Random Allocations, Budget Constraints & Walrasian Equilibrium

项目摘要这笔赠款资助了两个项目，一个涉及具有离散商品和代理人的经济体，另一个涉及宏观政策博弈。第一个是与普林斯顿大学的Faruk Gul合作，第二个是与西北大学的Christopher Phelan合作。第一个项目建立在早先与GUL合作的基础上，该工作涉及具有离散商品但没有预算限制的经济体，并将分析扩展到代理人面临预算限制的经济体。除了先前工作中已经存在的不可分割性问题外，这些限制为Walrasian均衡的存在引入了新的障碍。为了规避这一新的困难，我们引入了随机分配，并将商品空间扩展到彩票空间。我们认为，由此产生的经济可以被视为一个标准的阿罗-德布鲁经济，其中包含国家应急大宗商品。虽然允许彩票产生一个标准的凸经济，因此均衡的存在是有保证的，但并不是这种经济的每一个均衡都能实现。可能不存在在代理人之间随机分配离散商品的方法，从而使每个代理人的(随机)分配与他的最优彩票之一重合。除了竞争性市场，我们还探讨了激励相容机制，包括无策略性、(临时)激励相容、机制的动态实施(或瓦尔拉斯均衡)，以及在这种背景下的生产。第二个项目扩展了早先与费兰就拉姆齐税收模型所做的工作。宏观政策游戏让理论家面临具有挑战性的技术问题。它们涉及消费者和国家变量的连续体，比如股本和政府债务。大多数文献部分适应了为重复游戏开发的战略动态技术，并在极大简化的模型中使用了相当粗糙的惩罚策略。我们将标准的欧拉条件与重复对策的动态规划技术相结合，为一类具有策略性匿名玩家的对策发展了一种新的方法。我们建立了类似的自生成定理和因式分解定理，它们在刻画无限重复博弈的均衡值集方面起着核心作用。尽管这些宏观模型很复杂，但我们开发的方法就像在重复博弈中一样，提供了对均衡值集的完整表征。具体地说，我们能够研究在哪些情况下，第一好的政府政策无法实施。文献的一个主要焦点是，现成的惩罚措施是否能够可信地维持政府的最优政策。因此，次优解决方案几乎完全被忽视了。我们用目前的方法解决的另一个问题是所提出的惩罚的可信度。例如，在我们的拉姆齐税收模型中，在没有任何制度约束的情况下，最差的均衡是政府在每个时期都对资本征收100%的税，消费者什么也不存。在我们看来，这似乎不是一个非常可信的惩罚。在目前的项目中，我们考虑了强制实施防止重新谈判对政府行为的影响。

Project Abstract This grant funds two projects, one concerning economies with discrete goods and agents with budget constraints, the other dealing with macro policy games. The first is a collaboration with Faruk Gul from Princeton University, and the second with Christopher Phelan from Northwestern University. The first project builds on earlier work with Gul which concerns economies with discrete goods, but without budget constraints, and extends the analysis to economies where the agents face budget constraints. These constraints introduce a new obstacle for the existence of Walrasian equilibria, in addition to the indivisibility problem already present in the previous work. To circumvent this new difficulty, we introduce random allocations, and expand the commodity space to the space of lotteries. We argue that the resulting economy can be viewed as a standard Arrow-Debreu economy with state- contingent commodities. Although allowing for lotteries results in a standard convex economy, and thus the existence of equilibrium is guaranteed, not every equilibrium of this economy can be implemented. It is possible that there is no way of randomly allocating the discrete goods among the agents, so that each agent's (random) allocation coincides with one of his optimal lotteries. Besides competitive markets, we also explore incentive compatible mechanisms, including strategy-proofness, (interim) incentive compatibility, the dynamic implementation of mechanisms (or Walrasian equilibria), and production in this setting. The second project extends earlier work with Phelan concerning a Ramsey tax model. Macro policy games confront the theorist with challenging technical issues. They involve a continuum of consumers and state variables, like capital stock and government debt. Most of the literature has partially adapted the strategic dynamic techniques developed for repeated games, and uses rather crude punishment strategies in drastically simplified models. We combine standard Euler conditions with the dynamic programming techniques for repeated games, to develop a new method for a general class of games with strategically anonymous players. We establish analogues of the self-generation and factorization theorems, which play a central role in the characterization of the equilibrium value set of an infinitely repeated game. Despite the complexity of these macro models, the method we develop afford, as in a repeated game, a complete characterization of the equilibrium value set. Specifically, we are able to study situations in which the first-best government policy cannot be implemented. A main focus of the literature has been whether readily available punishments can credibly sustain the government's optimal policy. Hence, second best solutions have been almost totally neglected. Another issue we address with the current method is the credibility of the punishments being proposed. In our Ramsey tax model, for example, without any institutional constraints, the worst equilibrium has the government taxing capital at 100% in every period, and the consumers saving nothing. This doesn't seem to us a very credible punishment. In the current project we consider the impact of imposing renegotiation-proofness on the government's behavior.