Changes and additions
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چکیده
We consider market situations with two corners. One corner consists of a single seller with one or more identical objects, and the other corner consists of buyers who all want at most one object. We suppose that the valuation of an object for the different buyers is known by all buyers. We consider two cooperative games corresponding to such a market situation. First we study properties of the related market games. These games turn out to be special total big boss games [2,3,6]. The core of a big boss game consists of all efficient vectors between two points: the big boss point and the union point. In case the interaction between the market corners is regulated via one of the four standard auctions, the resulting pay-off allocation, coincides in all four cases with the union point, which is the best point in the core for all the buyers. The total union point is a bi-monotonic allocation scheme for the market game. Secondly, we study properties of ring games (also called peer group games [4]) which appear when bidders collude. The player set in a ring game consists only of the bidders and the game turns out to be a convex game of a special type. Characterizations of the Shapley value [5] and the compromise value [1] for such games can be given in terms of the valuation vector of the market situation. If the seller has only one object, a duality relation between the market game and the ring game exists.
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تاریخ انتشار 2005