The University of Windsor’s Christian Trudeau says he’s honored to be featured in an upcoming special journal issue commemorating Nobel Prize-winning economist Lloyd Shapley.
The issue, scheduled to be published early this year in Games and Economics Behavior, will contain original research articles related to the many contributions Dr. Shapley made during his career.
“I had never met Dr. Shapley personally but I’ve read tons of his work,” Dr. Trudeau said. “To be associated, even as far as this to what he’s done, is a great honour.”
Shapley won the 2012 Nobel Memorial Prize in Economics Sciences with Alvin E. Roth for his contributions in the theory of stable allocations and the practice of market design. He died in March 2016 at the age of 92.
When Trudeau learned of the memoriam issue, he was elated to find he had a nearly finished paper fitting all the criteria.
The paper relates the two classic sharing problems, the assignment and bankruptcy problems, and is titled From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution. The assignment problem attempts to efficiently match buyers with sellers. The bankruptcy problem looks at sharing an endowment among people who have claims for it, with the sum of the claims totalling more than the endowment.
“The assignment problem was first proposed by Shapley in the ‘60s and I’m showing a mathematical equivalence between the two models which allows us to go a bit deeper and propose some interesting mechanisms,” Trudeau said.
An example of the assignment problem can be seen in the residential housing market. Trudeau considers a scenario where housing prices are set outside of the market, by the government, for example.
In his paper, Trudeau shows that setting the price at which the unit will be sold and sharing the surplus that the buyer and seller generate by trading with each other is mathematically equivalent to settling a bankruptcy or inheritance problem: the endowment being the surplus generated by the trade, and the claims being the surplus agents can obtain with other trading partners.
Trudeau is the first to point out this link and uses it to show that a method to choose prices in the assignment problem is equivalent to the well-studied concede-and-divide method for the bankruptcy problem.
“The prices proposed for the assignment problem now have a much simpler interpretation,” Trudeau said. “After compensating the buyer and seller for their market power, we split equally what remains of the gain to trade with each other.”
A date has not yet been set for the journal’s publication, but Trudeau’s article can be read on Leddy Library’s online library catalogue.
“Professor Shapley has changed the way we approach many economics problems, and I’m happy to be among the many still working on the questions he was the first to look at,” Trudeau said.