Mesoscopic approach to minority games in herd regime

Karol Wawrzyniak and Wojciech Wiślicki

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 5, 2056-2082

Abstract: We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of the state of the game. Using this approach, the game can be represented as a Markov process with substantially reduced number of states with explicitly computable probabilities. For any payoff, the finiteness of the number of states is proved. Interesting features of an extensive random variable, called aggregated demand, viz. its strong inhomogeneity and presence of patterns in time, can be easily interpreted. Using Markov theory and quenched disorder approach, we can explain important macroscopic characteristics of the game: behavior of variance per capita and predictability of the aggregated demand. We prove that in the case of linear payoff many attractors in the state space are possible.

Keywords: Minority game; Adaptive system; Markov process; Mesoscopic scale (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:5:p:2056-2082

DOI: 10.1016/j.physa.2011.11.041

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