Distributed Protocols for Leader Election: A Game-Theoretic Perspective

Abstract

We do a game-theoretic analysis of leader election, under the assumption that each agent prefers to have some leader than to have no leader at all. We show that it is possible to obtain a fair Nash equilibrium, where each agent has an equal probability of being elected leader, in a completely connected network, in a bidirectional ring, and a unidirectional ring, in the synchronous setting. In the asynchronous setting, Nash equilibrium is not quite the right solution concept. Rather, we must consider ex post Nash equilibrium; this means that we have a Nash equilibrium no matter what a scheduling adversary does. We show that ex post Nash equilibrium is attainable in the asynchronous setting in all the networks we consider, using a protocol with bounded running time. However, in the asynchronous setting, we require that n > 2. We can get a fair -Nash equilibrium if n = 2 in the asynchronous setting, under some cryptographic assumptions (specifically, the existence of a pseudo-random number generator and polynomially-bounded agents), using ideas from bit-commitment protocols. We then generalize these results to a setting where we can have deviations by a coalition of size k. In this case, we can get what we call a fair k-resilient equilibrium if n > 2k; under the same cryptographic assumptions, we can a get a k-resilient equilibrium if n = 2k. Finally, we show that, under minimal assumptions, not only do our protocols give a Nash equilibrium, they also give a sequential equilibrium [Kreps and Wilson 1982], so players even play optimally off the equilibrium path.

Distributed computing building blocks for rational agents

“…Many different faults are considered, from fail-stop to Byzantine faults. Recently, a new model, that of distributed game theory has emerged, in which processors, now called rational agents, are not faulty but may cheat in order to increase their profit according to some utility function [4,1,18,2,5].…”

“…We present a comprehensive examination of the preferences and utilities of rational agents in a distributed network setting, building on the results presented in [4]. We take a closer look at factors that might affect the utilities of such agents in a distributed setting, and the actions that they may take as a result of these factors.…”

“…Finally, we demonstrate the usefulness of the two building blocks in the construction of new algorithms that achieve strong equilibrium for consensus, renaming, and reconstructing the leader election algorithms of [4].…”

“…

ABSTRACTFollowing [4] we extend and generalize the game-theoretic model of distributed computing, identifying different utility functions that encompass different potential preferences of players in a distributed system. A good distributed algorithm in the game-theoretic context is one that prohibits the agents (processors with interests) from deviating from the protocol; any deviation would result in the agent losing, i.e., reducing its utility at the end of the algorithm.

…”

“…Given these preferences we construct two basic building blocks for game theoretic distributed algorithms, a wake-up building block resilient to any preference and in particular to the communication preference (to which previous wake-up solutions were not resilient), and a knowledge sharing building block that is resilient to any and in particular to solution and output preferences. Using the building blocks we present several new algorithms for consensus, and renaming as well as a modular presentation of the leader election algorithm of [4]. …”