Cheating by Duplication: Equilibrium Requires Global Knowledge

The question of what global information must distributed rational agents a-priori know aboutthe network in order for equilibrium to be possible is researched here. Until now, distributedalgorithms with rational agents have assumed that n, the size of the network, is a-priori known tothe participants. We investigate the above question, considering different distributed computingproblems and showing how much each agent must a-priori know about n in order for distributedalgorithms to be equilibria. The main tool considered throughout the paper is the advantage anagent may gain by duplicationpretending to be more than one agent.We start by proving that when no bound on n is given equilibrium for Coloring and KnowledgeSharing is impossible. We provide new algorithms for both problems when n is a-priori known toall agents, thus showing that there are algorithms in which the only way for an agent to gain anadvantage is duplication. We further show that for each distributed problem there is an a-prioriknown range, an upper and a lower bound on n, such that if the actual n is guaranteed to lay inthat range, equilibrium is possible. By providing equilibria for a specific range, and impossibilityresults for any larger range, we prove the tight range necessary for equilibrium in: Leader Election,Knowledge Sharing, Coloring, Partition and Orientation. Regular submissionEligible for best student paper award. ∗This research was supported by the Israel Science Foundation (grant 1386/11).†Contact: [email protected]:1711.04728v2[cs.DC]8Apr2018