Phenomenology of minority games in efficient regime

We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function g(x)=\sgn (x) we explicitly represent the game as the Markov process and prove the finitness of number of states. We also demonstrate boundedness of the utility function. Using these facts we can explain all interesting observable features of the aggregated demand: appearance of strong fluctuations, their periodicity and existence of prefered levels. For another payoff, $g(x)=x$, the number of states is still finite and utility remains bounded but the number of states cannot be reduced and probabilities of states are not calculated. However, using properties of the utility and analysing the game in terms of de Bruijn graphs, we can also explain distinct peaks of demand and their frequencies

On the interplay between fluctuations and efficiency in a model economy with heterogeneous adaptive consumers

We discuss the stationary states of a model economy in which $N$ heterogeneous adaptive consumers purchase commodity bundles repeatedly from $P$ sellers. The system undergoes a transition from an inefficient to an efficient state as the number of consumers increases. In the latter phase, however, price fluctuations may be much larger than in the inefficient regime. Results from dynamical mean-field theory obtained for $N\to\infty$ compare fairly well with computer simulations.Comment: prepared for the proceedings of Fluctuations and Noise 200

Statics and dynamics of selfish interactions in distributed service systems

We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.Comment: 30 pages, 10 figure

Self-referential behaviour, overreaction and conventions in financial markets

We study a generic model for self-referential behaviour in financial markets, where agents attempt to use some (possibly fictitious) causal correlations between a certain quantitative information and the price itself. This correlation is estimated using the past history itself, and is used by a fraction of agents to devise active trading strategies. The impact of these strategies on the price modify the observed correlations. A potentially unstable feedback loop appears and destabilizes the market from an efficient behaviour. For large enough feedbacks, we find a `phase transition' beyond which non trivial correlations spontaneously set in and where the market switches between two long lived states, that we call conventions. This mechanism leads to overreaction and excess volatility, which may be considerable in the convention phase. A particularly relevant case is when the source of information is the price itself. The two conventions then correspond then to either a trend following regime or to a contrarian (mean reverting) regime. We provide some empirical evidence for the existence of these conventions in real markets, that can last for several decades.Comment: 15 pages, 12 .eps figure

Games in rigged economies

Modern economies evolved from simpler human exchanges into very convoluted systems. Today, a multitude of aspects can be regulated, tampered with, or left to chance; these are economic {\em degrees of freedom} which together shape the flow of wealth. Economic actors can exploit them, at a cost, and bend that flow in their favor. If intervention becomes widespread, microeconomic strategies of different actors can collide or resonate, building into macroeconomic effects. How viable is a `rigged' economy, and how is this viability affected by growing economic complexity and wealth? Here we capture essential elements of `rigged' economies with a toy model. Nash equilibria of payoff matrices in simple cases show how increased intervention turns economic degrees of freedom from minority into majority games through a dynamical phase. These stages are reproduced by agent-based simulations of our model, which allow us to explore scenarios out of reach for payoff matrices. Increasing economic complexity is then revealed as a mechanism that spontaneously defuses cartels or consensus situations. But excessive complexity enters abruptly into a regime of large fluctuations that threaten the system's viability. This regime results from non-competitive efforts to intervene the economy coupled across degrees of freedom, becoming unpredictable. Thus non-competitive actions can result in negative spillover due to sheer economic complexity. Simulations suggest that wealth must grow faster than linearly with economic complexity to avoid this regime and keep economies viable in the long run. Our work provides testable conclusions and phenomenological charts to guide policing of `rigged' economic systems.Comment: 9 pages and 9 figures in the main text. Appendices with 14 additional pages and 15 figure

Application of spin glass ideas in social sciences, economics and finance

Classical economics has developed an arsenal of methods, based on the idea of representative agents, to come up with precise numbers for next year's GDP, inflation and exchange rates, among (many) other things. Few, however, will disagree with the fact that the economy is a complex system, with a large number of strongly heterogeneous, interacting units of different types (firms, banks, households, public institutions) and different sizes. Now, the main issue in economics is precisely the emergent organization, cooperation and coordination of such a motley crowd of micro-units. Treating them as a unique ``representative'' firm or household clearly risks throwing the baby with the bathwater. As we have learnt from statistical physics, understanding and characterizing such emergent properties can be difficult. Because of feedback loops of different signs, heterogeneities and non-linearities, the macro-properties are often hard to anticipate. In particular, these situations generically lead to a very large number of possible equilibria, or even the lack thereof. Spin-glasses and other disordered systems give a concrete example of such difficulties. In order to tackle these complex situations, new theoretical and numerical tools have been invented in the last 50 years, including of course the replica method and replica symmetry breaking, and the cavity method, both static and dynamic. In this chapter we review the application of such ideas and methods in economics and social sciences. Of particular interest are the proliferation (and fragility) of equilibria, the analogue of satisfiability phase transitions in games and random economies, and condensation (or concentration) effects in opinion, wealth, etcComment: Contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific, 202