an:05575953
Zbl 1173.91372
Liggett, Thomas M.; Lippman, Steven A.; Rumelt, Richard P.
The asymptotic Shapley value for a simple market game
EN
Econ. Theory 40, No. 2, 333-338 (2009).
00250825
2009
j
91B26 91A12 91A40 60F99
simple market game; buyers; sellers; Shapley value; limit theorem
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.
Tadeusz Radzik (Jelenia G??ra)