The Role of A-priori Information in Networks of Rational Agents
This work addresses a foundational issue in distributed computing for rational agents, showing that prior knowledge of network size is critical for equilibrium, which is incremental as it builds on existing assumptions but introduces new impossibility results and bounds.
The paper tackles the problem of distributed algorithms for rational agents by challenging the assumption of a-priori knowledge of network size n, proving that without such knowledge, equilibrium is impossible for the Knowledge Sharing problem, and providing bounds on necessary prior intervals for equilibrium in cases with finite support.
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 $Ï$, 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 $Ï$ 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 $Ï$, i.e., $α\leq n \leq β$, for which we have an equilibrium. When possible, we extend these bounds to hold for any possible protocol.