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Econ Theory (2017) 63:191209
DOI 10.1007/s00199-016-1010-3
RESEARCH ARTICLE
Received: 21 September 2014 / Accepted: 9 July 2016 / Published online: 5 November 2016 The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract We provide a new proof of the nonemptiness of approximate cores of games with many players of a nite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their balanced cover games, which are nonempty, can be approximated by equal-treatment -cores of the games themselves. Our proof is novel in that we develop a limiting payoff possibilities set and rely on a xed point theorem.
Keywords NTU games Core Approximate cores Small group effectiveness
Coalition formation Payoff-dependent balancedness
JEL Classication C71 C78 D71
The authors are indebted to Alexander Kovalenkov, Konrad Podczeck, Arkadi Predtetchinski, Philip Reny, and seminar and conference participants at Fundao Getulio Vargas, Warwick, PET (2011), and SAET (2011) for helpful comments. The second author is indebted to the Douglas Grey Fund for Research in Economics at Vanderbilt University for nancial support.
B Nizar Allouch
Myrna Wooders [email protected] http://www.myrnawooders.com
1 School of Economics and Finance, Queen Mary University of London, London, UK
2 Department of Economics, Vanderbilt University, Nashville, TN, USA
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Web End = On the nonemptiness of approximate cores of large games
Nizar Allouch1 Myrna Wooders2
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192 N. Allouch, M. Wooders
1 Introduction
The core is an anchoring concept in game theory going back, in its origins, to Edge-worths contract curve, and the contributions of Debreu and Scarf (1963) and Aumann (1964). The core remains a central concept in economics and most recently, in market design; see, for example, Roth (2002). Even in games with many, but nite numbers of players, however, the core may be empty. The addition of a single player to a large game with a nonempty core may result in a game with an empty core. The problem of the emptiness of the core is especially salient in economies with public goods subject to congestion and exclusion (local public goods) or in economies with clubs. Even in pure exchange economies, the nonemptiness of the core can depend on whether commodities are innitely divisible. It...