Existence of non-cooperative equilibria in social systems

Prakash, Prem; Sertel, Murat R.

doi:10.1016/0304-4068(95)00713-x

Cited by 5 publications

(3 citation statements)

References 2 publications

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“…In a previous note (Trockel and Haake 2019) we had suggested a connection between Hurwicz's dichotomy of legal vs. illegal and Debreu's (1952) distinction between socially agreed choices and socially unaccepted actions. Inspired by those ideas of enforcement and a dichotomy of legal and illegal games within true games and based on Debreu's (1952) concept of a social system and extensions due to Shafer and Sonnenschein (1975), Prakash and Sertel (1996) and of Koray and Yildiz (2018), we shall introduce socio-legal systems and their Debreu-Hurwicz equilibria in Sect. 2.…”

Section: Introductionmentioning

confidence: 99%

Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium

Haake

Trockel

2021

Rev Econ Design

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In this article we combine Debreu’s (Proc Natl Acad Sci 38(10):886–893, 1952) social system with Hurwicz’s (Econ Design 1(1):1–14, 1994; Am Econ Rev 98(3):577–585, 2008) ideas of embedding a “desired” game form into a “natural” game form that includes all feasible behavior, even if it is “illegal” according to the desired form. For the resulting socio-legal system we extend Debreu’s concepts of a social system and its social equilibria to a socio-legal system with its Debreu–Hurwicz equilibria. We build on a more general version of social equilibrium due to Shafer and Sonnenschein (J Math Econ 2(3):345–348, 1975) that also generalizes the dc-mechanism of Koray and Yildiz (J Econ Theory 176:479–502, 2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (Designing rights: invisible hand theorems, covering and membership. Tech. rep. Mimeo, Bogazici University, 2001). In the second part we apply and illustrate these new concepts via an application in the narrow welfarist framework of two person cooperative bargaining. There we provide in a socio-legal system based on Nash’s demand game an implementation of the Nash bargaining solution in Debreu–Hurwicz equilibrium.

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Section: Introductionmentioning

confidence: 99%

Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium

Haake

Trockel

2021

Rev Econ Design

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“…It is interesting to note that the final version of this paper published in 1996 in Journal of Mathematical Economics [22] is almost identical to its first version which was written in 1974 and only very slightly modified in 1976. The only difference of the published version from the 1976 version is that what was called the feasibility dynamics in the earlier versions was renamed as the feasibility map in the final version.…”

Section: Fixed Point Theory and Non-cooperative Equilibria Of Social mentioning

confidence: 92%

“…The fixed point theorems of Kakutani, Tychonoff and Ky Fan follow as corollaries to these along with some new such theorems. These results, which are important in themselves and involve the construction of a machinery for "mass production" of fixed point theorems, were actually needed to prove the existence of non-cooperative equilibria in "social systems" [22]. A social system is a notion that was introduced by the Sertel and Prakash to deal with the problem of externalities that affect one's options in a very broad sense.…”

Section: Fixed Point Theory and Non-cooperative Equilibria Of Social mentioning

confidence: 99%

Obituary

Koray

2003

Review Economic Design

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due to a heart attack. He was a genuine scholar, a brilliant intellectual, an excellent teacher, an energetic entrepreneur, a beloved friend, an enthusiastic leader, a generous host, a wonderful company, a devoted son and an affectionate father. This man from the Bosphorus whose contributions to put Turkey on the academic map of economic theory have been tremendous was a special person for everyone who knew him. His untimely death was met with deep sorrow by his colleagues, friends and students from all over the world.

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