Knowledge that Transforms

THE PROBLEM OF ENTRY receives a great deal of attention in present-day Industrial Economics. The main question typically asked in this connection, ever since the work of Bain and Sylos-Labini, is what the best strategies are for oligopolists facing the threat of entry into their industry, that is, the implications of potential entry on their optimal policies regarding pricing, investment, research and development, advertising, and so on. Were entry to occur, conventional wisdom says, the effects would be unambiguous: profits per firm, and perhaps also output per firm would fall, while the industry as a whole would become competitive in some sense, in particular expanding output. These effects are commonly taken for granted in discussions on entry, as obvious truths or, at best, as underlying assumptions. The natural question arises of whether this deeprooted piece of conventional wisdom is in fact correct for the general case, as the behavior of oligopoloy is, alas, complex enough to keep many surprises in store. Of course, these remarks are not meant to apply to the limit case where barriers to entry are removed altogether, thus breaking entirely the oligopolistic set-up. The effect on profits, in particular, would in this extreme case be necessarily unambiguous, as they would need to be zero in the new equilibrium, be it perfect or monopolistic competition. This is no more than a definition of equilibrium, but perhaps our intuition draws too heavily on this trivial consideration 2 Some of the effects of entry we shall be examining, in particular those on output, have been studied before, albeit in a rather limited form. Frank [1], Okuguchi [3], and Ruffin [4] found that certain reasonable conditions were sufficient for aggregate output to rise and firm-output to fall as entry occurs in the simple Cournot model of oligopoly.3 However, these authors do not examine what

General concern about the scarcity of natural resources, including the present main sources of energy, leads to the following question addressed there: what should be the behavior of our societies if they are to use optimally over time both renewable and depletable resources. This paper derives rules of optimal allocation of resources in a multisectoral growth model. Attention is focused on the relations characterizing optimal allocations in such a model; it is shown, in particular, that all rules governing optimal-growth paths can be obtained through suitable extensions of the relation between the rate of interest and the own rate of a commodity. 13 references.

[In his paper, extasciicircum1 Roth has used a three-person game example to illustrate certain difficulties connected with generalizations of the Shapley value for games without side payment. This note argues that cooperative solution concepts in general often give rise to similar difficulties, and that the best way of avoiding them is to analyze cooperative games by means of noncooperative bargaining models.]

Nancy Brandon Tuma, Philip K. Robins, A Dynamic Model of Employment Behavior: An Application to the Seattle and Denver Income Maintenance Experiments, Econometrica, Vol. 48, No. 4 (May, 1980), pp. 1031-1052

A new way of looking at repeated games is introduced which incorporates a bounded memory and rationality. In these terms, a resolution of the prisoner's dilemma is given. THE GOAL HERE is to give a natural way of introducing dynamics into game theory, or at least for non-cooperative games. Perhaps the main idea in this treatment of dynamics is the way the past is taken into account. We suppose for both mathematical and model theoretic considerations that the agents only keep some kind of summary or average of the past outcomes (or payoffs) in their memory. Decisions are based on this summary. This kind of modeling reflects the fact that there exist substantive bounds to the storing and organizing of information. We give an axiomatization of bounded memory and rationality, with both institutions and people in mind. On the other hand, the hypothesis used in this treatment leads to a tractable mathematics. Differential equations on function spaces which contain little geometry are replaced by a dynamics on a finite dimensional space. And yet dynamics takes the past into account as a kind of substitute for the theory of delay equations. The perspective in this paper is that of no finite horizon and no discounting of the future. There is always a tomorrow in our plans, and it is as important as today. Also there is a history, a beginning of history, but no end. Decisions are based on the effect of past actions of agents, not on promises or binding agreements. However communication is certainly not precluded. Solutions in our games are asymptotic solutions. To be important for us, they must meet the criteria of stability. This criterion is well-defined by virtue of the dynamical foundations of the models. The first section deals with an example, the repeated prisoner's dilemma, in the language of an arms race. Here a class of strategies, is given where the solution is Pareto optimal, stable, and a Nash equilibrium. Thus at least asymptotically, we have a rather robust resolution of the prisoner's dilemma. We show how good strategies with optimal solutions might bifurcate into strategies with the worst solutions.

This paper reports both theoretical results and also computational experience with a method for approximating a competitive equilibrium in a piecewise linear economy. The algorithm consists of solving a sequence of linear programs, alternating between: (a) a problem which ensures a balancing bundle of choices and generates a price vector; and (b) a problem which indicates the maximum level of utility attainable by each household--given the initial resource endowments-and also given the prices generated at the current iteration of the master problem. Each subproblem provides a utility vector. The master problem determines a convex combination of the utility vectors generated at previous iterations. This convex combination is chosen so as to minimize the distance between the quantityconsistent and the price-consistent set. For the sequence of sub and master problems to approach a competitive equilibrium, this distance must approach zero. Thus far, the algorithm has failed whenever all equilibria are unstable, and it has converged rapidly when there are stable equilibria. It will be shown that the algorithm does not cycle. It will also be shown that if the sequence of solutions (obtained from the algorithm) converges, then it converges to a Walrasian equilibrium.

individual may indeed lead him to reject his sincere strategy. In the present paper, the same class of voting procedures is analyzed, and a similar result is shown to hold in terms of a new concept, that of weak domination in the extended sense between the strategies of an individual. The basic idea of the extension is to account for situations where only partial information on other individuals' preferences is held by members of the society, and to show that this partial would be sufficient for a rational individual to choose nonsincere strategies under certain conditions. The main motivation of this note is thus to relax the rather restrictive assumption of perfect knowledge underlying most of the analysis in the literature on strategic voting, and to examine the problem of strategic voting with a weaker assumption.

Three different forms of congestion of production factors are defined and analyzed within an axiomatic theory of production. These forms of congestion are used to characterize a law of variable proportion. (Author)