What is Econophysics?
Collective phenomena in economics, social sciences and ecology are very attractive for statistical physicists, especially in view of the empirical abundance of non-trivial fluctuation patterns and statistical regularities — think of returns in financial markets or of allometric scaling in ecosystems — which pose intriguing theoretical challenges. On an abstract level, the problems at stake are indeed not too different from, say, understanding how spontaneous magnetization may arise in a magnetic system, since what one wants in both cases is to understand how the effects of interactions at the microscopic scale can build up to the macroscopic scale. Clearly, ecologies or financial markets are quite more complex systems than magnets, being composed of units which themselves follow complex (and far from understood) behavioral rules. Still, in many cases it may be reasonable to assume that the collective behavior of a crowd of individuals presents aspects of a purely statistical nature which might be appreciated already in highly stylized models of such systems. This is ultimately the rationale for applying statistical mechanics to such problems. Economic systems are formed by agents who typically respond to incentives and act in a selfish way. This is usually modeled assuming that individuals strive to maximize their private utility functions, with no regard for social welfare. Not only agents might have conflicting goals, as their utility functions will in general be different, but their selfish behavior may lead to globally inefficient outcomes — e.g. to a coordination failure or to a lack of cooperation. Such outcomes, called Nash equilibria in Game Theory, are in general different from socially optimal states where the total utility is maximized. Hence, generally, in a system of interacting agents there is no global energy function to be minimized. This feature is reflected in the fact that their dynamics, in general, violates detailed balance. Another important difference between the dynamics of a physical system, such as a magnetic material, and that of an economic system is that, while in the former spins at a particular time depend at most on the past states of the system, in the latter the agents’ choices also depend on the expectations they harbor about the future states. This suggests that the collective dynamics may have a non-causal component. In many cases, however, it is reasonable to assume that agents are boundedly rational or `inductive’, i.e. that their behavior as well as their expectations adjust as a result of experience. We shall concentrate our analysis to these cases of adaptive agents following a learning dynamics. In a nutshell, the models we consider address the decentralized allocation of scarce resources by N heterogeneous selfish agents subject to public and/or private information. The word `allocation’ is to be intended here in a broad sense that includes the exchange of resources (for example, commodities) among agents, the production of resources by means of other resources and the consumption of resources. Agents take decisions on the basis of some type of\ information aiming at some pre-determined goals, like maximizing a certain utility function, and are to various degrees adaptive entities. We shall consider cases in which they are perfect optimizers (or `deductive’) as well as cases in which their decision-making is governed by a learning process (`inductive’). Heterogeneity may reside in a number of factors, like the agents’ initial endowments, their Nash equilibria in Game Theory, are in general different from socially optimal states where the total utility is maximized. Hence, generally, in a system of interacting agents there is no global energy function to be minimized. This feature is reflected in the fact that their dynamics, in general, violates detailed balance. Another important difference between the dynamics of a physical system, such as a magnetic material, and that of an economic system is that, while in the former spins at a particular time depend at most on the past states of the system, in the latter the agents’ choices also depend on the expectations they harbor about the future states. This suggests that the collective dynamics may have a non-causal component. In many cases, however, it is reasonable to assume that agents are boundedly rational or `inductive’, i.e. that their behavior as well as their expectations adjust as a result of experience. We shall concentrate our analysis to these cases of adaptive agents following a learning dynamics. In a nutshell, the models we consider address the decentralized allocation of scarce resources by N heterogeneous selfish agents subject to public and/or private information. The word `allocation’ is to be intended here in a broad sense that includes the exchange of resources (for example, commodities) among agents, the production of resources by means of other resources and the consumption of resources. Agents take decisions on the basis of some type of information aiming at some pre-determined goals, like maximizing a certain utility function, and are to various degrees adaptive entities. We shall consider cases in which they are perfect optimizers (or `deductive’) as well as cases in which their decision-making is governed by a learning process (`inductive’). Heterogeneity may reside in a number of factors, like the agents’ initial endowments, their learning abilities or in how differently they react to the receipt of certain information patterns. In general, the allocation is a stochastic dynamical process, where the noise may be present in both the information sources and the agent’s learning process. We shall mostly be concerned with the steady-state properties and, more than on individual performances, we shall focus on the resulting distribution of resource loads and in particular on
- how evenly are resources exploited on average (i.e. whether the allocation process leads typically to over- or under-exploitation of some resources)
- the fluctuations of resource loads (i.e. how large the deviations from the average can be) It is implicitly assumed that optimal allocations are those where resources are exploited as evenly as possible and where fluctuations are minimal. In an economic setting, this corresponds to allocations with minimal waste whereas in financial markets, optimality implies information being correctly incorporated into prices with minimal volatility.
Contacts:
Andrea De Martino is now at the Sapienza unit of CNR-IPCF
Irene Giardina
Guido Caldarelli