Best response dynamics on random graphs

Chellig, Jordan; Durbac, Calina; Fountoulakis, Nikolaos

doi:10.1016/j.geb.2021.11.003

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…As defecting is strictly more beneficial to the individual than cooperating, each of the selfish agents playing the game will best-response on its turn by defecting. This has been shown to lead to the end result that society converges on the least beneficial solution under which all the players defect [37].…”

Section: Games On Networkmentioning

confidence: 99%

Solving Multi-Agent Games on Networks

Vaknin,

Meisels

2024

Preprint

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Multi-agent games on networks (GoNs) have nodes that represent agents and edges that represent interactions among agents. Binary GoNs are composed of 2-Players games on each of their edges. Non binary GoNs have games that are played by all agents in each neighborhood.Solutions to games on networks are stable states (i.e., pure Nash equilibria), and in general one is interested in efficient solutions (i.e., of high social welfare).Incentives, in the form of side payments among agents, are known to promote increased-efficiency stable states. This study addresses the multi-agent aspect of games on networks - a system of multiple agents that compose a game and seek a solution. The agents playing the game are assumed to be strategic and the present study proposes an iterative distributed algorithm that lets the agents interact (i.e., negotiate) in neighborhoods in a process that guarantees the convergence of any multi-agent game on network to a stable state.The proposed algorithm treats the game as a repeated social choice action that takes place in one neighborhood at a time. A truthful enforcing mechanism is integrated into the process, collecting agents' valuations and computing incentives on the fly while eliminating strategic behavior. This method - the TECon algorithm - is proven to converge to solutions that are at least as efficient as the initial state, for any game on network.A specific version of the algorithm is given for the class of public goods games, where the main properties of the algorithm are guaranteed even when the strategic agents playing the game consider their possible future valuations when interacting.This opens an interesting new research direction on application-specific derivatives of TECon that, similarly to the case of public goods games, may lead to solutions of greater efficiency. An extensive experimental evaluation on randomly generated games on networks demonstrates that the TECon algorithm outperforms former solving methods on several classes of games on networks.

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Section: Games On Networkmentioning

confidence: 99%

Solving Multi-Agent Games on Networks

Vaknin,

Meisels

2024

Preprint

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“…Despite these two alternative proofs of the Fountoulakis–Kang–Makai theorem and deeper studies on somewhat “sharper” models, nobody ever managed to settle Conjecture 1.1 beyond the barrier

p\ge \lambda {n}^{-1/2}

. To quote very recent work [4] in the area, “the study of majority dynamics for

p=o\left({n}^{-1/2}\right)

imposes immense complications.” Our main result is to confirm Conjecture 1.1 for sparser random graphs

G\left(n,p\right)

with

{\lambda}^{\prime }{n}^{-3/5}\log n\le p\le \lambda {n}^{-1/2}

, thereby breaking the barrier for the first time.…”

Section: Introductionmentioning

confidence: 99%

“…Despite these two alternative proofs of the Fountoulakis-Kang-Makai theorem and deeper studies on somewhat "sharper" models, nobody ever managed to settle Conjecture 1.1 beyond the barrier p ≥ 𝜆n −1∕2 . To quote very recent work [4] in the area, "the study of majority dynamics for p = o(n −1∕2 ) imposes immense complications." Our main result is to confirm Conjecture 1.1 for sparser random graphs G(n, p) with 𝜆 ′ n −3∕5 log n ≤ p ≤ 𝜆n −1∕2 , thereby breaking the barrier for the first time.…”

Section: Introductionmentioning

confidence: 99%

Majority dynamics on sparse random graphs

Chakraborti

Kim

Lee

et al. 2023

Random Struct Algorithms

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Majority dynamics on a graph G is a deterministic process such that every vertex updates its ±1-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnell, Tamuz and Tan conjectured that, in the Erdős-Rényi random graph G(n, p), the random initial ±1-assignment converges to a 99%-agreement with high probability whenever p = 𝜔(1∕n). This conjecture was first confirmed for p ≥ 𝜆n −1∕2 for a large constant 𝜆 by Fountoulakis, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin, it was unknown whether the conjecture holds for p < 𝜆n −1∕2 . We break this Ω(n −1∕2 )-barrier by proving the conjecture for sparser random graphs G(n, p), where 𝜆 ′ n −3∕5 log n ≤ p ≤ 𝜆n −1∕2 with a large constant 𝜆 ′ > 0.

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“…Despite these two alternative proofs of the Fountoulakis-Kang-Makai theorem and deeper studies on somewhat "sharper" models, nobody ever managed to settle Conjecture 1.1 beyond the barrier p ≥ λn −1/2 . To quote very recent work [4] in the area, "the study of majority dynamics for p = o(n −1/2 ) imposes immense complications." Our main result is to confirm Conjecture 1.1 for sparser random graphs G(n, p) with λ ′ n −3/5 log n ≤ p ≤ λn −1/2 , thereby breaking the barrier for the first time.…”

Section: Introductionmentioning

confidence: 99%

Majority dynamics on sparse random graphs

Chakraborti¹,

Kim²,

Lee³

et al. 2021

Preprint

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Majority dynamics on a graph G is a deterministic process such that every vertex updates its ±1-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnell, Tamuz and Tan conjectured that, in the Erdős-Rényi random graph G(n, p), the random initial ±1-assignment converges to a 99%-agreement with high probability whenever p = ω(1/n).This conjecture was first confirmed for p ≥ λn −1/2 for a large constant λ by Fountoulakis, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin, it was unknown whether the conjecture holds for p < λn −1/2 . We break this Ω(n −1/2 )-barrier by proving the conjecture for sparser random graphs G(n, p), where λ ′ n −3/5 log n ≤ p ≤ λn −1/2 with a large constant λ ′ > 0.

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Best response dynamics on random graphs

Cited by 4 publications

References 27 publications

Solving Multi-Agent Games on Networks

Solving Multi-Agent Games on Networks

Majority dynamics on sparse random graphs

Majority dynamics on sparse random graphs

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