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Title:
Plenary Talk: Fair Division and Allocation
Speaker:
Abstract:
In this talk, I will introduce the mathematics and applications of bankruptcy problems and matching problems.
When a firm goes bankrupt, the firm’s assets are divided among the firm’s creditors based on how much each creditor is owed. This is known as the bankruptcy problem. The history of bankruptcy problems dates back 2000 years to a passage in the Babylonian Talmud. We will consider the history of the Talmud problem and its relationship to cooperative game theory. As an application, we will connect bankruptcy problems to the problem of reparations. Further, we will design a mechanism to apply noncooperative game theory to award travel funds, a problem that is similar to a bankruptcy problem.
David Gale and Lloyd Shapley introduced the stable marriage problem and an algorithm to match spouses in a stable way. The algorithm had been in use by the National Resident Matching Program (The Match) to match doctors to hospital residency training programs before the Gale-Shapley article. We will review the Gale-Shapley algorithm and discuss the application of algorithms to solve the school choice problem of matching students to public schools (as used in Boston and New York).
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