Collaborative Research: Bargaining and Reputation in Stochastic Games

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This research addresses one of the most ubiquitous problems in social science: how do two parties divide the gains that can be achieved through cooperation? The two parties may be neighbors discussing drainage, fencing or greenery, a corporation and its supplier considering investments that would enhance their business relationship, a union and a firm bargaining over wages and benefits, or two countries negotiating a trade agreement. Nobel Laureate John Nash showed almost fifty-five years ago that, for a simple class of bargaining problems, two branches of game theory ("cooperative" and "noncooperative") agreed on how the surplus from cooperation should be divided. Since that time, numerous developments in economics have lent support to the results Nash obtained. A major limitation of the analysis is that it is restricted to "static" situations, where the two parties' actions, and the world they inhabit, are completely unchanging. In other words, there is no scope for thinking about investments, learning by doing, economic growth, technological change or global warming. This Proposal moves the investigation from static strategic settings to dynamic situations called stochastic games. These models are sufficiently flexible to capture any of the phenomena mentioned above. The first step is to rephrase the classic results of Nash in an intertemporal (albeit unchanging) setting. Next, one needs to allow for all the complexities of a stochastic game, and express the strategic situation as a family of interlocking Nash bargaining problems. If that can be done, a full solution should emerge in a manner analogous to what happens in the original static analysis of Nash. Nash shed light not only on how the benefits of cooperation would be shared, but also on what each party will do to gain maximum advantage in negotiations. This research project will similarly generate predictions regarding behavior before a contract is signed. Applications include the speed at which patent races are fought, destructive behavior by negotiating parties, and the development of aggressive weaponryThe broader impact of this research is the development of a new game theory tool that will be of great use to social scientists and policymakers who seek to understand how individuals and nations compete over time.