Cores of convex and strictly convex games

Abstract

Abstract:We follow the path initiated in Shapley (1971) and study the geometry of the core of convex and strictly convex games. We define what we call face games and use them to study the combinatorial complexity of the core of a strictly convex game. Remarkably, we present a picture that summarizes our results with the aid of Pascal's triangle.JEL classification: C71.

A Bankruptcy Approach to the Core Cover

“…In this paper, we establish that all bankruptcy face games are new bankruptcy games. Combining the results of González-Díaz and Sánchez-Rodríguez (2008) and Theorem 3.2, we obtain that the core cover of a compromise admissible game can also be rebuilt with the core covers of some specific bankruptcy games.…”

“…Given a game (N, v) with a non-empty core and a coalition T ⊂ N, a T-face game is defined in such a way that the core of this T-face game coincides with the core allocations of the game (N, v) that provide the best payoff for coalition T and the worst payoff for its complementary coalition N \ T. González-Díaz and Sánchez-Rodríguez (2008) showed that the core of convex games can be rebuilt with the cores of the face games. Any face game is related to a specific coalition T, and there are so many face games as coalitions.…”

The Triple Helix of innovation as a double game involving domestic and foreign actors

“…② This could not apply to the case of the Triple Helix domestic and foreign games; otherwise, one would reach a total number of papers higher than the number of publications within the system. Thirdly, Shapley (1965Shapley ( , 1971) stated that a convex game is decomposable (therefore, may split into its finest components) and demonstrated that a strictly convex game is indecomposable (see also González-Díaz & Sánchez-Rodríguez, 2008). Because a Triple Helix game where all the bilateral and the trilateral relationships exist is strictly convex (cf., Mêgnigbêto, 2024), it is indecomposable.…”