assignment game. We consider the Core, three other notions of group stability and two alternative definitions of competitive … equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper …

-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set … competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive …

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 …

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 … usually defined on the core. …

. Those max-payoff vectors that are efficient turn up to give the extreme core allocations of the market. When the assignment … market has large core (that is to say, the assignment matrix is dominant diagonal and doubly dominant diagonal) all the max …-payoff vectors are extreme core allocations. …

The core of an assignment market is the translation, by the vector of minimum core payoffs, of the core of another … of the canonical representative by the vector of minimal core payoffs. …

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 extend Jackson and Watts's (2002) result on the coincidence of S-stochastically stable and core stable networks from … marriage problems to roommate problems. In particular, we show that the existence of a side-optimal core stable network, on …