Course 9 Minority games

Abstract

This chapter explains how to derive the Minority Game (MG) and how to solve it starting from the intractable E1 Farol bar problem, and finally illustrates the universality of minority mechanisms by building more and more complex and still exactly solvable models. MG is the prototype model of global competition between adaptive heterogeneous agents. The mathematical equivalence between agent heterogeneity and physical disorder makes it exactly solvable. The history of the MG is a nice example of how to simplify a complex model first to a workable model which still requires sophisticated analytical methods and long calculus, and then to a very simple Markovian model to which standard stochastic calculus applies. The chapter provides an overview of the historical motivations, leading to the introduction of the model, the properties of the model and its solution, and will end with discussing its relevance in modeling. The most relevant concept in game theory for this chapter is that of Nash equilibrium (NE). MG combines two important features: its mechanism makes it the prototype model of competition, and it is exactly solvable. Even more, any system where the agents learn collectively a resource level be it explicit or implicit contains a minority mechanism.