Reaching Distributed Equilibrium with Limited ID Space

Bank, Dor; Sulamy, Moshe; Waserman, Eyal

doi:10.1007/978-3-030-01325-7_9

Cited by 3 publications

(4 citation statements)

References 12 publications

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“…Yifrach and Mansour [38] studied fair Leader Election protocols, giving an almost tight resilience analysis. Bank, Sulamy, and Waserman [11] examined the case where the id space is limited, calculating the minimal threshold for equilibrium.…”

Section: Related Workmentioning

confidence: 99%

“…From this point on a acts as if it is 2 agents. We assume that the id space is much larger than n, allowing us to disregard the probability that the fake id collides with an existing id, an issue dealt with in [11].…”

Section: Sybil Attacksmentioning

confidence: 99%

“…Consider an agent a at the start of a protocol: If a pretends to be a group of d agents, it is caught when d + n − 1 > β, since when agents count the number of agents they identify that a deviation occurred. The finite support for σ creates a situation where any duplication now involves some risk since the actual value of n is not known to the cheater (similar to [11]).…”

Section: How Much Knowledge Is Necessary?mentioning

confidence: 99%

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

Afek,

Mansour,

Rafaeli

et al. 2019

Preprint

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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 σ, 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 σ 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 σ, i.e., α ≤ n ≤ β, for which we have an equilibrium. When possible, we extend these bounds to hold for any possible protocol.

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Section: Related Workmentioning

confidence: 99%

Section: Sybil Attacksmentioning

confidence: 99%

Section: How Much Knowledge Is Necessary?mentioning

confidence: 99%

See 1 more Smart Citation

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

Afek,

Mansour,

Rafaeli

et al. 2019

Preprint

Self Cite

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show abstract

“…In [5], the authors examine the impact of a-priori knowledge of the network size on the equilibrium of distributed algorithms, assuming the id space is unlimited and thus vulnerable to a Sybil attack [9]. In [7] the authors remove this assumption and assume the id space is bounded, examining the relation between the size of the id space and the number of agents in the network in which an equilibrium is possible.…”

Section: Related Workmentioning

confidence: 99%

Consensus in Equilibrium: Can One Against All Decide Fairly?

Afek,

Harel,

Jacob-Fanani

et al. 2019

Preprint

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Is there an equilibrium for distributed consensus when all agents except one collude to steer the decision value towards their preference? If an equilibrium exists, then an n − 1 size coalition cannot do better by deviating from the algorithm, even if it prefers a different decision value. We show that an equilibrium exists under this condition only if the number of agents in the network is odd and the decision is binary (among two possible input values). That is, in this framework we provide a separation between binary and multi-valued consensus. Moreover, the input and output distribution must be uniform, regardless of the communication model (synchronous or asynchronous). Furthermore, we define a new problem -Resilient Input Sharing (RIS), and use it to find an iff condition for the (n − 1)-resilient equilibrium for deterministic binary consensus, essentially showing that an equilibrium for deterministic consensus is equivalent to each agent learning all the other inputs in some strong sense. Finally, we note that (n − 2)-resilient equilibrium for binary consensus is possible for any n. The case of (n − 2)-resilient equilibrium for multi-valued consensus is left open.

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Reaching Distributed Equilibrium with Limited ID Space

Bank

Sulamy

Waserman

2018

Structural Information and Communication Complexity

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We examine the relation between the size of the id space and the number of rational agents in a network under which equilibrium in distributed algorithms is possible. When the number of agents in the network is not a-priori known, a single agent may duplicate to gain an advantage, pretending to be more than one agent. However, when the id space is limited, each duplication involves a risk of being caught. By comparing the risk against the advantage, given an id space of size L, we provide a method of calculating the minimal threshold t, the required number of agents in the network, such that the algorithm is in equilibrium. That is, it is the minimal value of t such that if agents a-priori know that n ≥ t then the algorithm is in equilibrium. We demonstrate this method by applying it to two problems, Leader Election and Knowledge Sharing, as well as providing a constant-time approximation t ≈ L 5 of the minimal threshold for Leader Election.

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Reaching Distributed Equilibrium with Limited ID Space

Cited by 3 publications

References 12 publications

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

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

Consensus in Equilibrium: Can One Against All Decide Fairly?

Reaching Distributed Equilibrium with Limited ID Space

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