Evolution of trust in a hierarchical population with punishing investors

Trust plays an essential role in the development of human society. According to standard trust game, investor decides whether keep or transfer a certain portion initial stake trustee. In latter case, is enhanced signal value trust. The trustee then chooses how much return investor. We here distinguish two types investors and trustees who can learn from each other. While be trustworthy untrustworthy, could normal punishing one. strategy punishes both untrustworthy are reluctant control misbehaving trustees. Importantly, we assume hierarchical population where fixed. By means replicator equation approach, study $N$-player game calculate level trustworthiness. find that introduction punishment induce stable coexistence state between Furthermore, intermediate fraction better promote evolution when intensity low. For more intensive punishment, however, higher efficient elevate level. addition, reveal appropriate increase enlarge attraction domain state.