Cheating by Duplication: Equilibrium Requires Global Knowledge

Abstract

The question of what global information must distributed rational agents a-priori know about the network in order for equilibrium to be possible is researched here. Until now, distributed algorithms with rational agents have assumed that n, the size of the network, is a-priori known to the participants. We investigate the above question, considering different distributed computing problems and showing how much each agent must a-priori know about n in order for distributed algorithms to be equilibria. The main tool considered throughout the paper is the advantage an agent may gain by duplication-pretending to be more than one agent.We start by proving that when no bound on n is given equilibrium for Coloring and Knowledge Sharing is impossible. We provide new algorithms for both problems when n is a-priori known to all agents, thus showing that there are algorithms in which the only way for an agent to gain an advantage is duplication. We further show that for each distributed problem there is an a-priori known range, an upper and a lower bound on n, such that if the actual n is guaranteed to lay in that range, equilibrium is possible. By providing equilibria for a specific range, and impossibility results 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.

Long-term Data Sharing under Exclusivity Attacks

“…Assume 𝑆 𝐼 ≠ 0, 𝑁 𝐼 = 2. 1 Instead of reporting 𝐷 𝐼 , the firm first reports 𝐷 ′ = [0], receives an average 𝑎 1 , then reports 𝐷 ′′ = [0] and receives the updated average 𝑎 2 . The average that others, following the mechanism as given, attain is 𝑆 𝑂 𝑁 𝑂 +2 , the true average is 𝑆 𝐼 +𝑆 𝑂 𝑁 𝐼 +𝑁 𝑂 , and they are different by our assumption on 𝑆 𝐼 , 𝑁 𝐼 .…”

“…Why should we not consider simply forbidding multiple subsequent updates by a firm? As noted in [1,13,40], modern internet-based environments lack clear identities and allow for multiple inputs by the same agent using multiple identities. A common distinction in blockchain networks separates public ("permissionless") and private ("permissioned") networks [24], where public networks allow open access for everyone, while private networks require additional identification for participation.…”

“…The rest of (2b)-(2d) consecutively add triangulation points (blue triangles). At the end of the triangulation attack (after (2d)), the linear regression estimator is different than in(1). It is possible to infer the estimator in (1) using knowledge of the triangulation points and estimators of (2a)-(2d) (without knowledge of the red points).…”

Fair Leader Election for Rational Agents in Asynchronous Rings and Networks

“…Recently, Afek et al [6], studied resilient protocols from another angle. They ask how much information about n processors must have in order to implement a resilient protocol.…”

“…At a high level we would like to design protocols which are resilient to such deviations. This line of research has been active for over a decade (see, [19,22,2,1,4,5,13,6]).…”