Game theoretic analysis of voting in committees
In: Econometric Society monographs 7
In: Econometric Society monographs in pure theory
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In: Econometric Society monographs 7
In: Econometric Society monographs in pure theory
In: Theory and decision library
In: Series C: Game theory, mathematical programming and operations research 34
In: Mathematical social sciences, Band 47, Heft 3, S. 275-287
In: Handbook of Social Choice and Welfare, S. 395-423
In: Freedom in Economics; Routledge Studies in Social and Political Thought
In: Mathematical social sciences, Band 11, Heft 1, S. 83-87
In: Studies in choice and welfare
This monograph studies representations of effectivity functions by game forms that are at least Nash consistent, which means that they have a Nash equilibrium for any profile of preferences. In the second part the focus is on social choice functions that admit a strong Nash equilibrium resulting in the sincere outcome. A central interpretation of an effectivity function is that it models a constitution.
In: Working papers 230
In: Mathematical social sciences, Band 95, S. 37-46
In: Research in economics: Ricerche economiche, Band 71, Heft 1, S. 43-50
ISSN: 1090-9451
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.
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In: Studies in Choice and Welfare; Strategic Social Choice, S. 97-103
In: Studies in Choice and Welfare; Strategic Social Choice, S. 81-94