Approximation of Nash equilibria in Bayesian games

Armantier, Olivier; Florens, Jean‐Pierre; Richard, Jean‐François

doi:10.1002/jae.1040

Cited by 27 publications

(13 citation statements)

References 37 publications

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“…The phenomenon of simple techniques providing highly effective solutions has also been observed elsewhere [18][19][20][21]. In addition to novelty of our influencedriven, network-based model, our work differs from these in other important ways.…”

Section: Discussionmentioning

confidence: 65%

Bayesian Security Games for Controlling Contagion

Tsai

Qian

Vorobeychik

et al. 2013

2013 International Conference on Social Computing

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Influence blocking games have been used to model adversarial domains with a social component, such as counterinsurgency. In these games, a mitigator attempts to minimize the efforts of an influencer to spread his agenda across a social network. Previous work has assumed that the influence graph structure is known with certainty by both players. However, in reality, there is often significant information asymmetry between the mitigator and the influencer. We introduce a model of this information asymmetry as a two-player zero-sum Bayesian game. Nearly all past work in influence maximization and social network analysis suggests that graph structure is fundamental in strategy generation, leading to an expectation that solving the Bayesian game exactly is crucial. Surprisingly, we show through extensive experimentation on synthetic and real-world social networks that many common forms of uncertainty can be addressed near-optimally by ignoring the vast majority of it and simply solving an abstracted game with a few randomly chosen types. This suggests that optimal strategies of games that do not model the full range of uncertainty in influence blocking games are typically robust to uncertainty about the influence graph structure. I INTRODUCTIONSocial contagion has long been of great interest in the literature on marketing, the spread of rumors, and, recently, in the context of Arab Spring [1][2][3]. Our specific focus is on counterinsurgency, which we view as a competition for the support of local leaders. Counterinsurgency can be modeled as a game with two strategic players, the insurgents and the peacekeepers, in which the insurgents aim to spread their views, unrest, etc. among the local population, while the peacekeepers wish to minimize the resulting contagion by engaging in their own influence campaign [4][5][6]. The key computational question we address is: given limited resources, how to select which of the local leaders to influence to minimize the global impact of the insurgency.These 'influence blocking' games have received recent attention in the security games literature [6], where they have been modeled using graphs with nodes representing the tribal leaders and edges representing possible transmission of influence. However, this line of work has assumed that full information about network structure is available to both players. In practice, informational challenges abound in counterinsurgency, where the insurgents are typically an indigenous group that has an informational advantage, and the mitigators are often uncertain about the the social network [4].We model counterinsurgency as an influence blocking game with asymmetric information. Specifically, we assume that the influencer (an insurgent group) has perfect knowledge of the influence graph structure, while the mitigator is uncertain about it. In the resulting Bayesian game, an influencer type is a particular instantiation of the influence graph, and the mitigator must reason over the distribution over these graphs (i.e., influencer types...

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Section: Discussionmentioning

confidence: 65%

Bayesian Security Games for Controlling Contagion

Tsai

Qian

Vorobeychik

et al. 2013

2013 International Conference on Social Computing

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“…Bajari's third algorithm is closely related to the concept of Constrained Strategic Equilibrium (CSE) introduced in [17]. In the CSE method, the bidding strategies are within a set with certain properties and the equilibrium is searched restricted to that set.…”

Section: Related Work: Numerical Methods For Computing the Best Biddimentioning

confidence: 99%

First-Price Auctions with Reimbursement in NSP Alliances with Asymmetric Buyers

Amigo

Vaton

Belzarena

2014

Proceedings of the Latin America Networking Conference on LANC 2014

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The emergence of Network Service Provider Alliances (NSPs) to provide end-to-end, quality-assured services, promises new business and service opportunities for NSPs and customers respectively. This new marketplace requires a suitable pricing mechanism that allows price fixation, control access and customer trust in the new -and thus without reputationseller. To work in this scenario, we propose a pricing scheme based on First-price auctions and where a pre-announced percentage of the price paid for the service is reimbursed if the quality is not satisfied. An optimal percentage of reimbursement can be analytically computed in simplified scenarios, where all buyers are equally modelled [1]. In more realistic scenarios, customers and services are asymmetric, e.g. buyers value the service on sale in a different way, and no analytical results can be derived. As a remedy, we propose a simulative approach in order to approximate buyers' willingness to pay, and subsequently compute the optimal percentage of reimbursement. We apply our simulator to different case studies, finding in all of them that the optimal percentage of reimbursement is 100% and this value prevents problems such as the market for lemons.

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“…This approach has also been applied to multi-unit settings, in particular, Treasury bill auctions; see, for example, Sbaï [2006, 2009]. We refer readers to Armantier et al [2008] for a comparison of this approach to the methods we describe here.…”

Section: Bidders From Two Different Urnsmentioning

confidence: 99%

On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm

Hubbard¹,

Paarsch²

2014

Handbook of Computational Economics

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We describe and compare numerical methods used to approximate equilibrium bid functions in models of auctions as games of incomplete information. In such games, private values are modelled as draws from bidder-specific type distributions and pay-your-bid rules are used to determine transactions prices. We provide a formal comparison of the performance of these numerical methods (based on speed and accuracy) and suggest ways in which they can be improved and extended as well as applied to new settings.

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Approximation of Nash equilibria in Bayesian games

Cited by 27 publications

References 37 publications

Bayesian Security Games for Controlling Contagion

Bayesian Security Games for Controlling Contagion

First-Price Auctions with Reimbursement in NSP Alliances with Asymmetric Buyers

On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm

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