Roger McCain, Ph.D., professor of economics, wrote a book that will be released by World Scientific in 2013 titled Value Solutions in Cooperative Games.
When people work together cooperatively, their joint action typically creates an additional value beyond what they could obtain individually. A value solutionis a mathematical model of the way they share out the common benefit. McCain explains that the classical instance of a value solution was provided by this year’s Nobel Laureate in economics, Lloyd Shapley.
McCain’s book begins with two chapters of review of key models, stressing the role of bargaining power. The chapters that follow explore a number of extensions and applications from his own recent research.
The research for this book began in November 2008, when McCain started work on a computer program based on Shapley’s approach which also adapted also ideas from Eric Maskin (Nobel 2007) and Reinhard Selten (Nobel 1994) – “pretty good sources,” he notes. McCain says he expected to complete the program in just a few days, but it took about four months, and the result was disappointing. However, it suggested other directions that kept Dr. McCain busy for almost three years.
McCain explains he thought his result was too mechanical. “I felt that the model needed to leave room for creativity. I went back to the lesser-known work of David Schmeidler, which I had used and extended in an earlier book I wrote that was published in 2009, Game Theory and Public Policy, and I was able to synthesize that approach with one that has roots in ideas from John Nash (Nobel 1994) extended by Al Roth (Nobel 2012) and Jan Svejnar,” who McCain notes is an old friend. “That gave rise to a very complicated mathematical model, but one that I think is applicable.”
While he waits for this book to hit the shelves, McCain is wasting no time. He’s working on his next book, which will be published by Elgar and is tentatively titled Economic Action as Imperfect Cooperation. McCain says this one will be much less mathematical, and one objective will be to draw together ideas from a number of different schools of economic thought, including, of course, game theory.