The Role of A-priori Information in Networks of Rational Agents
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Until now, distributed algorithms for rational agents have assumed a-priori knowledge of n, the size of the network. This assumption is challenged here by proving how much a-priori knowledge is necessary for equilibrium in different distributed computing problems. Duplication - pretending to be more than one agent - is the main tool used by agents to deviate and increase their utility when not enough knowledge about n is given. The a-priori knowledge of n is formalized as a Bayesian setting where at the beginning of the algorithm agents only know a prior σ, a distribution from which they know n originates. We begin by providing new algorithms for the Knowledge Sharing and Coloring problems when n is a-priori known to all agents. We then prove that when agents have no a-priori knowledge of n, i.e., the support for σ is infinite, equilibrium is impossible for the Knowledge Sharing problem. Finally, we consider priors with finite support and find bounds on the necessary interval [α,β] that contains the support of σ, i.e., α≤ n ≤β, for which we have an equilibrium. When possible, we extend these bounds to hold for any possible protocol.
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