Context dependent games as quantifiers and selection functions

Hedges, Jules ; Oliva, Paulo ; Winschel, Evguenia ; Winschel, Viktor ; Zahn, Philipp

Hedges,_Oliva,_Winschel,_Winschel,_Zahn_14-13.pdf - Published

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URN: urn:nbn:de:bsz:180-madoc-361786
Document Type: Working paper
Year of publication: 2014
The title of a journal, publication series: Working Paper Series
Volume: 14-13
Place of publication: Mannheim
Publication language: English
Institution: School of Law and Economics > Geldpolitik und Makroökonomik (Adam 2008-)
MADOC publication series: Department of Economics > Working Paper Series
Subject: 330 Economics
Classification: JEL: C0 , D01 , D03 , D63 , D64,
Keywords (English): context dependent refinement of Nash equilibrium , higher order functions , quantifiers , selection functions , beauty contest , minority game , endogenous economist
Abstract: We use quantifiers and selection functions to represent simultaneous move games. Quantifiers and selection functions are examples of higher-order functions. A higher order function is a function whose domain is itself a set of functions. Thus, quantifiers and selection func- tions allow players to form goals not only about outcomes but about the whole (or parts) of the game play. They encompass standard pref- erences and utility functions as special cases, but also extend to non-maximizing behavior and context-dependent motives. We adapt the Nash equilibrium concept to our new representation and also introduce a refinement to capture the essential features of context-dependent motives. As an example, we discuss fixpoint operations as context dependent goals of coordination and differentiation in simultaneous game variants of Keyne's beauty contest and the minority game.

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