Variable Payoffs in the Minority Game

Robert Savit (), Yi Li () and Adrian Vandeemen ()
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Robert Savit: Physics Department and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
Yi Li: Physics Department and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
Adrian Vandeemen: University of Nijmegen, Nijmegen, Netherlands

Advances in Complex Systems (ACS), 2000, vol. 03, issue 01n04, 271-281

Abstract: In the standard minority game, each agent in the minority group receives the same payoff regardless of the size of the minority group. Of great interest for real social and biological systems are cases in which the payoffs to members of the minority group depend on the size of the minority group. This latter includes the fixed sum game. We find, remarkably, that the phase structure and general scaling behavior of the standard minority game persists when the payoff function depends on the size of the minority group. There is still a phase transition at the same value ofz, the ratio of the dimension of the strategy space to the number of agents playing the game. We explain the persistence of the phase structure and argue that it is due to the absence of temporal cooperation in the dynamics of the minority game. We also discuss the behavior of average agent wealth and the wealth distribution in these variable payoff games.

Date: 2000
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DOI: 10.1142/S0219525900000200

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