Incentive-based search for efficient equilibria of the public goods game

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

doi:10.1016/j.artint.2018.04.004

Cited by 12 publications

(24 citation statements)

References 18 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. No other algorithmic results are known for either of these special classes of graphical games.…”

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%

“…However, best-shot games make a strong assumption about the structure of the player utility functions. While Levit et al (Levit et al 2018) recently showed that equilibria for best-shot games can be computed in polynomial time by best response dynamics, these may fail to find social welfareoptimal equilibria, and nothing is known about BNPGs more generally.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computing Equilibria in Binary Networked Public Goods Games

Zhou

Brantingham

et al. 2020

AAAI

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“…social welfare) in the limit of infinite time, and suggested a simulated annealing alternative. Levit et al [38] proved that the general version of the best-shot PGG is a potential game and derived an algorithm for finding equilibria based on side payments, which are used by agents that are unhappy with their outcome to convince neighbors to switch. While superior results were obtained over best-response dynamics, there is still a wide gap between the equilibria found by this approach and optimal equilibria as found by exhaustive search on small graphs.…”

Section: ( )mentioning

confidence: 99%

Solving Graph-based Public Good Games with Tree Search and Imitation Learning

Darvariu¹,

Hailes²,

Musolesi³

2021

Preprint

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Public goods games represent insightful settings for studying incentives for individual agents to make contributions that, while costly for each of them, benefit the wider society. In this work, we adopt the perspective of a central planner with a global view of a network of self-interested agents and the goal of maximizing some desired property in the context of a best-shot public goods game. Existing algorithms for this known NP-complete problem find solutions that are sub-optimal and cannot optimize for criteria other than social welfare. In order to efficiently solve public goods games, our proposed method directly exploits the correspondence between equilibria and the Maximal Independent Set (mIS) structural property of graphs. In particular, we define a Markov Decision Process, which incrementally generates an mIS, and adopt a planning method to search for equilibria, outperforming existing methods. Furthermore, we devise an imitation learning technique that uses demonstrations of the search to obtain a graph neural network parametrized policy which quickly generalizes to unseen game instances. Our evaluation results show that this policy is able to reach 99.5% of the performance of the planning method while being approximately three orders of magnitude faster to evaluate on the largest graphs tested. The methods presented in this work can be applied to a large class of public goods games of potentially high societal impact.Preprint. Under review.

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“…Finally, our model is also related to the literature that studies network effects. For example, Levit et al (2018) study the impact of network effects on users' actions and social welfare. Ghosh and Ligett (2013) show how users make their participation decisions considering the network effect.…”

Section: Related Workmentioning

confidence: 99%

A Differential Privacy Mechanism that Accounts for Network Effects for Crowdsourcing Systems

Luo

Jennings²

2020

jair

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In crowdsourcing systems, it is important for the crowdsource campaign initiator to incentivize users to share their data to produce results of the desired computational accuracy. This problem becomes especially challenging when users are concerned about the privacy of their data. To overcome this challenge, existing work often aims to provide users with differential privacy guarantees to incentivize privacy-sensitive users to share their data. However, this work neglects the network effect that a user enjoys greater privacy protection when he aligns his participation behaviour with that of other users. To explore this network effect, we formulate the interaction among users regarding their participation decisions as a population game, because a user’s welfare from the interaction depends not only on his own participation decision but also the distribution of others’ decisions. We show that the Nash equilibrium of this game consists of a threshold strategy, where all users whose privacy sensitivity is below a certain threshold will participate and the remaining users will not. We characterize the existence and uniqueness of this equilibrium, which depends on the privacy guarantee, the reward provided by the initiator and the population size. Based on this equilibria analysis, we design the PINE (Privacy Incentivization with Network Effects) mechanism and prove that it maximizes the initiator’s payoff while providing participating users with a guaranteed degree of privacy protection. Numerical simulations, on both real and synthetic data, show that (i) PINE improves the initiator’s expected payoff by up to 75%, compared to state of the art mechanisms that do not consider this effect; (ii) the performance gain by exploiting the network effect is particularly good when the majority of users are flexible over their privacy attitudes and when there are a large number of low quality task performers.

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Incentive-based search for efficient equilibria of the public goods game

Cited by 12 publications

References 18 publications

Computing Equilibria in Binary Networked Public Goods Games

Computing Equilibria in Binary Networked Public Goods Games

Solving Graph-based Public Good Games with Tree Search and Imitation Learning

A Differential Privacy Mechanism that Accounts for Network Effects for Crowdsourcing Systems

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