Rothschild, and three most helpful referees. Very special thanks for many years of helpful insights are due to Richard Day and Luigi Ermini. Hamlet: “What a piece of work is a man! how noble in reason! how infinite in faculties!”

Abstract. The WALRAS algorithm calculates competitive equilibria via a distributed tatonnementlike process, in which agents submit single-good demand functions to market-clearing auctions. The algorithm is asynchronous and decentralized with respect to both agents and markets, making it suitable for distributed implementation. We present a formal description of this algorithm, and prove that it converges under the standard assumption of gross substitutability. We relate our results to the literature on general equilibrium stability and some more recent work on decentralized algorithms. We present some experimental results as well, particularly for cases where the assumptions required to guarantee convergence do not hold. Finally, we consider some extensions and generalizations to the WALRAS algorithm.

This article argues that the agent-based computational model permits a distinctive approach to social science for which the term “generative ” is suitable. In defending this terminology, features distinguishing the approach from both “inductive ” and “deductive ” science are given. Then, the following specific contributions to social science are discussed: The agent-based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent-based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent-based (“bottom up”) models. The agent-based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent-based modeling offers powerful new forms of hybrid theoretical-computational work; these are particularly relevant to the study of non-equilibrium systems. The agentbased approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent-based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. � 1999 John Wiley &

. This paper presents a general C++ platform for the implementation of a trade network game (TNG) that combines evolutionary game play with preferential partner selection. In the TNG, successive generations of resource constrained traders choose and refuse trade partners on the basis of continually updated expected payoffs, engage in risky trades modelled as two-person games, and evolve their trade strategies over time. The modular design of the TNG platform facilitates experimentation with alternative specifications for market structure, trade partner matching, trading, expectation formation, and trade strategy evolution. The TNG platform can be used to study the evolutionary implications of these specifications at three different levels: individual trader attributes; trade network formation; and social welfare. Key words. C++ platform, trade networks, evolutionary game, partner matching, endogenous interactions, agent-based computational economics, artificial life. 1 Introduction A...

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this paper witnessed at a seminar the horror of most colleagues when Werner Hildebrand, presenting some further development on his theory of demand (Hildebrand (1994)) provocatively suggested more or less that "preferences and choices are matters for psychiatrists and not for economists", while the task of the latter should be primarily to establish some statistical conditions under which basic propositions of economic theory -- such as downward sloping demand curves etc. -- hold in the aggregate, in presence of heterogeneous, and possibly "irrational" consumers. In a nutshell, the provocation highlights, first of all, a major divide cutting across the economic discipline -- as well as other social sciences --, namely, how seriously should one take standard utility theory (with or without its more recent refinements) and the associated "rational" theory of decision making as the foundation of a descriptive theory of demand? (Another major problem concerns the aggregate properties of diverse demand schedules, no matter how constructed: we shall come to that below.) Needless to say, the majority of the economic profession seems to take that type of microeconomic foundations of decisions very seriously indeed, entrenched as they are with deep ("anthropological") views on the nature of "rationality" and self-seeking behaviours, passed through successive generations via conventional teaching tools such as "indi#erence curves" and the like, and further justified by their purported role in bridging descriptive and normative analyses (welfare theorems, etc.). However, admittedly minority views in economics (but nearly "mainstream" in other social disciplines) claim that classic decision theory has little to o#er by way of the interpretation of what people actually do and that o...

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Introduction Since the 1980s, the deterioration of the academic job market in physics has been attracting a large number of physicists to investment banks: many of them are now working as \quants", designing sophisticated new derivative products or developing numerically intensive data analysis techniques for price and volatility forecasting. More recently, several teams of physicists have launched their own rms, oering services in the elds of nancial software design and forecasting. There exists however another set of motivations { scientic ones { which have also been prompting theoretical physicists { especially those with a background in statistical physics { to become interested in nance. Although this phenomenon may seem a bit mysterious to the outsider, we will attempt to convince the reader that it is not: nancial markets may well be considered as objects of high potential interest for researchers in statistical physics. 1.1 Motivations Statist

The paper extends the Brock-Durlauf model of interactive discrete choice, where individuals’ decisions are influenced by the decisions of others, to richer social structures. Social structure is modelled by a graph, with individuals as vertices and interaction between individuals as edges. The paper extends the mean field case to stylized interaction topologies like the Walrasian star, the cycle and the one-dimensional lattice (or path) and compares the properties of Nash equilibria when agents act on the basis of expectations over their neighbors ’ decisions versus actual knowledge of neighbors ’ decisions. It links links social interactions theory with the econometric theory of systems of simultaneous equations modelling discrete decisions. The paper obtains general results for the dynamics of adjustment towards steady states and shows that they combine spectral properties of the adjacency matrix with those associated with the nonlinearity of the reaction functions that lead to multiplicity of steady states. When all agents have the same number of neighbors the dynamics of adjustment exhibit relative persistence. Cyclical interaction is associated with endogenous and generally transient spatial oscillations that take the form of islands of conformity, but multiplicity of equilibria leads to permanent effects of initial conditions. The paper also analyzes stochastic dynamics for general interaction topologies, when agents acts with knowledge of their neighbors ’ actual decisions, which involve networked Markov chains in sample spaces of very high dimensionality.