Limited trust in social network games

We consider agents in a social network competing to be selected as partners in collaborative, mutually beneficial activities. We study this through a model in which an agent i can initiate a limited number k_{i}>0 of games and selects partners from its one-hop neighborhood. Each agent can accept as many games offered by its neighbors. Each game signifies a productive joint activity, and the players attempt to maximize their individual utilities. Unsurprisingly, more trustworthy agents, as measured by the game-theoretic concept of limited-trust, are more desirable as partners. Agents learn about their neighbors' trustworthiness through interactions and their behaviors evolve in response. Empirical trials conducted on realistic social networks show that when given the option, many agents become highly trustworthy; most or all become highly trustworthy when knowledge of their neighbors' trustworthiness is based on past interactions rather than known a priori. This trustworthiness is not the result of altruism; instead, agents are intrinsically motivated to become trustworthy partners by competition. Two insights are presented: First, trustworthy behavior drives an increase in the utility of all agents, where maintaining a relatively minor level of trustworthiness may easily improve net utility by as much as 14.5%. If only one agent exhibits a small degree of trustworthiness among self-centered ones, then it can increase its personal utility by up to 25% in certain cases. Second, and counterintuitively, when partnership opportunities are abundant, agents become less trustworthy.