Strategy updating rules and strategy distributions in dynamical multiagent systems

TL;DR

This paper investigates how strategy updating rules influence the dynamics and distribution of strategies in a multiagent evolutionary game, revealing oscillatory behaviors and the advantage of a coin-tossing strategy.

Contribution

It introduces a specific strategy updating rule and analyzes its effects on strategy distributions and oscillations in a multiagent system.

Findings

Strategy distribution depends on prize-to-fine ratio, update step size, and boundary conditions.

Oscillations in strategy frequencies are driven by these parameters.

The coin-tossing strategy ($p=0.5$) offers the best long-term survival chances.

Abstract

In the evolutionary version of the minority game, agents update their strategies (gene-value $p$) in order to improve their performance. Motivated by recent intriguing results obtained for prize-to-fine ratios which are smaller than unity, we explore the system's dynamics with a strategy updating rule of the form $p \to p \pm \delta p$ ($0 \leq p \leq 1$). We find that the strategy distribution depends strongly on the values of the prize-to-fine ratio $R$, the length scale $\delta p$, and the type of boundary condition used. We show that these parameters determine the amplitude and frequency of the the temporal oscillations observed in the gene space. These regular oscillations are shown to be the main factor which determines the strategy distribution of the population. In addition, we find that agents characterized by $p={1 \over 2}$ (a coin-tossing strategy) have the best chances of survival at asymptotically long times, regardless of the value of $\delta p$ and the boundary conditions used.