We study the structure of the underlying network of connections in the Minority Game. There is not an explicit interaction among the agents, but they interact via global magnitudes of the model and mainly through their strategies. We define a link between two agents by quantifying the similarity among their strategies, and analyze the structure of the resulting underlying complex networks as a function of the number of agents in the game and the value of the agents' memory, in games with two strategies per player. We characterize the different phases of this system with networks with different properties, for this link definition. Thus, the Minority Game phase characterized by the presence of crowds can be identified with a small world network, while the phase with the same results as a random decision game as a random network. Finally, we use the Full Strategy Minority Game model, to explicitly calculate some properties of its networks, such as the degree distribution, for the same link definition, and to estimate, from them, the properties of the networks of the Minority Game, obtaining a very good agreement with its measured properties.
In the Minority Game (MG), an odd number of heterogeneous and adaptive agents choose between two alternatives and those who end up on the minority side win. When the information available to the agents to make their choice is the identity of the minority side for the past $m$ days, it is well-known that emergent coordination among the agents is maximum when $m \sim \log_2(N)$. The optimal memory-length thus increases with the system size. In this work, we show that, in MG when the information available to the agents to make their choice is the strength of the minority side for the past $m$ day…
Resource allocation systems provide the fundamental support for the normal functioning and well being of the modern society, and can be modeled as minority games. A ubiquitous dynamical phenomenon is the emergence of herding, where a vast majority of the users concentrate on a small number of resources, leading to a low efficiency in resource allocation. To devise strategies to prevent herding is thus of high interest. Previous works focused on control strategies that rely on external interventions, such as pinning control where a fraction of users are forced to choose a certain action. Is it …
We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase ($α\equiv P/N\gtrsim 1$) of the basic Minority Game using sign-payoff, with $N$ agents holding two strategies over $P$ histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent's strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score $x\in\mathbb{Z}$ of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities,…
Active-Absorbing Phase Transitions in the Parallel Minority Game
School of Computational & Integrative Sciences, Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学计算与整合科学学院）；Department of Physics, SRM University - AP（安得拉邦SRM大学物理系）
We introduce a version of the Minority Game where the total number of available choices is $D>2$, but the agents only have two available choices to switch. For all agents at an instant in any given choice, therefore, the other choice is distributed between the remaining $D-1$ options. This brings in the added complexity in reaching a state with the maximum resource utilization, in the sense that the game is essentially a set of MG that are coupled and played in parallel. We show that a stochastic strategy, used in the MG, works well here too. We discuss the limits in which the model reduces to…
We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the majority, while the rest want to make the minority choice. This resembles opinion spreading with "contrarian" agents, but has the game theoretic aspect that agents try to optimize their own situation in ways that are incompatible with the common good. When this fraction is less than 1/2, the population can efficiently self-organize to a state where agents ge…
