Evolutionary Rotation in Switching Incentive Zero-Sum Games

TL;DR

This paper analyzes how social evolutionary rotation in population strategies changes with incentive parameters in a laboratory setting, using experimental data and dynamical models to interpret the observed phenomena.

Contribution

It introduces a quantitative analysis of social evolutionary rotation changes in switching incentive zero-sum games using eigenvalues and rank tests, providing new insights into evolutionary game theory.

Findings

Rotation direction and strength change with incentive switching

Eigenvalue analysis captures rotation dynamics

Relative response coefficients persist across game switches

Abstract

In a laboratory experiment, round by round, individual interactions should lead to the social evolutionary rotation in population strategy state space. Successive switching the incentive parameter should lead to successive change of the rotation ---- both of its direction and its strength. In data from a switching payoff matrix experiment of extended 2x2 games (Binmore, Swierzbinski and Proulx, 2001 [1]), we find the changing of the social evolutionary rotation can be distinguished quantitatively. The evolutionary rotation can be captured by evolutionary dynamics. With eigenvalue from the Jacobian of a constrained replicator dynamics model, an interpretation for observed rotation strength is given. In addition, equality-of-populations rank test shows that relative response coefficient of a group could persist cross the switching parameter games. The data has successively been used to support Von Neumann's minimax theory. Using the old data, with observed evolutionary rotation, this report provides a new insight into evolutionary game theory and experimental social dynamics.