Economic Theory of Fuzzy Equilibria

Billot, Antoine

doi:10.1007/978-3-642-79949-5

Cited by 37 publications

(31 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most prominent theoretical work in this area is the formulation of noncooperative fuzzy games due to Butnariu (1978Butnariu ( , 1979 and Billot (1992). In the Butnariu-Billot formulation players have the usual strategies and beliefs about what strategies the other players will choose in the game.…”

Section: Review Of the Existing Literaturementioning

confidence: 99%

“…6 The two other theoretical approaches in the literature only provide techniques to analyze zero-sum games. Campos (1989) uses linear programming to model matrix games, and Billot (1992) uses lexicographic fuzzy preferences to identify equilibria in a normal form game. We also discuss two application of fuzzy sets to Industrial Organization.…”

Section: Review Of the Existing Literaturementioning

confidence: 99%

“…The equilibrium concept will be identical to the Nash equilibrium, except that it will now be deÞned on the fuzzy extension of the game. This is unlike the formulation of fuzzy noncooperative games in Butnariu (1978Butnariu ( , 1979 and Billot (1992) where the payoffs functions are completely absent since they are subsumed into abstract beliefs. The solution in their model imposes very high information requirements on the deÞnition of a game making the equilibrium unappealing.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Games in Fuzzy Environments

Aristidou¹,

Sarangi²

2006

Southern Economic Journal

View full text Add to dashboard Cite

A noncooperative model of a normal form game is developed using tools from fuzzy set theory. The paper extends the decision theory framework of Bellman and Zadeh (1970) to a game-theoretic setting. We identify conditions for the existence of equilibrium in this setting and provide a duopoly example. The paper also provides a review of the existing literature on noncooperative fuzzy games and their applications. JEL Classification: C7, D8Keywords: Noncooperative games, Fuzzy sets. * We would like thank Hans Haller, Rob Gilles, two annonymous referees and the Editor for helpful suggestions. All errors, omissions and misinterpretations are our responsibility. AbstractA noncooperative model of a normal form game is developed using tools from fuzzy set theory. The paper extends the decision theory framework of Bellman and Zadeh (1970) to a game-theoretic setting. We identify conditions for the existence of equilibrium in this setting and provide a duopoly example. The paper also provides a review of the existing literature on noncooperative fuzzy games and their applications.

show abstract

Section: Review Of the Existing Literaturementioning

confidence: 99%

Section: Review Of the Existing Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Games in Fuzzy Environments

Aristidou¹,

Sarangi²

2006

Southern Economic Journal

View full text Add to dashboard Cite

show abstract

“…Cooperative fuzzy games have proved to be suitable for modelling cooperative behavior of agents in economic situations (Billot (1995), Nishizaki and Sakawa (2001)) and political situations (Butnariu (1978), Lebret and Ziad (2001)) in which some agents do not fully participate in a coalition but only to a certain extent. For example in a class of production games, partial participation in a coalition means to offer a part of the resources while full participation means to offer all the resources.…”

Section: Introductionmentioning

confidence: 99%

Egalitarianism in convex fuzzy games

Brânzei

Dimitrov

Tijs

2004

Mathematical Social Sciences

View full text Add to dashboard Cite

In this paper the egalitarian solution for convex cooperative fuzzy games is introduced. The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game. This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence * This paper was written while the authors were research fellows at the ZiF (Bielefeld) for the project "Procedural Approaches to Conflict Resolution", 2002. We thank our hosts for their hospitality.

show abstract

“…the following conditions are satised, 2 A sample of the literature on fuzzy preferences is Orlovsky (1978), Ovchinnikov (1981), Basu (1984), Billot (1995), Dutta, Panda, Pattanaik (1986), Dutta (1987), Jain (1990), Ponsard (1990), Dasgupta and Deb (1991, 1996), Roubens (1991, 1992) and Banerjee (1993Banerjee ( , 1994. The philosophical underpinnings of these ideas are discussed in Piggins and Salles (2007).…”

mentioning

confidence: 99%