Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly … dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this … von Neumann-Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present roommate …

coincide and give the midpoint between the buyers-optimal core allocation and the sellers-optimal core allocation, and thus … they belong to the core. Moreover, under the assumption that all agents in the market are active, the subset of core … set of stable allocations where each agent is paid at least half of his maximum core payoff. All allocations in this last …

geometric and algebraic structure of the core, which is always nonempty. We also characterize the extreme points of the core and … we show that prices that are obtained from core allocations are competitive and vice versa. …

We provide a different axiomatization of the core interpreted as a reasonable set (Milnor, 1952) and introduce a new … particular, it is shown that the core is the only solution satisfying projection consistency, reasonability, max-intersection and …

matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only … if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts … have been proposed to extend the core to all roommate markets (including those with an empty core). An important …

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set … of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core … generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications …

-solution exists and is unique. It belongs to the bargaining set and to the core whenever the latter is not empty. In fact, when the …

division core (Selten, 1972). …

matching, a stable set is defined as the union of the core of the game and the core of the subgames that are compatible with … this matching. All these stable sets exclude third-party payments and form a lattice with respect to the same partial order … usually defined on the core. …