Stochastic Evolutionary Dynamics of Trust Games with Asymmetric Parameters

TL;DR

This paper demonstrates that stochastic evolutionary dynamics with asymmetric demographic parameters can naturally lead to high levels of trust and trustworthiness in the Trust Game without additional mechanisms, contrasting previous deterministic predictions.

Contribution

It reveals that asymmetry in population parameters can promote trust and trustworthiness through stochastic evolution, a novel insight beyond existing models.

Findings

Asymmetric parameters promote trust evolution in finite populations.

Stochastic dynamics can lead to high trust levels without extra mechanisms.

Results differ from deterministic models predicting no trust.

Abstract

Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The Trust Game has been widely used to quantitatively study trust and trustworthiness, involving a sequential exchange between an investor and a trustee. The deterministic evolutionary game theory predicts no trust and no trustworthiness whereas the behavioural experiments with the one-shot anonymous Trust Game show that people substantially trust and respond trustworthily. To explain these discrepancies, previous works often turn to additional mechanisms, which are borrowed from other games such as Prisoner's Dilemma. Although these mechanisms lead to the evolution of trust and trustworthiness to an extent, the optimal or the most common strategy often involves no trustworthiness. In this paper, we study the impact of asymmetric demographic parameters (e.g. different population sizes) on game dynamics of the Trust Game. We show that, in weak-mutation limit, stochastic evolutionary dynamics with the asymmetric parameters can lead to the evolution of high trust and high trustworthiness without any additional mechanisms in well-mixed finite populations. Even full trust and near full trustworthiness can be the most common strategy. These results are qualitatively different from those of the previous works. Our results thereby demonstrate rich evolutionary dynamics of the asymmetric Trust Game.