We examine the structure of the core of a trading economy with three competitive equilibria as the number of traders (N) is varied. The core first splits into two pieces at N = 5 and then splits a second time into three pieces at N = 12. Both of these splits occur not at a point but as a contiguous gap. We find that the speed of convergence of the core toward the three competitive equilibria is...

Infinite time horizon stationary cooperative games are considered where at each date the instantaneous NTU-game is determined by the state of nature. The strong sequential core selects those utility streams that no coalition can improve upon by deviating at any moment in time. The main result of the paper states that the strong sequential core is non-empty provided that (i) the instantaneous NT...

All quasivalues rest on a set of three basic axioms (efficiency, null player, and additivity), which are augmented with positivity for random order values, and with positivity and partnership for weighted values. We introduce the concept of Möbius value associated with a sharing system and show that this value is characterized by the above three axioms. We then establish that (i) a Möbius value...

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. ...

We propose a class of sharing schemes for the distribution of the gains from cooperation for coalition games with externalities. In the context of the partition function, it is shown that any member of this class of sharing schemes leads to the same set of stable coalitions in the sense of d’Aspremont et al. (1983). These schemes are “almost ideal” in that they stabilize these coalitions which ...

I consider the problem of assigning agents to indivisible objects, in which each agent pays a price for his object and all prices sum to a given constant. The objective is to select an assignment-price pair that is envyfree with respect to the agents’ true preferences. I propose a simple mechanism whereby agents announce valuations for all objects and an envy-free allocation is selected with re...

This paper reinterprets the γ -core (Chander and Tulkens in Int Tax Pub Financ 2:279–293, 1995; in Int J Game Theory 26:379–401, 1997) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. The problem of coalition formation is formulated as an infinitely repeated game in which the players must choose whether to co...

In Lowest-Unmatched Price Auctions (LUPA) all participants pay a bidding fee and the lowest bid placed by only one participant wins. Many LUPAs do not specify what happens with the item on offer if there is no unmatched bid. The item may remain with the auctioneer which may appear unfair given that the auctioneer collects the bidding fees. We show that in a symmetric Nash equilibrium of a LUPA ...

We consider envy-free and budget-balanced allocation rules for problems where a number of indivisible objects and a fixed amount of money is allocated among a group of agents. In “small” economies, we identify under classical preferences each agent’s maximal gain from manipulation. Using this result we find the envy-free and budget-balanced allocation rules which are least manipulable for each ...

When an agent decides whether to join a coalition or not, she must consider both i) the expected strength of the coalition and ii) her position in the vertical structure within the coalition. We establish that there exists a positive relationship between the degree of inequality in remuneration across ranks within coalitions and the number of coalitions to be formed. When coalition size is unre...