On the testable implications of collective choice theories
type: Item
instance of: scholarly article
title: On the testable implications of collective choice theories
zbMATH Open document ID: 0976.91014
author: Yves Sprumont
published in: Journal of Economic Theory
publication date: 2000-12-03T00:00:00Z
review text: Consider the case of two agents whose set of all conceivable actions are finite sets \(A_1\), \(A_2\), respectively; the agents' preferences are not observable; what is observed is the choice made by agents when the set of feasible actions \(B_1\), \(B_2\) alter: a joint choice function \(f\), which records for every possible pair of feasible sets \(B_1\), \(B_2\) the joint actions selected from \(B_1\times B_2\). Given a particular \(f\), it is asked whether the agents are behaving cooperatively or non-cooperatively. Non-cooperative behavior to a Nash equilibrium while cooperative behavior is related to a Pareto optimum. Formally, a joint choice function \(f\) is Nash-rationalizable if there exist preferences on \(A_1\times A_2\), one for each agent such that the joint actions selected by \(f\) from \(B_1\times B_2\) for each \(B_1\), \(B_2\) are precisely the Nash equilibria of the normal form game defined by \(B_1\), \(B_2\) and the restriction of the proposed preference to \(B_1\times B_2\). Similarly when the joint actions selected by \(f\) from \(B_1\times B_2\) coincide with the Pareto ptima of the game corresponding to \(B_1\), \(B_2\) for each \(B_1\), \(B_2\), \(f\) is said to be Pareto-rationalizable. It is shown for the two agent case if any joint choice function is Nash rationalizable, it is also Pareto rationalizable. Next, the paper allows for any number of agents and non-deterministic choice. Necessary and sufficient conditions for a joint choice function to be Nash-rationalizable are identified; for cooperative behavior, every choice function is remarkable to be partially Pareto-rationalizable.
reviewed by: Anjan Mukherji
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 1538239
zbMATH Keywords: Nash-rationalizable
zbMATH Keywords: Pareto-rationalizable
MaRDI profile type: Publication
full work available at URL: jeth.2000.2657
OpenAlex ID: W1973871892
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DOI: 10.1006/JETH.2000.2657
description: scientific article; zbMATH DE number 1538239