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.
