Norma Olaizola

Cost-Saving Production Technologies and Strategic Delegation

This work analyses a managerial delegation model in which firms choose between two production technologies: a low marginal cost technology and a high marginal cost technology. For the former to be adopted more investment is needed than for the later. By giving managers of firms an incentive scheme based on a linear combination of profit and sales revenue, we find that Bertrand competition provides a stronger incentive to adopt the cost-saving technology than the strict profit maximisation case. However, the results may be reversed under Cournot competition. If the degree of product substitutability is sufficiently low (high), the incentive to adopt the cost-saving technology is larger under strict profit maximisation (strategic delegation).

Absorbing and generalized stable sets

Within the framework of an abstract system we establish the existing relationship between the following two solutions: The absorbing sets solution and the generalized stable sets solution.

Asymmetric flow networks

This paper provides a new model of network formation that bridges the gap between the two benchmark game-theoretic models by Bala and Goyal (2000a) – the one-way flow model, and the two-way flow model – and includes both as limiting cases. As in both the said models, a link can be initiated unilaterally by any player with any other in what we call an “asymmetric flow” network, and the flow through a link towards the player who supports it is perfect. Unlike those models, there is friction or decay in the opposite direction. When this decay is complete there is no flow and this corresponds to the one-way flow model. The limit case when the decay in the opposite direction (and asymmetry) disappears corresponds to the two-way flow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. A study of the efficiency of these architectures shows that in general stability and efficiency do not go together. We also prove the convergence of Bala and Goyal’s dynamic model in this context.

Unilateral vs. bilateral link-formation: A transition without decay

We provide a model that bridges the gap between the simplest variation of two benchmark models of strategic network formation: Bala and Goyal’s two-way flow model without decay, where links can be unilaterally formed, and a variation of Jackson and Wolinsky’s model based on bilateral formation of links assuming no decay. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the flow through the link suffers some degree of decay, but when it is supported by both the flow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have a simple variation of Jackson and Wolinsky’s connections model assuming no decay, while when flow in those links is perfect we have Bala and Goyal’s two-way flow model without decay. We study Nash, strict Nash and pairwise Nash stability for the intermediate models. Efficiency and dynamics are also examined.

A dynamic approach to cartel formation

We study the endogenous formation of cartels from a dynamic point of view. First, we review some stability analyses from existing literature, which usually predict a rather small cartel as the outcome. We then study a dynamic model, in which firms can freely leave the cartel if they wish, and firms can enter the cartel if both the cartel and the firm so desire. We show that the dynamic process converges to a strongly stable cartel if one exists. Otherwise, the process does not converge, but during the process the cartel-size will never go below any size predicted by a stability analysis.

A unifying model of strategic network formation

We provide a model that merges two basic models of strategic network formation and incorporates them as extreme cases: Jackson and Wolinsky’s connections model based on bilateral formation of links, and Bala and Goyal’s two-way flow model, where links can be unilaterally formed. In our model a link can be created unilaterally, but when it is only supported by one of the two players the flow through it suffers some friction or decay, but more than when it is supported by both players. When the friction in singly-supported links is maximal (i.e. there is no flow) we have Jackson and Wolinsky’s connections model, while when flow in singly-supported links is as good as in doubly-supported links we have Bala and Goyal’s two-way flow model. In this setting, a joint generalization of the results relative to efficiency and stability in both seminal papers is achieved, and the robustness in both models is tested with positive results.