The Minority Game: evolution of strategy scores

Abstract

Abstract The Minority Game is an agent based model that simulates competition for a scarce resource, situations in which two options are available to the agents at every time step and the winner option is the minority one. It was originally developed as a model for financial markets, although it has been applied in different fields, like genetics and transportation problems (choose less frequented road, lane, etc). This model has been studied in detail in the last fifteen years, with more than a thousand papers published on the topic, covering a wide range of analytical techniques, improvements and modifications, and in the recent years, large integration with different market mechanisms that reproduce the stylized facts of real markets. We will first explain the model in detail and state its most important features, such as the existence of a phase transition that divides the game in two possible different regimes. We are interested in the so-called dilute regime, and we will describe in detail its particularities, which inspired our own work: it presents two different kinds of agents with very different behaviours, all depending on the random initial conditions. We will focus on the analysis of the strategy scores, which are the key factor determining which category an agent lies in. We use a probability theory to devise an analytical model for the so-called coin-toss limit inside this regime, and a phenomenological model that explains the behaviour of the strategy scores in the whole regime. In the last chapter, we will introduce a similar game in which we constrain this mentioned strategy scores, yielding simplified dynamics with similar outcomes: the dynamics are trapped in typically small cycles in the state space, different cycles being present and depending on the initial conditions of the game.