On the existence of maximal elements, fixed points and equilibria of generalized games in a fuzzy environment

Scalzo, Vincenzo

doi:10.1016/j.fss.2015.02.006

Cited by 29 publications

(4 citation statements)

References 24 publications

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“…If the upstream and downstream information for eco-compensation is symmetric (i.e., the concept of v and c shared by the watershed), the above problem is called the Nash demand game ( Nash, 1953 ). To make sense of the problem, the manuscript assumes that

; then, there is a continuous pure strategy effective equilibrium in this symmetric information game ( Scalzo, 2015 ). In these equilibria, the upstream and downstream of the basin bid the same, that is,

.…”

Section: Methodsmentioning

confidence: 99%

Interactive influences of ecosystem services and socioeconomic factors on watershed eco-compensation standard “popularization” based on natural based solutions

Zhang

Peng

et al. 2022

Heliyon

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.…”

Section: Methodsmentioning

confidence: 99%

Interactive influences of ecosystem services and socioeconomic factors on watershed eco-compensation standard “popularization” based on natural based solutions

Zhang

Peng

et al. 2022

Heliyon

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“…37 See also Shafer and Sonnenschein (1975, Tarafdar (1977Tarafdar ( , 1991, Mehta and Tarafdar (1987), Uyanık (2016), Moore (1975Moore ( , 2007, McKenzie (2002), Baye et al (1993), Shafer and Sonnenschein (1975), Geller (1986), Tian and Zhou (1992); Park (1999Park ( , 2011, Ding and Park (2002), Askoura and Godet-Thobie (2006) and Scalzo (2015) for results on continuous selections and existence of an equilibrium in games and economies.…”

Section: Continuity Assumptionmentioning

confidence: 99%

The Yannelis-Prabhakar Theorem on Upper Semi-Continuous Selections in Paracompact Spaces: Extensions and Applications

Khan,

Uyanik

2020

Preprint

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In a 1983 paper, Yannelis-Prabhakar rely on Michael's selection theorem to guarantee a continuous selection in the context of the existence of maximal elements and equilibria in abstract economies. In this tribute to Nicholas Yannelis, we root this paper in Chapter II of Yannelis' 1983 Rochester Ph.D. dissertation, and identify its pioneering application of the paracompactness condition to current and ongoing work of Yannelis and his co-authors, and to mathematical economics more generally. We move beyond the literature to provide a necessary and sufficient condition for upper semi-continuous local and global selections of correspondences, and to provide application to five domains of Yannelis' interests: Berge's maximum theorem, the Gale-Nikaido-Debreu lemma, the Gale-McKenzie survival assumption, Shafer's non-transitive setting, and the Anderson-Khan-Rashid approximate existence theorem. The last resonates with Chapter VI of the Yannelis' dissertation.

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“…The proof is a direct application of Shafer and Sonnenschein (1975) existence theorem. Remark 2.9: Shafer and Sonnenschein's theorem has been generalized to the case of discontinuous preferences in many different papers (see, for instance, Scalzo (2015) and references therein). However, the way those results can be applied to the model in this paper, in order to have more refined condition on the primitives of the model, remains an open problem.…”

Section: Preliminaries On Set-valued Mapsmentioning

confidence: 99%

Ambiguous games without a state space and full rationality

Marco

2018

International Journal of Approximate Reasoning

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This work aims to differentiate and to better understand the assumptions that must be imposed on the structure of ambiguity and on the attitudes towards ambiguity in order to have existence of equilibria in games under ambiguous belief correspondences. In the present paper, this class of games is studied under substantially weaker assumptions on agents' preferences, as they are not required to be rational and therefore do not have any functional representation. A new approach is required to deal with preferences that are not rational, in this particular framework; in fact, the present work shows that the attitudes of agents towards the imprecision of probabilistic beliefs play a key role in the issue of equilibrium existence, whenever they are combined with some property of convexity/concavity of the ambiguous belief correspondences. The paper also studies the role played by these assumptions in different specific models, (such as incomplete information games with multiple priors or games under strategic ambiguity), so as to illustrate the applicability of the results of equilibrium existence and connections with previous literature.

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On the existence of maximal elements, fixed points and equilibria of generalized games in a fuzzy environment

Cited by 29 publications

References 24 publications

Interactive influences of ecosystem services and socioeconomic factors on watershed eco-compensation standard “popularization” based on natural based solutions

Interactive influences of ecosystem services and socioeconomic factors on watershed eco-compensation standard “popularization” based on natural based solutions

The Yannelis-Prabhakar Theorem on Upper Semi-Continuous Selections in Paracompact Spaces: Extensions and Applications

Ambiguous games without a state space and full rationality

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