Damien Challet

EMERGENCE OF COOPERATION AND ORGANIZATION IN AN EVOLUTIONARY GAME

A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players use a finite set of ad hoc strategies to make their decision, based on the past record. The analysing power is limited and can adapt when necessary. Interesting cooperation and competition patterns of the society seem to arise and to be responsive to the payoff function.

On the minority game: Analytical and numerical studies

We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of σ2/N in the N⪡2M region. The ability of the players to learn a given payoff is also analyzed, and we show that the Darwinian evolution process tends to a self-organized state, in particular, the lifetime distribution is a power-law with exponent −2. Furthermore, we study the influence of identical players on their gain and on the systems performance. Finally, we show that large brains always take advantage of small brains.

Statistical Mechanics of systems with heterogeneous agents:Minority Games

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytical findings.

Modeling Market Mechanism with Minority Game

Using the minority game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow: producers feed in the information whereas speculators make it away. How well each agent fares in the common game depends on the market conditions, as well as their sophistication. Sometimes there is much to gain with little effort, sometimes great effort virtually brings no more incremental gain. Market impact is also shown to play an important role, a strategy should be judged when it is actually used in play for its quality. Though the minority game is an extremely simplified market model, it allows to ask, analyze and answer many questions which arise in real markets.

Analyzing and modeling 1+1d markets

We report on a statistical analysis of the Island ECN (NASDAQ) order book. We determine the static and dynamic properties of this system, and then analyze them from a physicists viewpoint using an equivalent particle system obtained by treating orders as massive particles and price as position. We identify the fundamental dynamical processes, test existing particles models of such markets against our findings, and introduce a new model of limit order markets.

From Minority Games to Real Markets

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behaviour close to what is observed in real markets. In particular we find that (i) fat tails and clustered volatility arise at the phase transition point and that (ii) the crossover to random walk behaviour of prices is a finite-size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real markets, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different species of traders. This clarifies the nature of the interaction and the particular role played by the various populations.

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable — which plays a role similar to price — whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the “thermodynamic” limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even “infinitesimally” for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a “price taker” behavior if agents account for their market impact.

Statistical mechanics of competitive resource allocation using agent-based models

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and others) and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model of competitive resource allocation made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines. (This abstract was borrowed from another version of this item.)

Relevance of memory in minority games

By considering diffusion on De Bruijn graphs, we study in detail the dynamics of the histories in the minority game, a model of competition between adaptative agents. Such graphs describe the structure of the temporal evolution of M bit strings, each node standing for a given string, i.e., a history in the minority game. We show that the frequency of visit of each history is not given by 1/2(M) in the limit of large M when the transition probabilities are biased. Consequently, all quantities of the model do significantly depend on whether the histories are real or uniformly and randomly sampled. We expose a self-consistent theory of the case of real histories, which turns out to be in very good agreement with numerical simulations.

Criticality and market efficiency in a simple realistic model of the stock market.

We discuss a simple model based on the minority game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit. Stylized facts arise only close to a line of critical points with nontrivial properties, marking the transition to an unpredictable market. We show that the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets, where stylized facts and verge of unpredictability are intimately related aspects of the same critical systems.