TY - JOUR
T1 - Distributed protocols for leader election
T2 - A game-theoretic perspective
AU - Abraham, Ittai
AU - Dolev, Danny
AU - Halpern, Joseph Y.
N1 - Publisher Copyright:
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.
PY - 2019/2
Y1 - 2019/2
N2 - We do a game-theoretic analysis of leader election, under the assumption that each agent prefers to have some leader than 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 show that we can get a fair ex post ϵ-Nash equilibrium if n = 2 in the asynchronous setting under some cryptographic assumptions (specifically, the existence of a one-way functions), using a commitment protocol. 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 in a completely connected network if n > 2k; under the same cryptographic assumptions, we can a get a k-resilient equilibrium in a completely connected network, unidirectional ring, or bidirectional ring if n > k. Finally, we show that under minimal assumptions, not only do our protocols give a Nash equilibrium, they also give a sequential equilibrium, so players even play optimally off the equilibrium path.
AB - We do a game-theoretic analysis of leader election, under the assumption that each agent prefers to have some leader than 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 show that we can get a fair ex post ϵ-Nash equilibrium if n = 2 in the asynchronous setting under some cryptographic assumptions (specifically, the existence of a one-way functions), using a commitment protocol. 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 in a completely connected network if n > 2k; under the same cryptographic assumptions, we can a get a k-resilient equilibrium in a completely connected network, unidirectional ring, or bidirectional ring if n > k. Finally, we show that under minimal assumptions, not only do our protocols give a Nash equilibrium, they also give a sequential equilibrium, so players even play optimally off the equilibrium path.
KW - Ex post Nash equilibrium
KW - Leader election
UR - http://www.scopus.com/inward/record.url?scp=85062338292&partnerID=8YFLogxK
U2 - 10.1145/3303712
DO - 10.1145/3303712
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85062338292
SN - 2167-8375
VL - 7
JO - ACM Transactions on Economics and Computation
JF - ACM Transactions on Economics and Computation
IS - 1
M1 - a4
ER -