Nash consistent representation of effectivity functions through lottery models

• 成果类型: Article
• 署名作者: Peleg, Bezalel; Peters, Hans
• 署名单位: Maastricht University; Hebrew University of Jerusalem; Hebrew University of Jerusalem
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2008.02.009
• 发表日期: 2009
• 页码: 503-515
• 关键词: Effectivity function; Game form; Nash consistent representation; Lottery model

摘要

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model-i.e., an effectivity function that preserves the original effectivity in terms Of Supports of lotteries-which has a Nash consistent representation. The latter means that there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions satisfying the minimal requirement of respecting first order stochastic dominance among lotteries. No additional condition on the original effectivity function is needed. (C) 2008 Elsevier Inc. All rights reserved.