Eur. Phys. J. B 31, 141-145 (2003)
https://doi.org/10.1140/epjb/e2003-00017-7

The $-game

¹ UFR de Sciences Économiques, Gestion, Mathématiques et Informatique (CNRS UMR7536) , and Université Paris X-Nanterre, 92001 Nanterre Cedex, France
² Laboratoire de Physique de la Matière Condensée (CNRS UMR6622) and Université de Nice-Sophia Antipolis, 06108 Nice Cedex 2, France
³ Institute of Geophysics and Planetary Physics and Department of Earth and Space Science University of California, Los Angeles, California 90095, USA

Corresponding author: ^a sornette@unice.fr

Received: 5 June 2002
Revised: 21 November 2002
Published online: 27 January 2003

Abstract

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In contrast with previous MG, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. The emergent properties of the price dynamics and of the wealth of agents are strikingly different from those found in MG. As the memory of agents is increased, we find a phase transition between a self-sustained speculative phase in which a “stubborn majority” of agents effectively collaborate to arbitrage a market-maker for their mutual benefit and a phase where the market-maker always arbitrages the agents. A subset of agents exhibit a sustained non-equilibrium risk-return profile.