The Role of A-priori Information in Networks of Rational Agents

TL;DR

This paper investigates how the amount of prior knowledge about network size affects the existence of equilibrium in distributed algorithms for rational agents, highlighting the necessity of a-priori information for certain problems.

Contribution

It formalizes the role of a-priori knowledge in distributed algorithms, providing new algorithms and bounds for knowledge sharing and coloring problems under different prior assumptions.

Findings

Equilibrium is impossible without finite support priors.

New algorithms are provided for known network size scenarios.

Bounds are established for priors with finite support.

Abstract

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 $\sigma$, 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 $\sigma$ is infinite, equilibrium is impossible for the Knowledge Sharing problem. Finally, we consider priors with finite support and find bounds on the necessary interval $[\alpha,\beta]$ that contains the support of $\sigma$, i.e., $\alpha \leq n \leq \beta$, for which we have an equilibrium. When possible, we extend these bounds to hold for any possible protocol.