The quasi-periodicity of the minority game revisited

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 analyze the outcome dynamics of the MG, it is useful to define the MGprior, 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 MGprior.