Lexicographic Composition of Simple GamesBarry O'Neill and Bezalel Peleg () Discussion Paper Series from Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem Abstract: A two-house legislature can often be modelled as a proper simple game whose outcome depends on whether a coalition wins, blocks or loses in two smaller proper simple games. It is shown that there are exactly five ways to combine the smaller games into a larger one. This paper focuses on one of the rules, lexicographic composition, where a coalition wins in G1 => G2 when it either wins in G1, or blocks in G1 and wins in G2. It is the most decisive of the five. A lexicographically decomposable game is one that can be represented in this way using components whose player sets partition the whole set. Games with veto players are not decomposable, and anonymous games are decomposable if and only if they are decisive and have two or more players. If a player's benefit is assessed by any semi-value, then for two isomorphic games a player is better off from having a role in the first game than having the same role in the second. Lexicographic decomposability is sometimes compatible with equality of roles. A relaxation of it is suggested for its practical benefits. New Economics Papers: this item is included in nep-cdm and nep-fin Published in Games and Economic Behavior, 2008, vol. 62, pp. 628-642. Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: http://EconPapers.repec.org/RePEc:huj:dispap:dp415 Access Statistics for this paper More papers in Discussion Paper Series from Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem |
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