Efficient Equilibria in a Public Goods Game

Komarovsky, Zohar; Levit, Vadim E.; Grinshpoun, Tal; Meisels, Amnon

doi:10.1109/wi-iat.2015.91

Cited by 9 publications

(9 citation statements)

References 11 publications

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“…Other related variations of graphical games include supermodular network games (Manshadi and Johari 2009) and best-shot games (Dallasta, Pin, and Ramezanpour 2011;Galeotti et al 2010;Komarovsky et al 2015;Levit et al 2018). The latter are a special case of BNPGs, and Levit et al (Levit et al 2018) recently showed that these are potential games with better response dynamics converging to a pure strategy equilibrium in polynomial time.…”

Section: Related Workmentioning

confidence: 99%

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Computing Equilibria in Binary Networked Public Goods Games

Zhou

Brantingham

et al. 2020

AAAI

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Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions, and focus on the algorithmic aspects of such games. First, we show that checking the existence of a pure-strategy Nash equilibrium is NP-complete. We then identify tractable instances based on restrictions of either utility functions or of the underlying graphical structure. In certain cases, we also show that we can efficiently compute a socially optimal Nash equilibrium. Finally, we propose a heuristic approach for computing approximate equilibria in general binary networked public goods games, and experimentally demonstrate its effectiveness. Due to space limitation, some proofs are deferred to the extended version1.

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Section: Related Workmentioning

confidence: 99%

“…A special case of binary public goods games (BNPGs), commonly known as best-shot games, has received some prior attention (Dallasta, Pin, and Ramezanpour 2011;Galeotti et al 2010;Komarovsky et al 2015;Levit et al 2018). However, best-shot games make a strong assumption about the structure of the player utility functions.…”

Section: Introductionmentioning

confidence: 99%

Computing Equilibria in Binary Networked Public Goods Games

Zhou

Brantingham

et al. 2020

AAAI

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“…Correspondingly, best responses converge in two fair rounds for the best-shot public goods game. We can compare this with the complexity analysis of best-shot public goods games in [34],…”

Section: Best-shot Public Goods Gamementioning

confidence: 99%

“…Despite this rich and multifaceted literature, we still lack a systematic understanding and classification of graphical games in terms of (distributed) computational complexity; in particular, the convergence time of strategy-proof algorithms and local dynamics such as best-response to Nash equilibria is still not properly understood, except for special cases such as [34]. This paper presents a novel approach for shedding light on the distributed complexity of Nash equilibria and the dynamics of the convergence behavior in graphical games, using the perspective of distributed computing.…”

Section: Introductionmentioning

confidence: 99%

Classifying Convergence Complexity of Nash Equilibria in Graphical Games Using Distributed Computing Theory

Hirvonen,

Schmid,

Chatterjee

et al. 2021

Preprint

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Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology.Yet, even though a player's payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of "natural" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with a constant-round local algorithm. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of "time-constrained" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.

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“…prior attention [7,11,15,17]. However, best-shot games make a strong assumption about the structure of the player utility functions.…”

Section: Introductionmentioning

confidence: 99%

Computing Equilibria in Binary Networked Public Goods Games

Yu¹,

Zhou²,

Brantingham³

et al. 2019

Preprint

View full text Add to dashboard Cite

Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions, and focus on the algorithmic aspects of such games. First, we show that checking the existence of a pure-strategy Nash equilibrium is NP-Complete. We then identify tractable instances based on restrictions of either utility functions or of the underlying graphical structure. In certain cases, we also show that we can efficiently compute a socially optimal Nash equilibrium. Finally, we propose a heuristic approach for computing approximate equilibria in general binary networked public goods games, and experimentally demonstrate its effectiveness.

show abstract

Efficient Equilibria in a Public Goods Game

Cited by 9 publications

References 11 publications

Computing Equilibria in Binary Networked Public Goods Games

Computing Equilibria in Binary Networked Public Goods Games

Classifying Convergence Complexity of Nash Equilibria in Graphical Games Using Distributed Computing Theory

Computing Equilibria in Binary Networked Public Goods Games

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