Theory of Networked Minority Games based on Strategy Pattern Dynamics

Abstract

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. The novel feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system's temporal evolution. We apply it to the Minority Game (MG) with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with $k$ neighbors are derived. We also use the theory to estimate the value of connectivity $p$ above which the Binary-Agent-Resource system with high resource level goes into the high-connectivity state.

24 pages, 3 figures, submitted to PRE

References in corpus (26)

• Statistical mechanics of complex networks
• Random graphs with arbitrary degree distributions and their applications
• Evolution of networks
• Specificity and stability in topology of protein networks
• The Web of Human Sexual Contacts
• Emergence of Cooperation and Organization in an Evolutionary Game
• On the Minority Game : Analytical and Numerical Studies
• Phase Transition and Symmetry Breaking in the Minority Game
• Large Stock Market Price Drawdowns Are Outliers
• A thermal model for adaptive competition in a market
• Stylized facts of financial markets and market crashes in Minority Games
• Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency
• Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact
• Relevance of memory in Minority Games
• Volatility and Agent Adaptability in a Self-Organizing Market
• Crowd-anticrowd theory of the Minority Game
• Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information
• Minority game with arbitrary cutoffs
• Deterministic Dynamics in the Minority Game
• Dynamics of the Batch Minority Game with Inhomogeneous Decision Noise
• Generalized strategies in the Minority Game
• Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''
• Dynamics of the Time Horizon Minority Game
• Statistical properties of the attendance time series in the minority game
• Enhanced Winning in a Competing Population by Random Participation
• An Investigation of Crash Avoidance in a Complex System

Cited by in corpus (8)

• Dynamics of opinion formation in a small-world network
• Effects of Contrarians in the Minority Game
• Artificial intelligence meets minority game: toward optimal resource allocation
• Theory of enhanced performance emerging in a sparsely-connected competitive population
• The Emergence of Leadership in Social Networks
• Emergence of grouping in multi-resource minority game dynamics
• Controlling herding in minority game systems
• Evolutionary dynamics in financial markets with heterogeneities in strategies and risk tolerance