Trust and reciprocation of it form the foundation of economic, social and other interactions. While the Trust Game is widely used to study these concepts for interactions between two players, often alternating different roles (i.e., investor and trustee), its extensions to multi-player scenarios have been restricted to instances where players assume only one role. We propose a symmetric N-player Trust Game, in which players alternate between two roles, and the payoff of the player is defined as the average across their two roles and drives the evolutionary game dynamics. We find that prosocial strategies are harder to evolve with the present symmetric N-player Trust Game than with the Public Goods Game, which is well studied. In particular, trust fails to evolve regardless of payoff function nonlinearity in well-mixed populations in the case of the symmetric N-player trust game. In structured populations, nonlinear payoffs can have strong impacts on the evolution of trust. The same nonlinearity can yield substantially different outcomes, depending on the nature of the underlying network. Our results highlight the importance of considering both payoff structures and network topologies in understanding the emergence and maintenance of prosocial behaviours.

翻译：信任及其互惠构成了经济、社会及其他互动的基础。虽然信任博弈被广泛用于研究两个参与者之间的这些概念，通常交替扮演不同角色（即投资者与受托人），但其向多参与者场景的扩展仅限于参与者仅承担单一角色的情况。我们提出了一种对称的N人信任博弈，其中参与者在两种角色间交替，其收益定义为两种角色收益的平均值，并驱动演化博弈动力学。我们发现，与已有深入研究的公共物品博弈相比，在当前的对称N人信任博弈中，亲社会策略更难演化。具体而言，在混合良好群体中，无论收益函数的非线性如何，信任在对称N人信任博弈中均无法演化。在结构化群体中，非线性收益能对信任的演化产生强烈影响。相同的非线性可能产生显著不同的结果，这取决于底层网络的性质。我们的结果突显了在理解亲社会行为的涌现与维持时，同时考虑收益结构与网络拓扑的重要性。