Collaborative Research: Bargaining and Reputation in Stochastic Games

这项研究解决了社会科学中最普遍存在的问题之一：双方如何分配通过合作获得的收益？双方可能是讨论排水、围栏或绿化的邻居，可能是一家公司和它的供应商考虑投资以加强他们的商业关系，可能是一个工会和一家公司就工资和福利讨价还价，也可能是两个国家在谈判一项贸易协定。诺贝尔奖得主约翰·纳什（John Nash）在大约55年前就表明，对于一类简单的议价问题，博弈论的两个分支（“合作”和“非合作”）对如何分配合作产生的剩余达成了一致。从那时起，经济学的许多发展为纳什的结论提供了支持。该分析的一个主要局限是它仅限于“静态”情况，即双方的行动和他们所处的世界是完全不变的。换句话说，没有考虑投资、在实践中学习、经济增长、技术变革或全球变暖的余地。这一建议将调查从静态战略设置转移到称为随机博弈的动态情况。这些模型足够灵活，可以捕捉上述任何现象。第一步是在跨期（尽管不变）的背景下重新表述纳什的经典结果。接下来，我们需要考虑到随机博弈的所有复杂性，并将战略情况表达为一系列连锁的纳什议价问题。如果能做到这一点，一个完整的解决方案应该以类似于纳什最初的静态分析的方式出现。纳什不仅阐明了如何分享合作的好处，而且阐明了各方将如何在谈判中获得最大利益。这个研究项目同样会在签订合同之前产生关于行为的预测。应用包括专利竞争的速度，谈判各方的破坏性行为，以及攻击性武器的发展。这项研究的更广泛影响是开发了一种新的博弈论工具，对于那些试图了解个人和国家如何随着时间的推移而竞争的社会科学家和政策制定者来说，这将是非常有用的。

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.