: (a) equivalence of the core and the set of competitive outcomes; (b) the Shapley value is contained in the core or … approximate cores; (c) the equal treatment property holds -- that is, both market equilibrium and the core treat similar players …

of approximate core payoffs (the equal treatment property). The conditions are: (a) essential superadditivity -- an … core. …

game, a payoff is in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any … coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered … core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are …

and Wooders (1986) to obtain nonemptiness of the core of the economy. We then demonstrate, under the stronger condition of … strict small group effectiveness, that the equal treatment core coincides with the set of price-taking equilibrium outcomes … equilibrium follows from nonemptiness of the core and equivalence of the core to the set of equilibrium outcomes. Our approach …