The Shapley-Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core. In this paper we generalize this result by distinguishing equivalence classes of balanced games that share the same core structure. We then associate a system of linear...

This paper follows the interpretation of the bankruptcy problems in terms of TU games given in O'Neill (1982). In this context we propose the analysis of the Transition Game associated to each bankruptcy problem. We explore an old solution described by Ibn Ezra in the XII century. Firstly, we...

A 2law of scarcity2 is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we demonstrate conditions under which all payoffs in the core of any game in a parametized collection have an equal treatment property and show that equal...

Solutions for cooperative games with side-payments can be manipulated by merging a coalition of players into a single player, or, conversely, splitting a player into a number of smaller players. This paper establishes some (im-)possibility results concerning merging- or splitting-proofness of...

A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally...

In this note we study uncertainty sequencing situations, i.e., 1-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et...

The simplest and most common interpretation of a coalitional form game is that it pertains to a single interaction among the players. However, many if not most cooperative endeavors occur more than once or even repeatedly over time. In this paper we begin a systematic study of dynamic...

We consider a communications network in which users transmit beneficial information to each other at a cost. We pinpoint conditions under which the induced cooperative game is supermodular (convex). Our analysis is in a lattice-theoretic framework, which is at once simple and able to encompass a...

The two most fundamental questions in cooperative game theory are: When a game is played, what coalitions will be formed and what payoff vectors will be chosen? No previous solution concepts or theories in the literature provide satisfactory answers to both questions; answers are especially...

In a seminal paper relating economic and game theoretic structures, Shapley and Shubik (1969) demonstrate that a game is a market game -- that is, a game derived from a finite-dimensional private goods exchange economy where all participants have continuous, concave utility functions. In this...