Lexicographic Composition of Simple Games
AbstractCertain voting bodies can be modeled as a simple game where a coalition's winning depends on whether it wins, blocks or loses in two smaller simple games. There are essentially five such ways to combine two proper games into a proper game. The most decisive is the lexicographic rule, where a coalition must either win in G1, or block in G1 and win in G2. When two isomorphic games are combined lexicographically, a given role for a player confers equal or more power when held in the first game than the second, if power is assessed by any semi-value. A game is lexicographically separable when the players of the two components partition the whole set. Games with veto players are not separable, and games of two or more players with identical roles are separable only if decisive. Some separable games are egalitarian in that they give players identical roles.
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Date of creation: 03 Mar 2006
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Other versions of this item:
- Barry O'Neill & Bezalel Peleg, 2006. "Lexicographic Composition of Simple Games," Cowles Foundation Discussion Papers 1559, Cowles Foundation for Research in Economics, Yale University.
- Barry O'Neill & Bezalel Peleg, 2006. "Lexicographic Composition of Simple Games," Discussion Paper Series dp415, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
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