about network topology, under a wide range of shock distributions. Expected losses from network effects are small without substantial heterogeneity in bank sizes and a high degree of reliance on interbank funding. They are also small unless shocks are magnified by some mechanism beyond simple spillover effects; these include bankruptcy costs, fire sales, and mark-to-market revaluations of assets. We illustrate the results with data on the European banking system.

The dynamics of social innovation

Social norms and institutions are mechanisms that facilitate coordination between individuals. A social innovation is a novel mechanism that increases the welfare of the individuals who adopt it compared with the status quo. We model the dynamics of social innovation as a coordination game played on a network. Individuals experiment with a novel strategy that would increase their payoffs provided that it is also adopted by their neighbors. The rate at which a social innovation spreads depends on three factors: the topology of the network and in particular the extent to which agents interact in small local clusters, the payoff gain of the innovation relative to the status quo, and the amount of noise in the best response process. The analysis shows that local clustering greatly enhances the speed with which social innovations spread. It also suggests that the welfare gains from innovation are more likely to occur in large jumps than in a series of small incremental improvements.

Learning efficient Nash equilibria in distributed systems

An individualʼs learning rule is completely uncoupled if it does not depend directly on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient (welfare-maximizing) pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: (i) the sum of payoffs over all agents, and (ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games.

Equilibrium Selection in Bargaining Models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.

Social norms and economic welfare1

Abstract A norm is an established and self-reinforcing pattern of behaviour: everyone wants to play their part given the expectation that everyone else will continue to play theirs. It is, in short, an equilibrium of a game. This paper surveys some of the ways in which norms structure economic life: in the definition (and division) of property, in the terms of contracts, and in the assignment of social roles. We argue that norms can evolve from the cumulative effect of many decentralized interactions by individuals who are trying to solve a coordination problem. The theory suggests circumstances under which evolutionary forces favor norms that are efficient and more or less egalitarian in their distributive implications.

Cooperation in the long-run

Abstract The long-run behavior of economic and biological processes is often dramatically altered when stochastic influences are taken into account. In fact, the smaller the noise, the more drastic the change can be. This seemingly paradoxical point is illustrated with the evolution of cooperation in repeated Prisoners Dilemma.