Achieving perfect coordination amongst agents in the co-action minority game

TL;DR

This paper analyzes a strategy for agents to achieve perfect coordination in the co-action minority game by reaching a cyclic state, providing exact timing and behavior analysis without direct communication.

Contribution

It introduces a strategy for agents to rapidly reach a cyclic state in the minority game using only public information, with an exact analysis of the convergence time.

Findings

Agents can reach a cyclic state in expected time proportional to N/ln 2.

The convergence time exhibits log-periodic oscillations with a specific amplitude.

The amplitude of oscillations is approximately 7×10^{-11}.

Abstract

We discuss the strategy that rational agents can use to maximize their expected long-term payoff in the co-action minority game. We argue that the agents will try to get into a cyclic state, where each of the $(2N +1)$ agent wins exactly $N$ times in any continuous stretch of $(2N+1)$ days. We propose and analyse a strategy for reaching such a cyclic state quickly, when any direct communication between agents is not allowed, and only the publicly available common information is the record of total number of people choosing the first restaurant in the past. We determine exactly the average time required to reach the periodic state for this strategy. We show that it varies as $(N/\ln 2) [1 + \alpha \cos (2 \pi \log_2 N)$], for large $N$, where the amplitude $\alpha$ of the leading term in the log-periodic oscillations is found be $\frac{8 \pi^2}{(\ln 2)^2} \exp{(- 2 \pi^2/\ln 2)} \approx {\color{blue}7 \times 10^{-11}}$.