The boundary of the core of a balanced game: face games

Miguel Ángel Mirás Calvo, Carmen Quinteiro Sandomingo () and Estela Sánchez Rodríguez
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Miguel Ángel Mirás Calvo: Universidade de Vigo
Carmen Quinteiro Sandomingo: Universidade de Vigo
Estela Sánchez Rodríguez: Universidade de Vigo

International Journal of Game Theory, 2020, vol. 49, issue 2, No 9, 579-599

Abstract: Abstract This paper extends the concept of face games, introduced by González-Díaz and Sánchez-Rodríguez (Games Econ Behav 62:100–105, 2008) for convex games, to the general class of balanced games. Each face of the core is the core of a face game and contains the best stable allocations for a coalition provided that the members of the complement coalition get their miminum worth inside the core. Since face games are exact we investigate several properties of the exact envelope of a balanced game that allow us to characterize exactness, convexity and decomposability of a game in terms of its face games. The close connection between extreme points of the core and extreme points of the face games is analyzed. In particular, we show that the marginal vectors that belong to the core and the lexinal vectors must be marginal vectors and lexinal vectors, respectively, of the single player face games. Finally, we present several subclasses of games where face games could provide some insight on the core structure.

Keywords: Coalitional games; Core; Face games; Exact games; Decomposable games; Marginal vectors; Lexinal vectors; Extreme core points (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00182-019-00703-2

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