Mesoscopic approach to minority games in herd regime |
| |
Authors: | Karol Wawrzyniak Wojciech Wi?licki |
| |
Institution: | Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Pawinskiego 5A, PL-02-106 Warszawa, Poland National Centre for Nuclear Research, Ho?a 69, PL-00-681 Warszawa, Poland |
| |
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 |
本文献已被 ScienceDirect 等数据库收录! |
|