Collaborative Research: On Experience-Weighted Attraction Learning in Games

在战略形势下，个人、公司或国家关心别人可能会做什么。这种情况的例子包括讨价还价，需要协调各种活动的商业决策，或“信号游戏”，其中人们采取的行动表明了他们的能力或意图。在过去的几十年里，大量的数学“博弈论”已经发展起来，研究人们在这些情况下如何做出选择。然而，这些理论通常假设人们知道或能够弄清楚其他人在战略情况下可能会如何表现。事实上，人们通常通过从经验中学习来了解别人可能会做什么。我们的项目提出了一个关于这种学习如何发生的一般理论。这一理论结合了两种截然不同的力量——“强化”和“信念学习”，前者指的是成功的策略会被重复，后者指的是玩家通过跟踪其他人的行为来推测其他人未来会做什么，然后选择在猜测正确的情况下回报最大的策略。50年来，人们一直认为这些不同的学习方式是不同的。在早期nsf资助的研究中，我们发现这两种理论实际上是一种特殊的学习方式，即“经验加权吸引”（EWA）学习。目前的研究建议从三个方面扩展EWA理论——将不同的人可能以不同的方式学习这一明显的事实纳入其中；为了将这一理论扩展到人们不确定不同选择的回报是什么（这当然更现实）的情况；让人们有可能意识到，当他们了解对手在做什么时，他们的对手也在学习。当这些扩展被纳入其中时，我们将有一个非常通用的学习理论，它可以解释人们讨价还价、协调和相互传递信号的方式随着时间的推移而变化。

In strategic situations, people, firms, or nations care about what others are likely to do. Examples of such situations include bargaining, business decisions which require coordinating various activities, or 'signaling games' in which the actions people take signal something about their abilities or intentions. In the last few decades, a large body of mathematical 'game theory' has developed about how people will make choices in these situations. However, these theories generally assume that people know or can figure out how other people in the strategic situation are likely to behave. In fact, people usually figure out what others are likely to do by learning from experience. Our project proposes a general theory of how this learning occurs. The theory combines two very different forces - 'reinforcement,' which means that successful strategies will be repeated, and 'belief learning,' which means that players keep track of what other people have done to figure out what those people will do in the future, then they choose strategies which will give the biggest payoff if their guesses are right. These different types of learning were thought to be different for about 50 years. In earlier NSF-funded research, we discovered that the two theories are actually special kinds of a single kind of learning, 'experience weighted attraction' (EWA) learning. The current research proposes to extend the EWA theory in three ways -- to incorporate the obvious fact that different people may learn in different ways; to extend the theory to cases where people aren't sure what the payoffs from different choices are (which is of course more realistic); and to allow the possibility that people realize, as they learn about what their opponents do, that their opponents are learning also. When the extensions are incorporated we will have a very general theory of learning which can explain the way people bargain, coordinate, and signal to each other changes over time in response to experience.