This paper considers economies involving one public good, one private good, and convex technology and proposes an informationally decentralized dynamic nontatonnement procedure that converges in general from the initial endowments to an allocation in the core. The procedure may be seen as enunciating a plausible method of cooperation among the agents for achieving an optimal provision of a public good and an equitable sharing of its cost. The viewpoint of noncooperative game theory is also considered and it is shown that there exists a trade-off between the requirements of local incentive compatibility and equitable cost sharing. Copyright 1993 by The Econometric Society.
THE ECONOMIC LITERATURE concerning agents' reputations has grown steadily since the seminal work of Kreps, Milgrom, Roberts, and Wilson.2Early work focused on how incomplete information leads to equilibria that are vastly different (but more intuitive) than those possible in the complete information game.Recently, however, game theorists have been studying how incomplete information might refine the set of equilibria.3One important class of games is that in which a single long-run agent plays a simultaneous move (stage) game with a sequence of opponents, each of whom plays only once, yet observes all previous play.Fudenberg and Levine (1989) study the reputation of the long-run player in this type of game.They argue that the "'most reasonable' equilibrium is the one which the long-run player most prefers."Their intuition is sustained when one perturbs the game with the "Stackelberg strategy."Fudenberg and Levine show that in the perturbed game the equilibrium payoffs of the long-run player are bounded below by a number that converges to the "Stackelberg payoff."Fudenberg and Levine (and the others who have developed reputation models) take the notion of Nash equilibrium as fundamental in the analysis.However, it would seem as though our intuition about reputations relies little on equilibrium concepts.This leads to two questions.First, can meaningful reputations develop apart from equilibria?Second, if so, under what circumstances can reputations develop?As I will demonstrate, equilibrium concepts are not required in order for players to establish significant reputations.I study (following Fudenberg and Levine (1989)) games in which a long-run player faces a sequence of short-run opponents.Like Fudenberg and Levine, I consider perturbations of the game involving the Stackelberg strategy.However, whereas they focus on equilibria, I will only require that players "best-respond" to their beliefs.Whenever the conjectures of the short-run players are "generally comparable" (e.g.contained in a compact set), I obtain the same refinement as do Fudenberg and Levine, but without an equilibrium assumption.What is important for reputations is that the beliefs of the short-run agents not be too dispersed in a sense to be made precise.Players can thus establish meaningful reputations from within the loose confines of individual rationality.This paper borrows heavily from the work of Fudenberg and Levine (1989).In fact, their statistical result (their Lemma 1), which establishes the potential gain of building a reputation, requires no notion of equilibrium.It does require that the short-run agents hold the same belief, which is implied by equilibrium.I simply invoke their lemma in a more general setting (in which short-run players may hold different beliefs) and study the type of beliefs which allow it to refine the set of rational outcomes.Note that a similar style of research has been followed on another front as well.Cho (1991) extends the Coase conjecture to a nonequilibrium setting.Cho's work is similar to mine in that we both take as fundamental a rationalizability notion.Our analyses require additional restrictions, however, and it is the nature of these restrictions in which our 11 am grateful to David Kreps, Marco LiCalzi, two referees, and the editor for comments.This is Chapter 2 of my Ph.D.
A limit theory for Wald tests of Granger causality in levels vector autoregressions (VAR's) and error correction models (ECM's) is developed, which allows for stochastic trends and cointegration. Earlier work is extended to the general case, thereby characterizing when these Wald tests are asymptotically valid as 'x'(superscript 2) criteria. Our results for inference from unrestricted levels VAR are not encouraging: the limit theory often involves nuisance parameters and nonstandard distributions, a situation offering no satisfactory statistical basis for these tests. Granger causality tests in ECM's also suffer from nuisance parameter dependencies asymptotically and in some cases nonstandard limit theory. Both these results are somewhat surprising in light of earlier research. Copyright 1993 by The Econometric Society.
Different extensive form games with the same reduced normal form can have different information sets and subgames. This generates a tension between a belief in the strategic relevance of information sets and subgames and a belief in the sufficiency of the reduced normal form. We identify a property of extensive form information sets and subgames which we term strategic independence. Strategic independence is captured by the reduced normal form, and can be used to define normal form information sets and subgames. We prove a close relationship between these normal form structures and their extensive form namesakes. Using these structures, we are able to motivate and implement solution concepts corresponding to subgame perfection, sequential equilibrium, and forward induction entirely in the reduced normal form, and show close relations between their implications in the normal and extensive form.
A model of optimal consumption and portfolio choice that captures the notions of local substitution and irreversible purchases of durable goods is studied. Necessary and sufficient conditions for a consumption and portfolio policy to be optimal are provided. A closed-form solution of the optimal consumption and portfolio policy is given. The optimal consumption policy consists of a possible initial "gulp" of consumption, or a period of no consumption, followed.by a process of accumulated consumption with singular sample paths. The equilibrium risk premium in a representative investor economy with a single physical production technology is computed. Copyright 1993 by The Econometric Society.
In this model, shareholders can use auditors' reports to contract with a privately-informed manager. Imperfect audit technology allows the auditor and the manager to collude. Auditors are useful when they have good information and the manager's liability is high. Expected maximum deterrence is not desirable and production is suboptimal, even with unbounded punishments. Raising the manager's punishment raises the bribe he may offer the auditor, which raises the cost of preventing collusion. The authors also distinguish internal auditors (costless but collusive) from external ones (costly but not collusive) and show that the optimal contract may specify random external audits. Copyright 1993 by The Econometric Society.
The authors consider the problem of allocating a bundle of commodities among a group of agents who are collectively entitled to them. It is proved that, for an atomless economy with possibly satiated preferences, any solution that is efficient, equitable, and consistent must select allocations that are supported by equal-budget Walrasian equilibria with slack. Copyright 1993 by The Econometric Society.
It is shown that any informationally decentralized mechanism that realizes fair allocations over the class of classical pure exchange environments has a message space of dimension no smaller than the number of agents times the number of commodities. Since the equal income Walrasian mechanism, in which all agents take prices parametrically and maximize utility subject to the average income constraint, realizes fair outcomes over the class of classical pure exchange environments and has a message space of that dimension it is informationally efficient. Further, it is shown that it is the unique informationally efficient mechanism realizing fair allocations.