Ambiguity in Games: The Role of Uncertainty in Strategic Interactions

不确定性在战略冲突中起着至关重要的作用，无论是以环境不确定性的形式，还是以战略选择的不确定性形式。在许多现实世界的冲突中，不可能用概率模型来建模不确定性；相反，代理人面临着所谓的奈特不确定性或(模型)模糊性：参与者并不确切地知道结果的概率分布。在社会冲突中，我们经常会有环境变量，如过去的经验、预演交流或文化规范，这些变量会影响均衡结果，但不是模型回报的直接组成部分。因此，将这种模型的不确定性或模糊性纳入战略冲突的分析中是很重要的。该项目旨在发展一种关于战略互动中这种(客观)模糊性的一般理论。将制定两个主要主题。首先，在战略冲突中，制造不确定性往往很重要，因为对手会利用关于自己行为的完美信息来损害自己。传统上，这种战略不确定性是由具有已知概率的概率设备模拟的，比如骰子或轮盘赌轮盘。在真实的互动中，玩家可以获得更多种类的战略不确定性。这当然反映在关于谈判的政策文献中，并直观地感受到这一点，讨价还价的人都知道这一点。我们学习了决策理论的最新进展，这些进展允许对这种不确定性进行建模，并研究博弈论均衡预测的结果变化。第二，环境本身可能是模棱两可的。玩家可能不会像传统假设的那样，对所玩的游戏、对手的类型等有足够的概率信息。在现实环境中，信息往往很稀缺，不允许进行概率评估。这种不确定性如何影响在均衡状态下采取的策略？是否有可能通过环境的模糊程度来确定一组均衡的参数？当前项目的目标是发展关于这种情况的整个理论，包括其决策理论和认识论基础，广泛的形式理论，以及对从经济角度来看重要的特定战略冲突的应用。例如，我们打算研究我们的理论对经济各方之间的沟通博弈或讨价还价情况的影响。我们还将通过实验来配合我们的研究，在实验室里检验我们的预测。

Uncertainty plays a crucial role in strategic conflicts, either in the form of uncertainty of the environment or uncertainty in strategy choices. In many real--world conflicts, it is not possible to model the uncertainty by probabilistic models; instead, agents face what is called Knightian uncertainty or (model) ambiguity: the probability distribution of outcomes is not exactly known to the actors. In social conflicts, we frequently have environmental variables as past experience, preplay communication, or cultural norms that influence the equilibrium outcome but are not directly part of the modeled payoffs. It is thus important to incorporate such model uncertainty or ambiguity into the analysis of strategic conflicts.The project aims to develop a general theory of such (objective) ambiguity in strategic interactions. Two main themes will be developed. First, in strategic conflicts it is frequently important to create uncertainty as opponents would exploit perfect information about one's behavior to one's own detriment. Traditionally, such strategic uncertainty has been modeled by probabilistic devices with known probabilities, as dices or roulette wheels. In real interactions, a much wider variety of strategic uncertainty is available to players. This is certainly reflected and intuitively felt in the policy literature on negotiations and is known to bargainers alike. We take up recent advances in decision theory that allow to model such uncertainty and study the resulting changes in equilibrium predictions for game theory.Second, the environment might itself be ambiguous. Players might not have sufficient probabilistic information over the game played, the type of the opponents etc as is traditionally assumed. In real environment, information is often scarce and does not allow probabilistic assessments. How does this uncertainty affect the strategies played at equilibrium? Is it possible to parametrize the set of equilibria by the degree of ambiguity of the environment?The aim of the current project is to develop the whole theory of such situations, including its decision--theoretic and epistemological foundations, the extensive form theory, and applications to specific strategic conflicts that are important from an economic point of view. For instance, we intend to study the consequences of our theory for communication games or bargaining situations between economic parties. We will also accompany our studies by experiments to test our predictions in the laboratory.