L. S. Shapley與M. Shubik於論文[2]所提出的指派賽局適用於描述一個由持有貨品者與非持有貨品者雙方所構成的交易市場，並且此市場中的貨品是不可被分割的。論文[2][3]證明了指派賽局之核心解恰巧就是某種線性規劃的解集合。可是論文[2][3]並沒有提出指派賽局之核心解的明確表示方式。而在這篇論文中，我們考慮一種推廣的指派賽局。在此賽局中，貨品具有同質性而且每一位持有貨品者可以持有超過一單位的貨品。本篇論文提出在一組給定的參數下，此賽局之核心解的明確表示法。

Shapley and Shubik [2] propose a famous game called the assignment game. Such a game models two-sided markets in which multiple units of an indivisible good are traded
between owners and nonowners. In [2][3], it is shown that the core of the assignment game can be obtained by solving a linear programming problem. Nonetheless, no explicit expression of the core of the assignment game is given. In this thesis, we consider a variant of the assignment game in which the goods are homogenous and each owner is allowed to have more than one unit of the good. This thesis provides an explicit expression of the core for a special case.

Abstract i
Contents ii
1 Introduction 1
2 The Assignment Game and a Horse Trading Market 3
3 The Core of a Horse Trading Game for a Special Case 7
4 Conclusion 10
Bibliography 11

[1] A. E. Roth and M. A. O. Sotomayor, Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge, UK: Cambridge University Press, 1990.
[2] L. S. Shapley and M. Shubik,“The assignment game I: The core,”International Journal of Game Theory, vol. 1, pp. 111–130, 1971/72.
[3] M. Kaneko,“On the core and competitive equilibria of a market with indivisible goods,”Naval Research Logistics Quarterly, vol. 23, pp321–337, 1976.
[4] M. J. Osborne, An Introduction to Game Theory, New York, NY: Oxford University Press, 2009.