Horse trading game with single seller:-

Find the core of the variant of the horse trading game in which there is a single owner, whose valuation is less than the highest valuation of the non owners.

If you have studied economics you know that this outcome is the same as the "competitive equilibrium". The theories differ, however. The theory of competitive equilibrium assumes that all trades take place at the same price. It defines an equilibrium price to be one at which "demand" (the total number of nonowners whose valuations exceed the price) is equal to "supply" (the total number of owners whose valuations are less than the price).

This equilibrium may be justified by the argument that if demand exceeds supply then the price will tend to rise, and if supply exceeds demand it will tend to fall. Thus in this theory, "market pressures" generate an equilibrium price; no agent in the market chooses a price.

By contrast, the coalitional game we have studied models the players' actions explicitly; each group may exchange its horses and money in any way it wishes. The core is the set of actions of all players that survives the pressures imposed by the trading opportunities of each possible group of players. A uniform price is not assumed, but is shown to be a necessary property of any action in the core.