Adaptive Competition, Market Efficiency, and Phase Transitions

Abstract

In many social and biological systems agents simultaneously and adaptively compete for limited resources, thereby altering their environment. We analyze a simple model that incorporates fundamental features of such systems. If the space of strategies available to the agents is small, the system is in a phase in which all information available to the agents' strategies is traded away, and agents' choices are maladaptive, resulting in a poor collective utilization of resources. For larger strategy spaces, the system is in a phase in which the agents are able to coordinate their actions to achieve a better utilization of resources. The best utilization of resources occurs at a critical point, when the dimension of the strategy space is on the order of the number of agents. [S0031-9007(99)08619-6]

Dynamical spin-glass-like behavior in an evolutionary game

“…Such a sort of an on-line learning and agaptation leads to betterthan-random performance of the system as a whole. It was found, that the properties of the game depend on the memory length M and number of players N through the scaling variable α = 2 M /N [4,6,7]. The Minoriry game was thoroughly studied both numerically and analytically [8][9][10][11][12][13][14][15][16][17][18][19] along with the study of the original bar attendance problem [20,21] and various modifications of the Minority game [22][23][24][25][26][27][28][29] An important role is attributed to the observation that the dynamics of the memorized pattern and the strategies' scores are in certain regimes decoupled [30][31][32] and that the thermal noise can ge introduced in the players' decisions [33][34][35].…”

Minority game with local interactions due to the presence of herding behavior

“…This can be easily interpreted. In the original MG [6], the low-M phase is characterized by a crowded phase where the number of strategies is small when compared to the number of agents. The presence of herding behavior only reinforces this fact.…”

“…One of the most surprising properties presented first in [6] is that if one plots the ratio σ 2 /N as a function of α = 2 M /N , one may conclude: (1) For small values of α = 2 M /N , the agents would perform worse than if they had taken purely random decisions. (2) For large values of α = 2 M /N , the agents' performance approaches the random decision.…”

Diversity of scales makes an advantage: The case of the Minority Game

“…The Minority Game (MG), introduced slightly more than a decade ago [1,2,3,4,5], gained the reputation of an "Ising model" in the field of Econophysics [6,7]. It is surely an exaggeration, as the complexity of the Ising model is many orders of magnitude higher, but nevertheless, the MG is a widely accepted framework for testing a variety of ideas in modelling socio-economic phenomena.…”