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Games 2017, 8(4), 46; doi:10.3390/g8040046

Representations of Political Power Structures by Strategically Stable Game Forms: A Survey

1
Institute of Mathematics and Center for the Study of Rationality, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
2
Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel
*
Author to whom correspondence should be addressed.
Received: 1 September 2017 / Revised: 17 October 2017 / Accepted: 17 October 2017 / Published: 23 October 2017
(This article belongs to the Special Issue Choice and Decision Making)
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Abstract

We survey the results on representations of committees and constitutions by game forms that possess some kind of equilibrium strategies for each profile of preferences of the players. The survey is restricted to discrete models, that is, we deal with finitely many players and alternatives. No prior knowledge of social choice is assumed: As far as definitions are concerned, the paper is self-contained. Section 2 supplies the necessary general tools for the rest of the paper. Each definition is followed by a simple (but nontrivial) example. In Section 3 we give a complete account of representations of committees (proper and monotonic simple games), by exactly and strongly consistent social choice functions. We start with Peleg’s representations of weak games, and then provide a complete and detailed account of Holzman’s solution of the representation problem for simple games without veto players. In Section 4 we deal with representations of constitutions by game forms. Following Gärdenfors we model a constitution by a monotonic and superadditive effectivity function. We fully characterize the representations for three kinds of equilibrium: Nash equilibrium; acceptable equilibrium (Pareto optimal Nash equilibrium); and strong Nash equilibrium. We conclude in Section 5 with a report on two recent works on representations of constitutions under incomplete information. View Full-Text
Keywords: committee; simple game; constitution; effectivity function; representation; game form; social choice function; equilibrium; incomplete information committee; simple game; constitution; effectivity function; representation; game form; social choice function; equilibrium; incomplete information
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Peleg, B.; Holzman, R. Representations of Political Power Structures by Strategically Stable Game Forms: A Survey. Games 2017, 8, 46.

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