This paper addresses the question of nonmyopic strategic behavior in an MDP planning procedure which is terminated when the rate of adjustment in the quantity of the public good is below some prespecified threshold. The problem is formulated as a dynamic game in which utility functions are additively separable. It is shown that the game possesses perfect Nash equilibria whose outcomes are Pareto optima. Moreover, any individually rational Pareto optimum can be attained through one of these Nash equilibria. Strategies in these equilibria involve a rate of revision in the quantity of the public good that is equal to the threshold level and insures monotonic convergence of the procedure in finite time

IN THIS NOTE, we present a stochastic adjustment process which has nice optimality and (probablistic) dynamic stability properties for a large class of economic environments. In addition, the process relies on a strikingly simple information exchange procedure at each iteration. It can also be termed as strongly locally individually incentive compatible2 in that each consumer agent has no incentive to lie about his preferences provided he is concerned only with maximization of one-step expected utility gain at each iteration. The obvious source of inspiration for this process is the stochastic decentralized resource allocation mechanism (the B process) by Hurwicz, Radner, and Reiter [2]. Indeed, it should be regarded as the latter's informationally simplified descendent. For general background information on resource allocation mechanisms and motivations for designing such mechanisms, see Hurwicz, Radner, and Reiter [2] and Hahn [1]. In order to simplify the exposition, we present the process only for the case of pure exchange economies with possible consumption externalities. For more general cases, see Mitsui [4]. Mitsui [4] also constructs a core-convergent version of the process.

[The model considered is a two-equations model consisting of a binary choice equation and a regression equation. Tests for the bivariate normal distribution are derived for the truncated samples case and the censored samples case. The tests are Lagrangean multiplier tests for testing the bivariate normal distribution within the bivariate Edgeworth series of distributions. Simple intuitive interpretations for the statistics are provided.For the truncated case, the test compares with the estimated differences between some sample moments of order (r,s) for which r + s extgreater 2 and the corresponding hypothesized moments of the disturbances. For the censored case, the test is equivalent to the testing of some sample semi-invariants for which r + s extgreater 2 are zeros.]

[Introduction] To a large extent the cooperative theory of games has an altogether different appearance from the noncooperative theory. The noncooperative theory generally deals with games in either extensive form or normal form, while the cooperative theory is usually described in characteristic function form. One of the central concepts in the cooperative theory is that of the core, which is the set of utility allocations which no coalition can improve upon. This notion of the core and of the characteristic function form of a game depends heavily on the existence of a utility representation for players' preferences. Recently Gale and Mas-Colell [3] and Shafer and Sonnenschein [6] have proven theorems on the existence of a Nash equilibrium for noncooperative games in normal form in which the players' preferences over strategy vectors are not necessarily complete or transitive and so may fail to have a utility representation. Thus it might appear that the noncooperative theory is applicable in environments where the cooperative theory is not. In order to formulate theorems in the cooperative theory of games which can be applied to environments in which players may have nonordered preferences, the characteristic function must be reformulated in terms of physical outcomes as opposed to utility outcomes. The players' preferences can then be expressed in terms of the physical outcomes without the use of a utility function.

[When the error covariance matrix in a linear model depends on a few unknown parameters, the regression coefficients can be estimated by a two-step procedure. Consistent estimates of the covariance parameters are first obtained and then used in a generalized least squares regression. Under the assumption that the errors are normal and the covariance parameter estimates are well behaved, an asymptotic expansion is developed for the distribution function of the two-step GLS estimate. the error in treating the estimate as normal is found to be of order n extasciicircum- extasciicircum2 as the sample size n tends to infinity.]

[This paper investigates two-person bargaining under incomplete information where one player has strictly better information about the potential value of the transaction than the other. The implications of informational barriers to trade are explored, and optimal bargaining mechanisms are characterized

An approximation to the inconsistency introduced by imposing an incorrect restriction on a parametric model is given. The approximation can be applied to estimators generated by optimizing any objective function satisfying certain regularity conditions. Examples given include analysis of misspecification in discrete choice and time-series models estimated by maximum likelihood, and in a nonlinear regression model. SPECIFICATION ERROR ANALYSIS in the linear regression model has been studied by Theil [1], who gives formulas for, e.g., the effect of leaving out relevant variables on the expected values of the estimators of the coefficients of the included variables. In this paper we suggest analogous formulas for estimators obtained by optimizing an objective function subject to restrictions. We have in mind maximizing (1/n) x loglikelihood and will usually use this terminology. We consider the effect on the limit of the restricted estimator of a small violation of the restrictions. In the linear regression case our formula coincides with that given by Theil. In order to keep our results widely applicable and to avoid a mass of unnecessary detail we make assumptions on the asymptotic behavior of the loglikelihood function itself, rather than on the data-generating process per se. Many alternative sets of assumptions on the data densities can lead to the behavior we require of the loglikelihood functions. These will not be pursued here. The interested reader is referred to, e.g., White [12] for the case of independent observations and Kohn [8] for the time-series case. 1. GENERAL FORMULAS The general approach we take is based on a linear approximation to the likelihood function at the maximum likelihood estimator. It is in this sense that our analysis is local. For some models the local and global specification error results coincide; a well known case is the effect of omitted regressors in the linear regression model. Essentially the only cases involve linearity, although often there is agreement regarding the signs of the inconsistency. We show below that the local and global results even fail to coincide in the case of misspecified AR processes. Generally however, the global results are unknown.2 Taylor expansions are typically used together with assumptions on the data generating process to obtain the asymptotic distribution of the maximum likelihood estimator (Cramer [3]). In this paper we will not concern ourselves with asymptotic distributions of Vn -normed MLE's since these have been worked