Two-Stage Facility Location Games with Strategic Clients and Facilities

We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to its spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting time for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and we give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.

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From Recommendation Systems to Facility Location Games

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33011772 ◽

2019 ◽

Vol 33 ◽

pp. 1772-1779

Author(s):

Omer Ben-Porat ◽

Gregory Goren ◽

Itay Rosenberg ◽

Moshe Tennenholtz

Keyword(s):

Social Welfare ◽

Facility Location ◽

Recommendation Systems ◽

Semantic Space ◽

Open Questions ◽

Intervention Cost ◽

Equilibrium Profile ◽

Location Games ◽

Facility Location Models ◽

The One

Recommendation systems are extremely popular tools for matching users and contents. However, when content providers are strategic, the basic principle of matching users to the closest content, where both users and contents are modeled as points in some semantic space, may yield low social welfare. This is due to the fact that content providers are strategic and optimize their offered content to be recommended to as many users as possible. Motivated by modern applications, we propose the widely studied framework of facility location games to study recommendation systems with strategic content providers. Our conceptual contribution is the introduction of a mediator to facility location models, in the pursuit of better social welfare. We aim at designing mediators that a) induce a game with high social welfare in equilibrium, and b) intervene as little as possible. In service of the latter, we introduce the notion of intervention cost, which quantifies how much damage a mediator may cause to the social welfare when an off-equilibrium profile is adopted. As a case study in high-welfare low-intervention mediator design, we consider the one-dimensional segment as the user domain. We propose a mediator that implements the socially optimal strategy profile as the unique equilibrium profile, and show a tight bound on its intervention cost. Ultimately, we consider some extensions, and highlight open questions for the general agenda.

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A Game Theoretic Approach to Optimize Identity Exposure in Pervasive Computing Environments

International Journal of Information Security and Privacy ◽

10.4018/jisp.2010100101 ◽

2010 ◽

Vol 4 (4) ◽

pp. 1-20

Author(s):

Feng W. Zhu ◽

Sandra Carpenter ◽

Wei Zhu ◽

Matt Mutka

Keyword(s):

Pervasive Computing ◽

Fundamental Problem ◽

Personal Information ◽

Theoretic Approach ◽

Identity Information ◽

Identity Model ◽

Game Theoretic ◽

Computing Environments ◽

Subgame Perfect Equilibria ◽

Perfect Equilibria

In pervasive computing environments, personal information is typically expressed in digital forms. Daily activities and personal preferences with regard to pervasive computing applications are easily associated with personal identities. Privacy protection is a serious challenge. The fundamental problem is the lack of a mechanism to help people expose appropriate amounts of their identity information when accessing pervasive computing applications. In this paper, the authors propose the Hierarchical Identity model, which enables the expression of one’s identity information ranging from precise detail to vague identity information. The authors model privacy exposure as an extensive game. By finding subgame perfect equilibria in the game, the approach achieves optimal exposure. It finds the most general identity information that a user should expose and which the service provider would accept. The authors’ experiments show that their models can reduce unnecessary identity exposure effectively.

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A Game Theoretic Approach to Optimize Identity Exposure in Pervasive Computing Environments

Cyber Crime ◽

10.4018/978-1-61350-323-2.ch211 ◽

2013 ◽

pp. 375-394

Author(s):

Feng W. Zhu ◽

Sandra Carpenter ◽

Wei Zhu ◽

Matt Mutka

Keyword(s):

Pervasive Computing ◽

Fundamental Problem ◽

Personal Information ◽

Theoretic Approach ◽

Identity Information ◽

Identity Model ◽

Game Theoretic ◽

Computing Environments ◽

Subgame Perfect Equilibria ◽

Perfect Equilibria

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The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

Mathematics of Operations Research ◽

10.1287/moor.2018.0968 ◽

2019 ◽

Vol 44 (4) ◽

pp. 1286-1303 ◽

Cited By ~ 1

Author(s):

José Correa ◽

Jasper de Jong ◽

Bart de Keijzer ◽

Marc Uetz

Keyword(s):

Price Of Anarchy ◽

Subgame Perfect Equilibrium ◽

Network Routing ◽

Congestion Games ◽

Cost Functions ◽

Worst Case ◽

Subgame Perfection ◽

Subgame Perfect Equilibria ◽

Routing Games ◽

Perfect Equilibria

This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n − 2)/(2n + 1), where n is the number of players. This paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n − 2)/(2n + 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Second, we ask whether sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: we show that the sequential price of anarchy equals 7/5 and that computing the outcome of a subgame perfect equilibrium is NP-hard.

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Why You Should Charge Your Friends for Borrowing Your Stuff

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/56 ◽

2017 ◽

Author(s):

Kijung Shin ◽

Euiwoong Lee ◽

Dhivya Eswaran ◽

Ariel D. Procaccia

Keyword(s):

Social Networks ◽

Social Network ◽

Theoretical Analysis ◽

Nash Equilibria ◽

Price Of Anarchy ◽

Price Of Stability ◽

Free Riders ◽

The Social ◽

Access Cost ◽

Game Theoretic

We consider goods that can be shared with k-hop neighbors (i.e., the set of nodes within k hops from an owner) on a social network. We examine incentives to buy such a good by devising game-theoretic models where each node decides whether to buy the good or free ride. First, we find that social inefficiency, specifically excessive purchase of the good, occurs in Nash equilibria. Second, the social inefficiency decreases as k increases and thus a good can be shared with more nodes. Third, and most importantly, the social inefficiency can also be significantly reduced by charging free riders an access cost and paying it to owners, leading to the conclusion that organizations and system designers should impose such a cost. These findings are supported by our theoretical analysis in terms of the price of anarchy and the price of stability; and by simulations based on synthetic and real social networks.

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Game-theoretic Analysis of Effort Allocation of Contributors to Public Projects

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2021/57 ◽

2021 ◽

Author(s):

Jared Soundy ◽

Chenhao Wang ◽

Clay Stevens ◽

Hau Chan

Keyword(s):

Price Of Anarchy ◽

Price Of Stability ◽

Software Projects ◽

Allocation Model ◽

Effort Allocation ◽

Public Projects ◽

Game Theoretic Analysis ◽

Feature Request ◽

Original Goal ◽

Game Theoretic

Public projects can succeed or fail for many reasons such as the feasibility of the original goal and coordination among contributors. One major reason for failure is that insufficient work leaves the project partially completed. For certain types of projects anything short of full completion is a failure (e.g., feature request on software projects in GitHub). Therefore, project success relies heavily on individuals allocating sufficient effort. When there are multiple public projects, each contributor needs to make decisions to best allocate his/her limited effort (e.g., time) to projects while considering the effort allocation decisions of other strategic contributors and his/her parameterized utilities based on values and costs for the projects. In this paper, we introduce a game-theoretic effort allocation model of contributors to public projects for modeling effort allocation of strategic contributors. We study the related Nash equilibrium (NE) computational problems and provide NP-hardness results for the existence of NE and polynomial-time algorithms for finding NE in restricted settings. Finally, we investigate the inefficiency of NE measured by the price of anarchy and price of stability.

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Subgame Perfect Equilibria Under the Deferred Acceptance Algorithm

SSRN Electronic Journal ◽

10.2139/ssrn.3235068 ◽

2018 ◽

Cited By ~ 1

Author(s):

Yasushi Kawase ◽

Keisuke Bando

Keyword(s):

Deferred Acceptance Algorithm ◽

Deferred Acceptance ◽

Subgame Perfect Equilibria ◽

Perfect Equilibria

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Search for a moving target in a competitive environment

International Journal of Game Theory ◽

10.1007/s00182-021-00761-5 ◽

2021 ◽

Author(s):

Benoit Duvocelle ◽

János Flesch ◽

Hui Min Shi ◽

Dries Vermeulen

Keyword(s):

Markov Chain ◽

Discrete Time ◽

Competitive Environment ◽

Moving Target ◽

Time Varying ◽

Greedy Strategy ◽

Time Dynamic ◽

Dynamic Search ◽

Subgame Perfect Equilibria ◽

Perfect Equilibria

AbstractWe consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

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