The von Neumann-Morgenstern theory of games does not yield determinate solutions (corresponding to unique payoff vectors) for two-person variable-sum games and for n-person games. The present paper outlines a general theory of rational behavior in game situations which does yield determinate solutions for all classes of games. The theory is based on two classes of rationality postulates: those defining rational behavior as'such, and those defining rational expectations concerning the other players' behavior. It is argued that this new approach greatly increases the possibilities for the application of game theory in economics and the other social sciences.

This paper gives a non-linear growth model, which explains the development of an economy through stages somewhat similar to the Rostovian stages. Non-linearity is introduced by including the inaugmentable factor of land or natural resources in the production function along with labor and capital, and by recognising that net saving is not a linear homogeneous function of income alone, but might be affected by the distribution of income and the interest rate and tends to be negative when per capita income is very low. Furthermore, population growth is assumed to follow a NeoMalthusian pattern. The effects of non-neutral as well as neutral technical progress are discussed in this paper.

A natural generalization of least squares is proposed to estimate parameters in simultaneous linear equations. Full-information maximum likelihood is shown to be identical with this generalization. The extent to which other estimators deviate from the generalization is discussed. A paradox of Strotz is resolved, and application of canonical correlation theory to structural equations is indicated. 1. SUMMARY THIS PAPER compares various estimators of the parameters of linear simultaneous

A multi-sector buffer-stock inventory model is developed in an attempt to resolve the problem of aggregation involved in deriving implications for the stability of the economy from a consideration of inventory practices of individual firms. It is demonstrated that stability depends upon a multitude of parameters, some of which are suppressed in aggregative model construction. The economy is necessarily unstable when perfect, if myopic expectations are assumed. With naive expectations stability becomes a definite possibility, particularly if firms attempt only a delayed adjustment of inventories to the equilibrium level. Although the empirical evidence marshaled in order to illustrate the application of the theorems does not prove sufficiently accurate to permit precise conclusions, it is apparent that the conditions for stability may well be satisfied for reasonable values of the system's parameters. Tax schemes which have been suggested as means of stabilizing fluctuations in inventory investment are appraised in the concluding section.

In this note we study dynamic inventory problem for a follow-on provisioning in which program length is subject to uncertainty with a known distribution. It is shown that under rather general cost conditions, optimal policy is of (S, s) type. This is true whether or not there exists a time lag in delivery provided that excess demand is always backlogged. The case of an infinite program horizon is also briefly discussed. MODERN INVENTORY theory has been a relatively recent development, but its brief existence has proceeded at least along two fronts: theory and applications. The earliest work falling under this theory is that by Masse [6], followed by those of Arrow, Harris, and Marschak [1], Dvoretzky, Kiefer and Wolfowitz [5], Bellman, Glicksberg and Gross [4], and Modigliani and Hohn [7]. An excellent account of historical back ground of this theory was given by Arrow [2], and its applications to a great variety of economic and business may be found in many journals in such fields as operations research, management science, and production control. A detailed discussion of the nature and structure of inventory problems was given by Arrow, Karlin, and Scarf [2, Chap. 2], and a simple mathematical exposition of theory may also be found in Bellman [3, Chap. 5]. Briefly, problem involves determination of (optimal) stock levels for inventories which extend over a sequence of time periods and are subject to fluctuating demand in each such period. Such may arise in a number of ways, e.g., in scheduling production or determining distribution of commodities over certain markets, in finding replacement policy for aged equipment, or in combinations of some or all of these features. The treatment of demand in modern inventory theory is usually handled in two ways: (1) time periods are regularly spaced, and demand in each period is a random variable with a known probability distribution; or (2) size of each demand is fixed but times at which successive demands occur are random variables. We study here an inventory problem which is in some sense a hybrid between two and which occurs frequently in involving follow-on provisioning. (Follow-on provisioning is a subsequent provisioning of same item from same supply source.) Here, time periods are equally spaced (corresponding to budget cycles) and demand in each period is a random variable subject to a known

This paper investigates Bohm-Bawerk's idea of a preference for advancing the timing of future satisfactions from a somewhat different point of view. It is shown that simple postulates about the utility function of a consumption program for an infinite future logically imply impatience at least for certain broad classes of programs. The postulates assert continuity, sensitivity, stationarity of the utility function, the absence of intertemporal complementarity, and the existence of a best and a worst program. The more technical parts of the proof are set off in starred sections.