Evolution of trust in a hierarchical population with punishing investors
Ketian Sun, Yang Liu, Xiaojie Chen, Attila Szolnoki

TL;DR
This paper models the evolution of trust in a hierarchical population using a trust game with punishing investors, revealing how punishment influences trust and trustworthiness dynamics.
Contribution
It introduces a hierarchical population model with punishing investors and analyzes the impact of punishment on trust evolution using replicator dynamics.
Findings
Punishment can stabilize trust and trustworthiness coexistence.
Intermediate investor fractions promote trust at low punishment levels.
Higher punishment intensity requires a larger investor fraction to sustain trust.
Abstract
Trust plays an essential role in the development of human society. According to the standard trust game, an investor decides whether to keep or transfer a certain portion of initial stake to a trustee. In the latter case, the stake is enhanced to signal the value of trust. The trustee then chooses how much to return to the investor. We here distinguish two types of investors and two types of trustees who can learn from each other. While a trustee can be trustworthy or untrustworthy, an investor could be normal or punishing one. The latter strategy punishes both untrustworthy trustees and normal investors who are reluctant to control misbehaving trustees. Importantly, we assume a hierarchical population where the portion of investors and trustees is fixed. By means of replicator equation approach, we study the -player trust game and calculate the level of trust and trustworthiness. We…
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