Diffusion and localization in the Minority Game
Diffusion and localization in the Minority Game
Diffusion and localization in the Minority Game
The Minority Game is a model for adaptive competition for a scarce resource, related to the famous “El Farol Bar problem”. A group of players should decide individually each night whether too go to the bar or stay home, given that it’s a fun place, but only if it’s not crowded. Thus, the the right choice is to go only if less than half of the other players go, otherwise stay home. The information at the players’ disposal is the attendance for the last few nights. “If it was crowded last night, but not the night before, will it be crowded or not tonight?” This sort of question can olso be related to a market for some resource, relating demand to price.
The Minority Game puts this in a precise mathematical framework, where an agent (player) has two strategies for what decision to take (go or stay home, corresponding to -1 and 1). The agent uses at each time step the strategy that has the highest score corresponding to having been most successful historically.
We have studied some aspects of this problem, namely how the relative score of the strategies are distributed statistically. It turns out that the relative score can be described by a random walk on an integer chain. The probability distribution can be solved for either in terms of diffusion with a drift or exponential localization. We derive a quantitative statistical model that we compare to direct numerical simulations of the game.
Monday 12 October 2015