Socially Structured Games

Abstract

ABSTRACT. We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power.We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core.We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera.KEY WORDS: balancedness, core, non-transferable utility game, social stability.JEL CLASSIFICATION: C71.

Payoff-dependent balancedness and cores

“…Other contributions in various fields deal with core selections, see for instance Herings et al (2007), Ichiishi and Idzik (2002), Kannai and Wooders (2000), Page and Wooders (1996), Reny and Wooders (1998). The incorporation of appropriate transfer rate rules might lead to a unified treatment to describe core selections (e.g.…”

Cooperative game theory for sharing transmission charges in electricity markets

“…Correct choice of pay-off vector to share TSC ensures maximum benefit to all participants and hence stable operation. SSTU games [4][5][6] are cooperative games which maintain stability of coalitions by removing incentives for economic or social deviations. The solution to this game is a mapping which assigns a set of pay-off distributions over the players, assuring stability.…”