Games of social interactions with local and global externalities

Breton, Michel Le; Weber, Shlomo

doi:10.1016/j.econlet.2011.01.012

Cited by 12 publications

(6 citation statements)

References 49 publications

(34 reference statements)

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“…Another advantage of the variational approach is that it allows for an elementary (in-)efficiency analysis of the equilibrium and the design of a tax system to restore the efficiency of the equilibrium (see Section 5). Of course, the variational approach described above presents strong similarities with the potential games of Monderer and Shapley [1996] and our framework is very close to that of Konishi et al [1997] or LeBreton and Weber [2011] in the case of a finite number of players; however we are not aware of any extension of the analysis of Monderer and Shapley [1996] to the case of a continuum of players.…”

Section: Introductionmentioning

confidence: 94%

Optimal Transport and Cournot-Nash Equilibria

Blanchet

Carlier

2016

Mathematics of OR

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We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many relevant cases. This enables us to obtain new uniqueness results and a characterisation of equilibria in terms of some partial differential equations, a simple numerical scheme in dimension one as well as an analysis of the inefficiency of equilibria.

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Section: Introductionmentioning

confidence: 94%

Optimal Transport and Cournot-Nash Equilibria

Blanchet

Carlier

2016

Mathematics of OR

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“…In the particular case of symmetric matrices g ij and J ij the game is a potential one, see e.g. [16], with the potential of the form…”

Section: Non-random Casementioning

confidence: 99%

Quantal Response Equilibria in Binary Choice Games on Graphs

Leonidov,

Savvateev,

Semenov

2019

Preprint

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Static and dynamic equilibria in noisy binary choice games on graphs are considered. Equations defining static quantal response equilibria (QRE) for binary choice games on graphs with arbitrary topology and noise distribution are written. It is shown that in the special cases of complete graph and arbitrary noise distribution, and circular and star topology and logistic noise distribution the resulting equations can be cast in the form coinciding with that derived in the earlier literature. Explicit equations QRE for non-directed graphs in the annealed approximation are derived. It is shown that the resulting effect on the phase transition is the same as found in the literature on phase transition in the Ising model on graphs in the same approximation.Evolutionary noisy binary choice game having the earlier described QRE as its stationary equilibria in the mean field approximation is constructed using the formalism of master equation.

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“…In the former class, the players choose which facilities to use and do not choose anything else; in the latter, each player chooses how to use facilities from a fixed list. Actually, the possibility of certain combinations was overlooked there, see Le Breton and Weber (2011), but the range of permissible combinations is rather limited in any case. Here, both those classes are present too, but "which" and "how" choices could be combined arbitrarily.…”

Section: Introductionmentioning

confidence: 99%

Strong Nash equilibrium in games with common and complementary local utilities

Kukushkin

2017

Journal of Mathematical Economics

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A rather general class of strategic games is described where the coalitional improvements are acyclic and hence strong Nash equilibria exist: The players derive their utilities from the use of certain facilities; all players using a facility extract the same amount of local utility therefrom, which amount depends both on the set of users and on their actions, and is decreasing in the set of users; the ultimate utility of each player is the minimum of the local utilities at all relevant facilities. Two important subclasses are "games with structured utilities," basic properties of which were discovered in 1970s and 1980s, and "bottleneck congestion games," which attracted researchers' attention quite recently. The former games are representative in the sense that every game from the whole class is isomorphic to one of them. The necessity of the minimum aggregation for the existence of strong Nash equilibria, actually, just Pareto optimal Nash equilibria, in all games of this type is established.

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Games of social interactions with local and global externalities

Cited by 12 publications

References 49 publications

Optimal Transport and Cournot-Nash Equilibria

Optimal Transport and Cournot-Nash Equilibria

Quantal Response Equilibria in Binary Choice Games on Graphs

Strong Nash equilibrium in games with common and complementary local utilities

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