The authors model an oligopoly facing uncertain demand where each firm chooses as its strategy a "supply function" relating its quantity to its price. A supply function adapts better to an uncertain environment than either a fixed price or a fixed quantity; it could be committed to through the choice of organizational structure and employee decision rules. The authors give conditions for existence and for uniqueness of a Nash equilibrium in supply functions under uncertainty. They compare the equilibrium with the Cournot and Bertrand equilibria as they vary the demand and cost curves, the number of firms, and the form of uncertainty.
A lifetime utility model, in which the date of death is uncertain and in which bequests give utility, is analyzed and estimated. The parameter estimates imply that most bequests are accidental, the result of mortality risk, and that the shape of the desired consumption path is sensitive to variations in mortality rates. On average, the elderly in the sample dissave, which is consistent with a life-cycle model in which utility does not depend on bequests.
In this paper, we analyze the problem of designing incentive compatible mechanisms in pure exchange economic environments when agents have incomplete information. The equilibrium concept employed is Bayesian Nash equilibrium and the notion of implemantation is full implementation, which is stronger than the more commonly employed notion of truthful implementation. An allocation rule is truthfully implementable if there exists a direct mechanism to which truth telling is an equilibrium and which yields the allocation rule as its truthful equilibrium outcome. An allocation rule is fully implementable if there exists mechanism which yields the allocation rule as its unique equilibrium outcome. More generally, a set of allocation rules, or a social choice set, is fully implementable if there exist a mechanism whose equilibrium outcomes coincide with the set. This stronger notion of implemention avoids the well known problems of multiple equilibria which arise in direct revelation games. We develop a condition, termed Bayesian monotonicity, which we show is necessary for full implementation. An incentive compatibility condition is also necessary. We prove that Bayesian monotonicity and a slightly stronger incentive compatibility condition are sufficient for full implementation when there are at least three agents. We present several examples of allocation rules which do and do not satisfy our condition. One example is that of an allocation rule which is fully inplementable by an indirect mechanism, but for which every equivalent direct mechanism has multiple equilibrium outcomes.
On analyse l'équilibre d'un marché confrontant d'un côté le vendeur monopolistique d'un bien stockable, qui doit adapter son prix à l'inflation environnante mais pour lequel les changements de prix sont coûteux, et de l'autre ses clients, qui spéculent constamment sur les dates d'ajustement du prix, cherchant à stocker juste avant ces augmentations.Le problème est modélisé comme un jeu dynamique à horizon infini entre vendeur et spéculateurs.On montre qu'il existe un seul équilibre Markovien parfait et l'on caractéris.e complètement les dynamiques de prix et de stockage qui en résultent.Celles-ci comprennent en général une phase de stratégies mixtes, pendant laquelle le vendeur essaye de déjouer la spéculation en introduisant de l'incertitude dans son prix, tandis qu'un nombre croissant de spécu 1 ateurs stocke, culminant parfois en "ruée" spéculative généralisée sur le bien.On examine ensuite les conséquences macroéconomiques de ce type d'équilibre, calculant les coûts sociaux du tandem inflation-spéculation et établissant d'autre part un résultat d'agrégation des stratégies de prix aléatoires d'un grand nombre de vendeurs identiques.Les résultats du modèle montrent en particulier qu'en situation de concurrence imparfaite, la spéculation peut être déstab i 11 sante, et surtout ils fournissent un fondement théorique à l'idée fréquemment rencontréeet confirmée empiriquementque l'inflation, même anticipée, engendre de l'incertitude sur les prix.
In the context of the classical linear model, the problem of comparing two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included as special cases. Exact bounds on the null distribution of likelihood ratio statistics are derived. In an important special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are also studied
Larry G. Epstein, Stanley E. Zin, Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework, Econometrica, Vol. 57, No. 4 (Jul., 1989), pp. 937-969
Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. Applications in two illustrative models are presented.