The equivalence between two-person symmetric games and decision problems

M.S. Ismail
Additional contact information
M.S. Ismail: Microeconomics & Public Economics

No 23, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

Abstract: We illustrate an equivalence between the class of two-person symmetric games and the class of decision problems with a complete preference relation. Moreover, we show that a strategy is an optimal threat strategy (Nash, 1953) in a two-person symmetric game if and only if it is a maximal element in its equivalent decision problem. In particular, a Nash equilibrium in a two-person symmetric zero-sum game and a pair of maximal elements in its equivalent decision problem coincide. In addition, we show that a two-person symmetric zero-sum game can be extended to its von Neumann-Morgenstern (vN-M) mixed extension if and only if the extended decision problem satisfies the SSB utility (Fishburn, 1982) axioms. Furthermore, we demonstrate that a decision problem satisfies vN-M utility if and only if its equivalent symmetric game is a potential game. Accordingly, we provide a formula for the number of linearly independent equations in order for the independence axiom to be satisfied which grows quadratically as the number of alternatives increase.

Date: 2014-01-01
New Economics Papers: this item is included in nep-gth, nep-hpe, nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://cris.maastrichtuniversity.nl/ws/files/1016 ... d2d8d32-ASSET1.0.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:unm:umagsb:2014023

DOI: 10.26481/umagsb.2014023

Access Statistics for this paper

More papers in Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE) Contact information at EDIRC.
Bibliographic data for series maintained by Andrea Willems () and Leonne Portz ().