Template-type: ReDif-Paper 1.0
Author-Name: Ismail, M.S.
Author-workplace-name: Microeconomics & Public Economics
Title: The equivalence between two-person symmetric games and decision problems
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.
Series: GSBE Research Memoranda
Creation-Date: 20140101
Number: 023
File-URL: https://cris.maastrichtuniversity.nl/ws/files/1016481/guid-eb0758d3-d3ef-4dc9-ad4d-60f63d2d8d32-ASSET1.0.pdf
File-Format: application/pdf
File-Size: 469321
Handle: Repec:unm:umagsb:2014023
DOI: 10.26481/umagsb.2014023