Knowledge that Transforms

A two-person bargaining problem is considered. It is shown that under four axioms that describe the behavior of players there is a unique solution to such a problem. The axioms and the solution presented are different from those suggested by Nash. Also, families of solutions which satisfy a more limited set of axioms and which are continuous are discussed. WE CONSIDER a two-person bargaining problem mathematically formulated as follows. To every two-person game we associate a pair (a, S), where a is a point in the plane and S is a subset of the plane. The pair (a, S) has the following intuitive interpretation: a = (a1, a2) where ai is the level of utility that player i receives if the two players do not cooperate with each other. Every point x = (x1, x2) e S represents levels of utility for players 1 and 2 that can be reached by an outcome of the game which is feasible for the two players when they do cooperate. We are interested in finding an outcome in S which will be agreeable to both players. This problem was considered by Nash [3] and his classical result was that under certain axioms there is a unique solution. However, one of his axioms of independence of irrelevant alternatives came under criticism (see [2, p. 128]). In this paper we suggest an alternative axiom which leads to another unique solution. Also, it was called to our attention by the referee that experiments conducted by H. W. Crott [1] led to the solution implied by our axioms rather than to Nash's solution. We also consider the class of continuous solutions which are required to satisfy only the axioms of Nash which are usually accepted. We give examples of families of such solutions.

[Observations are made on the sources of cross-equation constraints and the ways they can be used as identification aids, on possible simplifying transformations of linear homogeneous cross-equation constraints, on a rank condition for identification of a block of equations under such linear constraints, and on a strategy for using these constraints for single-equation identification.]

This paper derives an asymptotically valid test for first-order autoregressive errors. The test is derived in a simultaneous system of equations context, and allows lagged endogenous variables to be present in the model.

WE CONSIDER THE PROBLEM of estimating the coefficients of the Cobb-Douglas production function when observations are obtained from a cross section of firms. Under the assumptions that the firms operate in competitive markets and maximize actual profits, a stochastic model of production of the firms can be represented

Consider a competitive economy with infinite horizon Ramsey behavior by households, present-value maximizing firms and infinitely many futures markets. If prices adjust according to excess demands, then the economy is locally stable. This is in marked contrast to the saddle-point instability exhibited by the myopic foresight dynamics in models of this genre. It is argued that infinite futures markets are idealizations of actual economic forces.

[The power function of the Durbin-Watson test for first-order serial correlation is examined. The power function depends upon the regression vectors, but useful upper and lower bounds for the power are established. The bounds are obtained from inequalities on the characteristic roots of real non-definite symmetric matrices developed in this article.]

[If two linear models have different sets of explanatory variables and the same variable to be explained, the residual variance of the correct model (S extasciicircum2"n) has a smaller mean value than that of the incorrect one (t extasciicircum2"n). This note shows under fairly general conditions that S extasciicircum2"n extless t extasciicircum2"n will hold with probability arbitrarily close to 1 provided that the sample size n is large enough.]

[This paper examines the determinants of the demand for labor by fourteen two-digit manufacturing industries of India, and in particular the role of factor prices and expectations, to aid understanding of the causes of the low rates of labor absorption in the manufacturing sector. This is done within the framework of neoclassical models of factor demand. A method is suggested for measuring expectations. Our results show that adverse factor prices, long adjustment lags, low output elasticities, and the shift in the industrial structure in favor of the capital goods sector are some of the more important factors responsible for the observed low rates of labor absorption. Finally, some implications of our results for studies relating to labor demand functions in general are discussed.]