Universität Bielefeld

Center for
Mathematical
Economics

Analysis of the Interplay between Markets and Cooperative Games

Funding: German Research Foundation (DFG) via grant TR 120/15-1
Members: Walter TROCKEL, Claus-Jochen HAAKE, Cheng-Zhong QIN
Duration: 2011 - 2012

Description:

The goal of the project was it to yield new insights and to gain a deeper understanding of the interrelations between various types of economies or market systems and the theories of cooperative coalitional TU- and NTU-games. The essence of the project results may be roughly summarized as follows:

- All TU-games and all compactly generated NTU-games can be generated from (possibly different types) of economies. [Inoue (2012, 2013); Bejan and Gomez (2011a)]

- Walras-allocations of generating competitive economies induce elements of the core or of modifications of the core of the generated games. [majority of project articles]

- Competitive payoff vector functions in TU-games are induced by Walras-allocations only in the case of direct markets. In the case of general markets one needs Walras allocations of economies that are extended by money as an additional explicit commodity and quasi-linear extensions of the original utility functions. [Qin and Trockel (2013)]

- The loss of information resulting from replacing economies or markets by representing games is considerable: Many different (types of) economies may generate the same game. This becomes particularly clear in the main result of Brangewitz & Gamp (2011b), that (almost) every given closed subset of the Inner Core of an NTU-market game is identical with the set of competitive payoff vectors of a suitably chosen economy that generates the given game.

- One may consider competitive payoff vectors even in some non-balanced games via consideration of equilibrium coalition structures instead of the grand coalition. [Bejan and Gomez (2012c)]

- The articles by Aubin(1973) and by Baudier (1973) may be coherently intehrated into the modern theory of cooperative market games. [Casajus (2011)]

- Bargaining games are market games. [Brangewitz and Gamp (2011c)]

- Various popular solution concepts of bargaining games allow a unified axiomatic characterization as maximizers of CES-functions with suitable parameters of distribution and of substitution. [Haake and Qin (2013)]

- The existing axiomatizations of the Discrete Raiffa bargaining solution are based on and can be derived from the standard midpoint solution for TU-game and allow an interpretation via markets and prices. Moreover, the Discrete Raiffa solution can be supported and mechanism theoretically implemented via unique sub-game perfect payoff vectors of suitable associated extensive games. [Trockel (2012, 2011)]

- Bargaining games with incomplete information may effectively used for the analysis of the problem of adequate internal transfer payments within firms. [Brangewitz and Haake (2013)]

Results:

Results produced within or in cooperation with the project:

- Bejan and Gomez (2012a): Axiomatizing core extensions, Int. J. Game Theory

- Bejan and Gomez (2012b): Using the core to predict coalition formation, Int. Game Theory Review, 14

- Bejan and Gomez (2012c): A market interpretation of the proportional extended core, Econ. Letters

- Brangewitz (2012): Coalitional and Strategic Market Games, Doctoral Dissertation (cotutelle), Bielefeld University and University Paris I

- Brangewitz and Gamp (2011a): Competitive Outcomes and the Core of TU Market Games, IMW Working Paper 454, Bielefeld University (under revision at Econ. Letters)

- Brangewitz and Gamp (2011b): Competitive Outcomes and the Inner Core of NTU Market Games, IMW Working Paper 449, Bielefeld University

- Brangewitz and Gamp (2011c): Inner Core, Asymmetric Nash Bargaining Solutions and Competitive Payoffs, IMW Working Paper 453, Bielefeld University (published as "Asymmetric Nash bargaining solutions and competitive payoffs", Econ. Letters, 2013)

- Brangewitz and Haake (2013): Negotiated Transfer Pricing under Incomplete Information, Manuscript, University of Paderborn

- Casajus (2012): Making sense of Aubin (1973), Manuskript, IMW, Bielefeld University

- Gamp (2012): Games and their Relation to Markets, Doctoral Dissertation (cotutelle), Bielefeld University and University Paris I

- Gonzalez and Grabisch (2012): Preserving coalitional rationality for non-balanced games, CES Working Paper 2012.22, University Paris I

- Haake and Qin (2013): A Unification of Solutions to the Bargaining Problem, Manuscript, University of Paderborn

- Inoue (2012): Representation of transferable utility games by coalition production economies, J. Math. Econ., 48, 143-147

- Inoue (2013): Representation of non-transferable utility games by coalition production economies, J. Math. Econ., 49, 141-149

- Qin and Trockel (2013): On Market representation of Games, Manuscript, IMW, Bielefeld University

- Trockel (2011): An exact non-cooperative support for the sequential Raiffa solution, J. of Math. Econ., 47, 77-83

- Trockel (2012): Robustness of Intermediate Agreements for the Discrete Raiffa Solution, IMW Working Paper 472, Bielefeld University (under revision at Games and Economic Behavior)