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The asymptotic Shapley value for a simple market game. (English) Zbl 1173.91372
Authors’ abstract: We consider the game in which $$b$$ buyers each seek to purchase 1 unit of an indivisible good from $$s$$ sellers, each of whom has $$k$$ units to sell. The good is worth $$0$$ to each seller and 1 to each buyer. Using the central limit theorem, and implicitly convergence to tied down Brownian motion, we find a closed form solution for the limiting Shapley value as $$s$$ and $$b$$ increase without bound. This asymptotic value depends upon the seller size $$k$$, the limiting ratio $$b/ks$$ of buyers to items for sale, and the limiting ratio $$[ks-b]/\sqrt{b+s}$$ of the excess supply relative to the square root of the number of market participants.

##### MSC:
 91B26 Auctions, bargaining, bidding and selling, and other market models 91A12 Cooperative games 91A40 Other game-theoretic models 60F99 Limit theorems in probability theory
##### Keywords:
simple market game; buyers; sellers; Shapley value; limit theorem
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##### References:
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