The quasi-periodicity of the minority game revisited

Abstract

We analyze two well-known related aspects regarding the sequence of minority sides from the Minority Game (MG) in its symmetric phase: period-two dynamics and quasi-periodic behavior. We also study the sequence of minority sides in a general way within a graph-theoretical framework. In order to analyse the outcome dynamics of the MG, it is useful to define the MG prior , namely an MG with a new choosing rule of the strategy to play, which takes into account both prior preferences and game information. In this way, each time an agent is undecided because two of her best strategies predict different choices while being equally successful so far, she selects her a priori favorite strategy to play, instead of performing a random tie-break as in the MG. This new choosing rule leaves the generic behavior of the model unaffected and simplifies the game analysis. Furthermore, interesting properties arise which are only partially present in the MG, like the quasi-periodic behavior of the sequence of minority sides, which turns out to be periodic for the MG prior .

Diffusion and Localization of Relative Strategy Scores in The Minority Game

“…The game is controlled by the parameter α = P/N , where P = 2 m is the number of distinct histories that agents take into account, which tunes the system through a phase transition (for N → ∞) at a critical value α c = 0.3374.... In the symmetric (or crowded) phase, α < α c , the game is quasi-periodic with period 2P where a given history gives alternately one or the other of the outcomes for minority group [3,18]. A somewhat oversimplified characterization of the dynamics is that the information about the last winning minority group for a given history gives a crowding effect [19] where many agents want to repeat the last winning outcome which then counterproductively instead puts them in the majority group.…”