Horse trading game with large seller:- 

Consider the variant of the horse trading game in which there is a single owner who has two horses.  Assume that the owner's payoff is σ₁ + r if she keeps one of her horses and 2σ₁ + r if she keeps both of them, where r is the amount of money she receives. Assume that there are at least two non owners, both of whose values of a horse exceed σ₁. Find the core of this game. (Do all trades take place at the same price, as they do in a competitive equilibrium?)