Theory of Networked Minority Games based on Strategy Pattern Dynamics

TL;DR

This paper develops a theoretical framework for networked agent-based models, focusing on strategy dynamics and ties, applied to minority games with network connections to analyze success rates and critical connectivity thresholds.

Contribution

It introduces a novel formalism emphasizing strategy pattern dynamics and ties, applied to networked minority games, providing analytical expressions for success rates and connectivity thresholds.

Findings

Derived mean success rates for agents and neighbors

Estimated critical connectivity p for high-resource systems

Analyzed strategy tie effects on system 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.