Limited-Trust in Social Network Games
Timothy Murray, Jugal Garg, Rakesh Nagi
TL;DR
The paper studies partner selection in social networks under Limited-Trust Stackelberg Equilibrium (LTSE), where each agent’s trust level $\delta_i$ governs willingness to incur costs to improve the net utility of all players. It develops a networked LTSE framework with leader–follower interactions confined to $1$- and $2$-hop neighborhoods, introduces learning mechanisms for unknown neighborhood trust levels, and analyzes a metagame where agents can adjust $\delta$ to maximize their utilities, proving the existence of mixed Nash equilibria. Through numerical experiments on real networks, it shows that many agents evolve toward high trust levels, increasing per-agent utility by about 20–25% on average, and that the density of partnership opportunities can paradoxically reduce trust in some regimes. Overall, the work provides both theoretical and empirical insights into how trust evolves endogenously in networked interactions and how selective trust can boost collective outcomes, with implications for designing trust-aware multi-agent systems.
Abstract
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 the ideal partners from its one-hop neighborhood. On the flip side it can accept as many games offered from its neighbors. Each game signifies a productive joint economic activity, and players attempt to maximize their individual utilities. Unsurprisingly, more trustworthy agents are more desirable as partners. Trustworthiness is measured by the game theoretic concept of Limited-Trust, which quantifies the maximum cost an agent is willing to incur in order to improve the net utility of all agents. Agents learn about their neighbors' trustworthiness through interactions and their behaviors evolve in response. Empirical trials performed 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 modest level of trustworthiness may easily improve net utility by as much as 14.5%. If only one agent exhibits modest trust among self-centered ones, it can increase its average utility by up to 25% in certain cases! Second, and counter-intuitively, when partnership opportunities are abundant agents become less trustworthy.