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SonderForschungsBereich 504 (Rationalitätskonzepte, Entscheidungsverhalten und Ökonomische Modellierung), Universität Mannheim, Germany.
Different societies establish different conventions or institutions. Sometimes these are established only for a short period and sometimes societies stick to them for a very long time. How societies establish conventions and move from one to another is explored in Professor Young's book with the help of a very abstract and yet very simple model.
His work goes back to 1993 when two articles appeared in the same issue of the prestigious journal Econometrica. These articles dealt with a new approach in evolutionary game theory. One article was by Kandori, Mailath and Rob (1993), the other by Young (1993). The approach advocated in these articles became popular among game theorists since it allows one to narrow down the set of plausible equilibria in a game while simultaneously describing the process by which a population might or might not move towards a specific equilibrium. Professor Young's book develops this approach and describes further applications.
He begins with a comparison of various simple theoretical learning models, proposing and justifying a kind of dynamics which the author calls 'adaptive play'. This is then used throughout the book. Any learning dynamics can always suffer from undesirable properties. It can be unstable or have no equilibria at all. Even if it is converging on equilibrium, there is still a danger that it could sometimes choose one equilibrium and sometimes another. Adaptive play may suffer from these problems too. The ingenious contribution of the Econometrica papers lies in their original modelling of the adaptive play process.
To make the process stable it must be slow. This is achieved in Young's model by restricting the amount of information which agents may access. Each agent remembers only a small number of past plays. Hence, when calculating a best reply each agent optimises against a different history. This prevents the learning dynamics from cycling.
To ensure that the process selects only one among several equilibria, a small amount of noise is introduced into the model. Sometimes agents make mistakes and choose random actions. If a sufficient number of players simultaneously (and coincidentally) make such a mistake, the population may move from one equilibrium position to another. The noise makes some equilibria more stable than others. Assuming that a population needs more mistakes to jump from equilibrium A to B than vice versa, then the population will spend more time close to equilibrium A. If mistakes become more and more infrequent, the system may achieve a single equilibrium where it stays almost all of the time.
The dynamics involved can be described as a perturbed Markov process. Having said that, the reader might fear that the book requires a detailed understanding of mathematics. However, it does not. Despite the fact that problems are often treated formally, Professor Young develops most concepts as he goes along and relegates lengthy proofs to the appendix. There are some formulas on most pages but the majority of the book comprises text and figures that appeal to the intuition of the reader.
In the first three chapters of his book, the author elaborates the model and the necessary concepts. Chapter four then gives a first application to small games, i.e. games played by two agents where each of them chooses between two strategies. The author finds that his learning dynamics always selects the risk dominant equilibrium in 2 x 2 co-ordination games, however this process may take a very long time before finding the equilibrium. Chapter five studies some of the assumptions in the model. The author lists examples in which more or less access to information about the past is a strategic advantage. He further relaxes the assumption that players' mistakes are completely independent of payoffs. He also studies a model with unbounded memory. Chapter six analyses the situation where players have locations and interact only with their neighbours. In terms of qualitative properties, the dynamics remain the same but they become substantially faster. Chapter seven extends the analysis to n-person games and finds that for co-ordination games and, more generally, weakly acyclic games, the perturbed adaptive play process converges to a unique equilibrium if the perturbation is small enough. For generic n persons games the process converges to a unique minimal curb configuration. Chapter eight investigates a bargaining situation, formulated as a Nash Demand Game. When both players have the same access to information about past play, the Nash solution emerges as a result of the perturbed adaptive play process. The division will be fifty-fifty if both bargaining players are drawn from the same population. Chapter nine applies this analysis to contracts. The author studies a contract selection game that can be formalised as a large co-ordination game. Adaptive play, under appropriate conditions, will select only efficient contracts, and, among these, ones with certain welfare properties. This result can be used to give a new motivation for the Kalai-Smorodinsky bargaining solution.
While Professor Young has himself contributed to much of the literature in this field, the book does refer to several contributions by other authors. It smoothly integrates foreign models translating them into the common framework in such a way that each new idea can be treated as a straightforward extension of Young's basic model. The author mixes formal analysis with provocative hints as to its possible applications, e.g. the result of the contract selection game suggests that it is only a matter of time before social inequalities between men and women are resolved.
The problems discussed in the book demonstrate that while agents may behave in a very simple way, i.e. not being aware of any strategic interaction, nevertheless a population of these agents forms a society that may solve a complex co-ordination problem with properties that are sometimes surprisingly efficient and egalitarian.
Who then should read this book? The author mentions that the book was derived from a course for graduate students. It is, hence, not a loose collection of papers but a sequence of steps where one chapter builds upon the other. It is not only interesting for graduate students but for any researcher who is interested in how evolutionary processes become more predictable if a small amount of noise is added.
KANDORI M., G. Mailath and R. Rob 1993. Learning, Mutation and Long Run Equilibria in Games. Econometrica, 61:29-56.
YOUNG H. Peyton 1993. The Evolution of Conventions. Econometrica, 61:57-84.
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© Copyright Journal of Artificial Societies and Social Simulation, 2000