7/16/2008 - John Nash. Roger Myerson. Robert Aumann. Eric Maskin. Just some of the quantitative luminaries on hand for the Game Theory Society’s Third World Congress
, hosted by the Kellogg School from July 13-17.
In addition to Nobel Prize-winning economists, several hundred other leading economists and mathematicians from around the world converged on Evanston for the “largest meeting of game theorists ever held,” according to Ehud Kalai
, the James J. O’Connor Professor of Decision and Game Sciences who helped found the Game Theory Society in 1998 and the Congress in 2000. The Congress meets every four years to promote the investigation, teaching and application of game theory, said Kalai.
|Professor Roger Myerson earned a 2007 Nobel Prize for economics research that he conducted during his 25-year tenure at the Kellogg School.|
|Photo © Rich Foreman|
|Professor Robert Aumann won a Nobel Prize in 2005 for his work to elucidate the dynamics of cooperation and conflict using game theoretic tools.|
|Photo © Rich Foreman|
This year, nearly 700 presentations — including one by Nash, considered a pioneering figure — gave participants insight into the thinking that continues to define game theory, an applied mathematical science founded some 60 years ago that studies strategic interaction in competitive and cooperative environments. Game theory’s influence and applicability have extended broadly across areas ranging from mathematics and computer science to various social and biological sciences.
Kalai, who joined Kellogg in 1975 and is founding editor of Games and Economic Behavior
, a top journal in game theory, moderated a July 14 “Nobel” panel discussion at the Congress that featured Myerson, Aumann and Maskin. Before a standing-room-only audience in the Donald P. Jacobs Center, panelists took stock of game theory’s contributions to date and contemplated how the field might develop in the years ahead.
To gauge game theory’s future, Myerson, an economist at the University of Chicago who was a member of the Kellogg School’s Managerial Economics and Decision Sciences
Department from 1976 until 2001, made a tongue-in-cheek proposition about “handing the microphone around” to audience members to learn about their recent, as-yet-unpublished research. He went on to state that game theory has seen “less fundamental breakthroughs” in the last 15 years in part because of “significant early gains.” He added that game theorists could find new ways to make contributions, particularly in designing good models that account for political phenomena or help address social problems.
During his tenure at Northwestern, Myerson conducted the research into mechanism design — the study and design of system rules — for which he earned the 2007 Nobel Prize, sharing the honor with fellow panelist Maskin, as well as Leonid Hurwicz, a former professor of economics at the University of Minnesota who died June 24.
Maskin, a Princeton University economist, noted game theory’s contributions along both theoretical and applied lines. In particular he outlined the value of global games, a kind of game defined by incomplete information among the players, and one with applications in economics, including with respect to currency crises and speculative market bubbles. He also said that another kind of game, called repeated games, had made a significant and broad impact.
Looking ahead, Maskin said he sees the challenges facing game theory as being “more conceptual and not always terrifically well defined.” He said there was value in bringing cooperative game theory — a major area of the discipline that stands in contradistinction to noncooperative games — back “into the mainstream,” where in recent years, according to Maskin, it has been eclipsed largely by a noncooperative focus. He said that cooperative games were important for helping address externalities in economic thought, something that he said noncooperative games “couldn’t handle very well” despite being theoretically “very beautiful.”
“Cooperative game theory, by its very nature, takes a broader view,” said Maskin, adding that another area of economics — behavioral — had demonstrated considerable development but remained “just a collection of anomalies” at the moment. Maskin said he would like to see efforts to integrate behavioral economics within game theory.
For his part, Myerson pointed out “a big problem” facing game theorists who are educating the next generation of scholars: “What models do you want to teach undergraduates?” he asked. “The question of how you export game theoretic insights in systematic ways for students who are not going to be game theorists, that’s our job.”
Aumann, a professor at the Hebrew University of Jerusalem who earned his Nobel Prize in 2005 for work in enhancing the understanding of cooperation and conflict using game theoretical analyses, reminded the audience that “some disciplines, like mountain climbing … have very visible challenges,” making it easier to see the road ahead. For game theory, and indeed for most sciences, Aumann said it’s less evident how the field will develop. “It doesn’t become obvious what’s important until much later,” said Aumann, providing an example from genetic research: “Before the discovery of DNA, you couldn’t say ‘Go discover DNA.’”
Thomas Schelling, University of Maryland economist and co-recipient of the 2005 Nobel with Aumann, was also scheduled to participate in the panel discussion, but travel difficulties prevented him from appearing.
During the Congress, John Nash also presented a new paper on “three-person cooperative games.” Nash, who made pathbreaking mathematical contributions that proved foundational for game theory, is perhaps best known to general audiences through the 2001 film, “A Beautiful Mind,” which was based on his life. He shared the 1994 Nobel Prize in economics. Another groundbreaking figure in the field, Lloyd Shapley, professor emeritus of mathematical economics at the University of California, Los Angeles, also delivered a lecture at the Congress, revisiting stable sets, an element in cooperative games.
Kalai said the diverse presentations during the Congress demonstrate game theory’s enduring applicability across many areas, something he said was not surprising.
“Just like older mathematical areas, such as statistics, the definition of a game is general and can be applied in many different contexts involving different types of players and different games,” Kalai said. As evidence, he cited the Nobel panel’s discussion of game theory’s wide influence, including in the areas of economics, politics, computer science, networks and anthropology.
“In a way, this panel served as an abstract of the entire Congress, where the issues highlighted were discussed in depth by studying a large variety of models with full attention to technical and conceptual detail,” Kalai said.