The $-game

TL;DR

This paper introduces an extended payoff function for Minority Games that models more realistic agent behavior, revealing new market dynamics, phase transitions, and non-equilibrium phenomena in agent wealth and price movements.

Contribution

It presents a novel payoff function allowing strategies to shift between minority and majority, leading to different emergent market behaviors and phase transitions.

Findings

Emergence of a phase transition with increasing memory.

Existence of a self-sustained speculative phase.

Identification of non-equilibrium risk-return profiles.

Abstract

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In constrast 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.