Knowledge that Transforms

It has recently been shown that the utility of playing a game with side payments depends on a parameter called strategic risk posture. The Shapley value is the risk neutral utility function for games with side payments. In this paper, utility functions are derived for bargaining games without side payments, and it is shown that these functions are also determined by the strategic risk posture. The Nash solution is the risk neutral utility function for bargaining games without side payments. RECENT WORK HAS SHOWN that the Shapley value for a game with side payments is a cardinal utility function which reflects the desirability of playing different positions in a game, or in different games (cf. Shapley [14], Roth [9]). A player's utility for playing some position in a game is determined in part by his assessment of the payoff he will receive in a class of games with side payments called bargaining games. Given a player's evaluation of these bargaining games, his utility for playing a position in any game with side payments can be determined (cf. Roth [11]). It is desirable to extend these results to games without side payments, since the assumption that side payments can be made is not appropriate in many situations. In this paper we will derive a class of utility functions for playing bargaining games without side payments. Games of this sort are studied by Nash [7], who developed a solution to bargaining games which is an extension of the Shapley value for games with side payments. That is, the Nash solution coincides with the Shapley value for bargaining games with side payments. Somewhat surprisingly, the utility of playing a bargaining game without side payments is determined by the same considerations which determine the utility of playing a game with side payments. Given a player's evaluation of bargaining games with side payments, his utility for bargaining without side payments is determined.

Since dynamic regression equations are often obtained from rational distributed lag models and include several lagged values of the dependent variable as regressors, high order serial correlation in the disturbances is frequently a more plausible alternative to the assumption of serial independence than the usual first order autoregressive error model. The purpose of this paper is to examine the problem of testing against general autoregressive and moving average error processes. The Lagrange multiplier approach is adopted and it is shown that the test against the nth order autoregressive error model is exactly the same as the test against the nth order moving average alternative. Some comments are made on the treatment of serial correlation.

Jerry A. Hausman, David A. Wise, A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences, Econometrica, Vol. 46, No. 2 (Mar., 1978), pp. 403-426

A GAME FORM IS ANY SYSTEM which makes an outcome depend on individual actions of some kind, called strategies. Prime examples are systems of voting. Where voting consists of each person's marking a ballot, a strategy is simply a way of marking one's ballot. In the case of sequential voting on a number of motions, a strategy will be a contingency plan which tells how to vote on each motion as a function of the way the votes on previous motions have gone. By no means all game forms, though, are systems of voting; any system through which people interact exemplifies a game form.' This paper deals with game forms with a special property: that each person, no matter what his preferences are, can choose his strategy without regard to what he expects others to do. Such a game form will be called straightforward. Straightforward game forms of one kind are characterized by Gibbard [2]. Call a game form determinate if it makes an outcome depend on individual strategies in a way that involves no element of chance. In the case of a determinate game form, a strategy is dominant for a player with respect to a weak ordering of the alternatives iff no matter what anyone else does, the strategy secures an outcome at least as high in that weak ordering as is any other lottery that that player can secure, with the strategies of everyone else held fixed. A determinate game form is straightforward iff each player, for each weak ordering of the alternatives, has a strategy which is dominant with respect to that weak ordering. The only straightforward determinate game forms, it turns out, are trivial: a straightforward determinate game form either restricts the attainable outcomes in advance to no more than two, or makes one player a dictator among attainable outcomes. The game forms in this paper are of a more general kind. They are systems which make an outcome depend on individual strategies in a way that may involve chance. The systems to be considered have finitely many alternatives, finitely many players, and finitely many strategies for each player. A game form

THE PURPOSE OF THIS PAPER is to consider the validity of Durbin's [1] h test when the h statistic is calculated from instrumental variable estimates of an autoregressive model. It seems useful to provide such an analysis since h tests based upon instrumental variable results have been reported in the empirical literature (for example, see McCallum [3]). The validity of the h test is investigated by deriving the asymptotic distribution (under the null hypothesis) of an estimator of the first order serial correlation coefficient of the instrumental variable residuals. The variance of this distribution is obtained using methods similar to those employed by Sargan [5, Section 3], and is compared to the value required to justify the h test. The derivation of this variance leads to a valid large sample test procedure. The statistical model examined below is a structural equation from a dynamic stnultaneous equation system, but the results obtained also apply to situations in which no 'unlagged endogenous variables appear in the regressors.

[In empirical analysis of data consisting of repeated observations on economic units (time series on a cross section) it is often assumed that the coefficients of the quantitative variables (slopes) are the same, whereas the coefficients of the qualitative variables (intercepts or effects) vary over units or periods.This is the constant-slope variable-intercept framework. In such an analysis an explicit account should be taken of the statistical dependence that exists between the quantitative variables and the effects. It is shown that when this is done, the random effect approach and the fixed effect approach yield the same estimate for the slopes, the "within" estimate. Any matrix combination of the "within" and "between" estimates is generally biased. When the "within" estimate is subject to a relatively large error a minimum mean square error can be applied, as is generally done in regression analysis. Such an estimator is developed here from a somewhat different point of departure.]

[The existence of pollution externalities calls for government intervention in developing policy measures that will improve social welfare. This paper suggests a method to predict and compare the short-run aggregate output, pollution, and labor input of a competitive industry facing various environmental policies. Assuming that the choice between alternative production technologies can only take place prior to the investment decision, the labor output ratios and the pollution output ratios are fixed in the short run but vary among plants; their distribution is the information used in the aggregation procedure. The performance of different environmental policies--taxes and standards--is examined and compared.]