Location Games on Networks: Existence and Efficiency of Equilibria

Fournier, Gaëtan; Scarsini, Marco

doi:10.1287/moor.2017.0921

Cited by 5 publications

(5 citation statements)

References 45 publications

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“…The Hotelling-Downs model was also analyzed for non-linear markets, e.g., on graphs [29,19,18], fixed locations on a circle [33], finite sets of locations [26,27], and optimal interval division [35]. Moreover, many facility location games are variants of the Hotelling-Downs model and there is a rich body of work analyzing competitive facility location in the noncooperative setting, e.g.…”

Section: Related Workmentioning

confidence: 99%

“…The social costs SC(s, f) of a strategy profile (s, f) is defined as the sum over the costs of all client agents, i.e., SC(s, f) = Z C z (s, f)dz. Similarly to the Price of Anarchy, we define the quality Q of an equilibrium as in [19]. We are interested in the costs of the client players, while the strategies of the facility players define the stable states.…”

Section: Quality Of the ρ-Spementioning

confidence: 99%

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From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation

Feldotto¹,

Lenzner²,

Molitor³

et al. 2019

Preprint

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Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotellings model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotellings model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotellings model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.

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Section: Related Workmentioning

confidence: 99%

Section: Quality Of the ρ-Spementioning

confidence: 99%

From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation

Feldotto¹,

Lenzner²,

Molitor³

et al. 2019

Preprint

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show abstract

“…The smaller the PoA (PoS), the fairer the worst (best) equilibrium. We are not the first to use social cost functions that are not the sum of individual costs (see for instance Fournier and Scarsini, 2019, Koutsoupias and Papadimitriou, 2009, 1999, Mavronicolas et al, 2008, Vetta, 2002.…”

Section: Fairness Of Equilibriamentioning

confidence: 99%

“…Since our buckpassing game is a constant-sum game, using this social cost produces only trivial results. Other social cost functions were considered, for instance, in Papadimitriou (2009, 1999), Vetta (2002), Mavronicolas et al (2008), Fournier and Scarsini (2019).…”

mentioning

confidence: 99%

The Buck-Passing Game

Cominetti¹,

Quattropani²,

Scarsini³

2018

Preprint

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We consider situations where a finite number of agents want to transfer the responsibility of doing a job (the buck) to their neighbors in a social network. This can be seen as network variation of the public good model. The goal of each agent is to see the buck coming back as rarely as possible. We frame this situation as a game where players are the vertices of a directed graph and the strategy space of each player is the set of her out-neighbors. Nature assigns the buck to a random player according to a given initial distribution. Each player pays a cost that corresponds to the asymptotic expected frequency of times that she gets the buck. We consider two versions of the game. In the deterministic one each player chooses one of her out-neighbors once and for all at the beginning of the game. In the stochastic version a player chooses a probability distribution that determines which of her out-neighbors will be chosen when she passes the buck. We show that in both cases the game admits a generalized ordinal potential whose minimizers provide equilibria in pure strategies, even when the strategy set of each player is uncountable. We also show the existence of equilibria that are prior-free, in the sense that they do not depend on the initial distribution used to initially assign the buck. We provide different characterizations for the potential, we analyze fairness of equilibria, and, finally, we discuss a buck holding variant in which players want to maximize the frequency of times they hold the buck. As an application of the latter we briefly discuss the PageRank game.

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“…In [127], the framework of potential games was exploited to analyze several applications like congestion games. In more recent works [86,97,90,107], the authors considered more involved, yet specific, games of which they carried out a complete characterization. Almost all these classical results, rely on the assumption that the players' actions can be represented by a scalar and that no complex coupling constraints among players are present.…”

Section: Introduction To Multi-agent Network Gamesmentioning

confidence: 99%

Multi-agent network games with applications in smart electric mobility

Cenedese¹

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Location Games on Networks: Existence and Efficiency of Equilibria

Cited by 5 publications

References 45 publications

From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation

From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation

The Buck-Passing Game

Multi-agent network games with applications in smart electric mobility

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