Cooperation in an Assortative Matching Prisoners Dilemma Experiment with Pro-Social Dummies

Chun-Lei Yang,Ching-Syang Jack Yue

doi:10.1038/s41598-019-50083-6

Abstract

Assortative matching (AM) can be theoretically an effective means to facilitate cooperation. We designed a controlled lab experiment with three treatments on multi-round prisoner’s dilemma. With matching based on weighted history (WH) as surrogate for AM, we show that adding pro-social dummies to the WH treatment may significantly improve cooperation, compared to both the random matching and the WH treatment. In society where assortative matching is effective and promoted by the underlying culture, institutional promotion of virtue role models can be interpreted as generating additional pro-social dummies, so as to move the initial state of cooperators into the basin of attraction for a highly cooperative polymorphic equilibrium.

Highlights

References[33,34] provide a thorough discussion of the common evolutionary models of assortative matching
Www.nature.com/scientificreports of a real-world sorting mechanism, it is reasonable to assume that individuals need to spend some small but positive search cost in pursuit of a proper match. The existence of such cost is exactly the very reason for the reasonable assumption of imperfect assortativity a(x) < 1. This implies that in the pure population states, the matching result must be equivalent to random matching due to zero likelihood to meet the lacking type, i.e. a(0) = a(1) = 0, where only defection prevails in the long run
34 demonstrates that non-constant Assortative matching (AM) that satisfies a(0) = a(1) = 0 exists, such as in the so-called stranger-in-the-night model, where cooperation survives in form of a locally stable mixed population equilibrium

Summary

Introduction

References[33,34] provide a thorough discussion of the common evolutionary models of assortative matching. Let s and m with 0 < m < s ≤ 1 denote the match success rates if the randomly encountered counterpart is of the same and different type, respectively, the resulting index of assortativity is a(x): = In this specific model, δ(x) = 0 has three solutions {0, xmin , xmax}, 0 < xmin < xmax < 1, where 0 and xmax are locally stable equilibria with respective basins of attraction (0, xmin) and While pure defection is the only stable population equilibrium in RM, AM potentially may admit additional stable equilibria with a higher share of cooperators, depending on the specifics of the mechanism In the latter case, the initial state of population is crucial at determining whether the dynamics converges to the bad pure defectors equilibrium of x* = 0 or some better ones such as x* = xmax. This, opens up the gate for culture, social conventions or state actions to be shaped and constructed in a way so as to positively affect either the effectiveness of AM mechanism, for example by increasing s or decreasing m in the strangers-in-the-night model above; or the initial state of aggregate pro-social propensity, for the long-term proliferation of cooperation

Objectives

Methods

Results