We study minority games in efficient regime. By incorporating the utilityfunction and aggregating agents with similar strategies we develop an effectivemesoscale notion of state of the game. Using this approach, the game can berepresented as a Markov process with substantially reduced number of stateswith explicitly computable probabilities. For any payoff, the finiteness of thenumber of states is proved. Interesting features of an extensive randomvariable, called aggregated demand, viz. its strong inhomogeneity and presenceof patterns in time, can be easily interpreted. Using Markov theory andquenched disorder approach, we can explain important macroscopiccharacteristics of the game: behavior of variance per capita and predictabilityof the aggregated demand. We prove that in case of linear payoff manyattractors in the state space are possible.
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