We use simple learning models to track the behavior observed in experiments concerning three extensive form games with similar perfect equilibria. In only two of the games does observed behavior approach the perfect equilibrium as players gain experience. We examine a family of learning models which possess some of the robust properties of learning noted in the psychology literature. The intermediate term predictions of these models track well the observed behavior in all three games, even though the models considered differ in their very long term predictions. We argue that for predicting observed behavior the intermediate term predictions of dynamic learning models may be even more important than their asymptotic properties.

We describe a general model, `experience-weighted attraction' (EWA) learning, which includes reinforcement learning and a class of weighted fictitious play belief models as special cases. In EWA, strategies have attractions which reflect prior predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter delta which weights the strength of hypothetical reinforcement of strategies which were not chosen according to the payoff they would have yielded. When delta = 0 choice reinforcement results. When delta = 1, levels of reinforcement of strategies are proportional to expected payoffs given beliefs based on past history. Another key feature is the growth rates of attractions. The EWA model controls the growth rates by two decay parameters, phi and rho, which depreciate attractions and amount of experience separately. When phi = rho, belief-based models result; when rho = 0 choice reinforcement results. Using three data se...

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition arising naturally in models of network congestion. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to equilibrium from all initial conditions. We propose a subclass of potential games in which evolution leads to efficient play. Finally, we show that the games studied here are the limits of convergent sequences of the finite player potential games studied by Monderer and Shapley (1996).

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: This paper presents a summary overview of the fast-developing field of artificial life, stressing aspects especially relevant for the study of decentralized market economies. In particular, a recently developed trade network game (TNG) is used to illustrate how the basic artificial life paradigm might be specialized to economics. The TNG traders choose and refuse trade partners on the basis of continually updated expected utility and evolve their trade behavior over time. Analytical and simulation work is reported to indicate how the TNG is currently being used to study the evolutionary implications of alternative market structures at three different levels: individual trade behavior; trade network formation; and social welfare. 1 Introduction Artificial life (alife) is the bottom-up study of basic phenomena commonly associated with living organisms, such as self-replication, evolution, adaptation, self-organization, parasitism, competition, and cooperation. Alife complements the tr...

Experimental results on the ultimatum game show clearly that (1) large fractions of players offer a 'fair' allocation and (2) that unfair (but positive) offers are systematically rejected. We offer an explanation of this behavior using the 'indirect evolutionary approach' which is based on the assumption that players behave rationally for given preferences but that their preferences change through an evolutionary process. We prove that despite anonymous interaction a preference for punishing unfair offers is an evolutionarily successful strategy if players interact in groups. This leads players to split the resource equally almost always. However, the equal split is not due to 'true fairness' (or 'altruism') but is entirely caused by the (justified) fear that unfair offers might be rejected. Our result can be interpreted as presenting an evolutionary foundation for the emergence of social norms. JEL-- classification numbers: C73, D 83. We thank Georg Noldeke, Karl Schlag,...

We present and analyze results from the 2004 Trading Agent Competition supply chain management scenario. We identify behavioral differences between the agents that contributed to their succcess in the competition. In market for components, early procurement remained an important factor despite rule changes from the previous year. We provide additional experimental evidence to confirm that this phenomenon is still rational. Strategic interations also played an important role in procurement; one agent, FreeAgent, employed a strategy designed to block other agents ’ access to suppliers at the start of the game. The different ways agents responded to this challenge were an important factor in the outcome of the tournament. In the customer sales market, average selling prices were a decisive difference between the top agents. Our analysis shows that the economic forces of supply and demand were key factors in determining overall market prices, and that some agents were more adept at finding and exploiting advantageous market conditions. 1

In this review article, we explore several recent advances in the quantitative modeling of financiial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate mathematical models that are capable of rationalizing the empirical facts, others taking a completely different tack in rejecting rationality altogether. One of the most promising directions is to view financial markets from a biological perspective and, specifically, within an evolutionary framework in which markets, instruments, institutions, and investors interact and evolve dynamically according to the "law" of economic selection. Under this view, financial agents compete and adapt, but they do not necessarily do so in an optimal fashion. Evolutionary and ecological models of financial markets is truly a new frontier whose exploration has just begun.

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Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context of trading with market orders. Because this is so much simpler than a standard inter-temporal equilibrium model, it is possible to study multi-period markets analytically. There price dynamics have second order oscillatory terms. Value investing does not necessarily cause prices to track values. Trend following causes short term trends in prices, but also causes longer-term oscillations. When value investing and trend following are combined, even though there is little linear structure, there can be boom-bust cycles, excess and temporally correlated volatility, and fat tails in price fluctuations. The long term evolution of markets can be studied in terms of flows of money. Profits can be decomposed in terms of aggregate pairwise correlations. Under reinvestment of profits this leads to a capital allocation model that is equivalent to a standard model in population