Israel Zang

Meet me halfway: research joint ventures and absorptive capacity

Abstract We propose a representation of a firm’s ‘effective’ R&D effort level that reflects how both its R&D approach and R&D budget influences its ability to realize spillovers from other firms’ R&D activity, i.e. its ‘absorptive capacity’, and generalizes the commonly employed representation. The ability to choose an R&D approach is accommodated by positing a three-stage game in which the choice of an R&D approach is made in its first stage. The firms’ R&D budgets and output levels are chosen in the game’s second and third stages, respectively. It is found that when firms cooperate in the setting of their R&D budgets, i.e. form a research joint venture, they choose identical broad R&D approaches. On the other hand, if they do not form a research joint venture, then they choose firm-specific R&D approaches unless there is no danger of exogenous spillovers. The analysis suggests that the commonly employed representation of firms’ effective R&D investment levels implicitly presupposes that the firms have chosen to cooperate in setting their R&D budgets.

A dual algorithm for the constrained shortest path problem

In this paper we develop a Lagrangian relaxation algorithm for the problem of finding a shortest path between two nodes in a network, subject to a knapsack-type constraint. For example, we may wish to find a minimum cost route subject to a total time constraint in a multimode transportation network. Furthermore, the problem, which is shown to be at least as hard as NP-complete problems, is generic to a class of problems that arise in the solution of integer linear programs and discrete state/stage deterministic dynamic programs. One approach to solving the problem is to utilize a kth shortest path algorithm, terminating with the first path that satisfies the constraint. This approach is impractical when the terminal value of k is large. Using Lagrangian relaxation we propose a method that is designed to reduce this value of k. Computational results indicate orders of magnitude savings when the approach is applied to large networks.

The Limits of Monopolization Through Acquisition

We address the question of whether competitive acquisition of firms by their rivals can result in complete or partial monopolization of a homogeneous product industry. This question is modeled in terms of two distinct three-stage noncoopera-tive games. Analysis of subgame perfect pure strategy Nash equilibria of these games discloses that, under simplifying assumptions, monopolization of an industry through acquisition is limited to industries with relatively few firms. Partial monopolization is either limited in scope or can be completely eliminated by prohibiting any owner from acquiring over 50 percent of the firms in the industry.

A smoothing-out technique for min—max optimization

In this paper, we suggest approximations for smoothing out the kinks caused by the presence of “max” or “min” operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofRn. Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented.

Generalized arcwise-connected functions and characterizations of local-global minimum properties

In this paper, new classes of generalized convex functions are introduced, extending the concepts of quasi-convexity, pseudoconvexity, and their associate subclasses. Functions belonging to these classes satisfy certain local-global minimum properties. Conversely, it is shown that, under some mild regularity conditions, functions for which the local-global minimum properties hold must belong to one of the classes of functions introduced.

An Application of the Aumann-Shapley Prices for Cost Allocation in Transportation Problems

The Aumann-Shapley A-S prices are axiomatically determined on certain classes of piecewise continuously differentiable cost functions. One of these classes consists of all cost functions derived from the transportation problems and some of their generalizations. These prices are used here to allocate costs among destinations in a way that each destination will pay its “real part” in the total transportation costs. An economic transportation model is presented in which the A-S prices are compatible with consumer demands. Finally an algorithm is provided to calculate both the optimal solution and the associated A-S prices for transportation problems.

Optimal license fees for a new product

Abstract We compare how much profit an inventor of a patented new ‘superior’ product can realize by licensing its manufacture, for a fixed fee, to an oligopolistic industry producing an ‘inferior’ substitute. Our analysis is conducted in terms of a three stage noncooperative game involving n + 1 players: the inventor, acting as a Stackelberg leader, and the n firms. Analysis of subgame perfect equilibria in pure strategies of this game disclose the circumtances under which an inventors optimal behavior ultimately leads to production of both products and when it allows for the production of the ‘superior’ product only. An extreme case of the latter possibility, namely when the ‘superior’ product is produced by a monopolist, is characterized also.

Competitively Cost Advantageous Mergers and Monopolization

Abstract We address two major questions. The first is, Does the potential for lower production costs lead to partial or complete monopolization of an industry through acquisition by one firm of all its rivals? The second is, Do competitively advantageous cost reducing mergers necessarily result in a lower equilibrium market price? These questions are addressed in terms of a two-stage noncooperative game in the first stage of which n owners, possessing n firms and producing a homogeneous product with a strictly convex cost function, bid for the possession of each other firm and then, in the second stage, operate the firms they acquired. Analysis of pure strategy subgame-perfect Nash equilibria of the game provides a mixed message. On one hand, there is no fear of complete or even substantial partial monopolization for industries with sufficiently numerous firms. But, some partial monopolization is possible and any such monopolization results in a product price increase and a total industry surplus decline.

A switching regression method using inequality conditions

Abstract This paper presents three simple approximations to the likelihood function of a switching regression model with inequality conditions. These approximations, which leave the likelihood function unchanged almost everywhere, have analytical derivatives that are continuously differentiable, and hence, allow the use of efficient gradient techniques.

On functions whose local minima are global

In this paper, necessary and sufficient conditions for a local minimum to be global are derived. The main result is that a real function, defined on a subset ofRn, has the property that every local minimum is global if, and only if, its level sets are lower-semicontinuous point-to-set mappings.