An Instance of Distributed Social Computation: The Multiagent Group Membership Problem

We consider a scenario in which agents in a network are rewarded if they collectively solve a group membership task from only local distributed interactions. We propose a simple distributed algorithm with a number of desirable features aimed at modeling distributed social computation: the algorithm is self-stabilizing, decisions are made using only local information, the exchanged messages are minimal and can be represented by a single bit, agents pursue local stability, and have no memory of the past. Using this model, we characterize mathematically the tradeoff between the quality of a solution and the time needed to reach it, proving that a good solution is always found quickly while improving it to the optimum might require excessive time. We also present laboratory experiments where a group of human subjects was rewarded if they solved the same group membership task. We observe a good fit between the humans' performance and our algorithm's predictions, showing that the global dynamics of agents with diverse strategies can be described by simple, synthetic agents with a uniform strategy of interaction. This suggests that simple models of distributed computation can be constructed to predict the aggregate performance of real populations of humans solving computational problems over networks, addressing a question recently posed by Kearns in 2012.