Marcel Boyer

Being a leader or a follower: Reflections on the distribution of roles in duopoly

This paper deals with the analysis of conflicts in duopoly situations, in particular with the distribution of roles in the von Stackelberg framework: which firm will be the leader, which firm the follower? Under what circumstances will firms find a mutually advantageous distribution of roles? Will they fight for leadership or followship? In von Stackelbergs analysis of duopoly, either firms do not choose their respective roles or they fight for leadership. This situation is due to the particular strategy space, namely the quantity to produce of an homogeneous good. We extend here the strategy space to price-quantity pairs. We show that if costs are identical or similar, then both firms will prefer the role of follower; if there is a significant cost differential between the firms, then the non-cooperative equilibrium can only be of two types: either the less efficient firm will act as the leader, selling a limited quantity at a low price, and the more efficient firm as the follower, selling to the residual demand at a higher price, or the more efficient firm acting as leader will drive the less efficient firm out of the market by adopting a limit pricing strategy, but in so doing that firm makes less profits than if it acts as follower. We suggest that it is not unreasonable to expect that firms in a duopoly framework will tend to coordinate on their mutually advantageous role distribution even if they compete in a non-cooperative strategic way in terms of both prices and quantities.

Rational Demand and Expenditures Patterns Under Habit Formation

Abstract This paper proposes a model in which habit formation is present in a relatively general but tractable way. The consumers problem is transformed into a sequence of two-period Fisherian problems by introducing a “reduced utility function” to ensure full dynamic rationality of the consumer. By making preferences dependent on past real expenditure levels rather than past consumption bundles, it is possible to characterize the long-run behavior of the consumer. Stability analysis is performed. The cases of “immediate habit formation” and “delayed habit formation” are discussed.

An Empirical Analysis of Moral Hazard and Experience Rating

For many years, economists and actuaries have studied multiperiod insurance contracts independently and differently. The aim of this article is to reduce the gap between empirical studies on the determination of insurance premiums and theoretical studies on moral hazard and experience rating. The first objective is to verify empirically the proposition that past experience is a good predictor of risk by using data from a random sample consisting of 19,013 car drivers in Quebec. The second objective is to construct a multivariate, multiperiod pricing formula for automobile insurance in order to reduce the ill effects of moral hazard. Copyright 1989 by MIT Press.

The Economics of Road Safety

In this paper we present a theoretical framework for the analysis of road safety in different contexts characterized by the following factors: the presence or the absence of externalities, moral hazard, taxes (subsidies), government regulation, liability insurance and multi-period insurance contracts. The main results are the following: (i) A Pareto optimal solution for insurance coverage and road safety is characterized by full insurance and a level of prevention which takes into account externalities between drivers. (ii) Without asymmetrical information, such a Pareto optimal solution can be obtained with or without a fault system for negligence if an adequate rating system is set up in order to induce individuals to take into account externalities. Taxes and subsidies can also be efficient. Government regulation of road safety is another way to reduce inefficies due to externalities. However, these interventions will not generally lead to a socially optimal level of road safety under asymmetrical information. (iii) Under asymmetrical information, two mechanisms are examined in some detail: fault for negligence and multi-period insurance contracts. It is shown that one-period liability insurance contracts (assuming that the legal system can observe the individuals level of road safety activities when accidents occur) or multi-period no-fault insurance contracts (assuming an infinite horizon with no discounting) based in part on the individuals past driving record can give individually rational self-protection activity levels which are socially efficient in presence of both moral hazard and externalities. Under less stringent assumptions, these contracts can give second-best solutions.

Econometric Models of Accident Distributions

This paper deals with the econometrics of car accidents, that is, the estimation of the relative importance or significance of the factors explaining the number of accidents in a given period on an individual basis. The number of car accidents is a discrete variable and, therefore, represents a count process: the dependent variable takes only nonnegative integer values. Hence, the observed dependent variable is the number of accidents an individual i had in the period considered. The individual characteristics are considered exogenous or predetermined and may or may not be significant factors in explaining the number of accidents. We have estimated four categorical models (linear probability, probit, logit, and multinomial logit) and four count data models (Poisson and negative binomial models with and without individual characteristics in the regression component). It is difficult to compare the econometric results of the different models since some of these models are not nested. However, it is shown that the negative binomial model with a regression component produces a reasonable approximation of the true distribution of accidents. Different statistical tests reject the Poisson models (with and without a regression component) and the negative binomial model without individual characteristics. It is also observed that all estimated models provide the same qualitative results (essentially the same significant variables), but differ when predictions of either the probabilities of accident or the expected number of accidents were made. For quantitative predictions, it is important to select the appropriate model. Moreover, it is shown that, in all models, the individual’s past driving experience is a good predictor of risk. Finally, we apply the statistical results to a model of insurance rating in the presence of moral hazard.

Conjectures, rationality and duopoly theory

Abstract The main results of this paper are twofold. First we show that any sustainable pair of production programs can be obtained as a locally rational conjectural equilibrium for appropriately chosen linear conjectural functions for the duopolists. Then we show that constant conjectural variations duopoly models could, in a sense, be made rational if the value of the conjectural variation is considered not as a constant but rather as a specific value taken at the equilibrium.

Perfect competition as the limit of a hierarchical market game

Abstract It is shown that competitive equilibrium can be seen as the limit of some hierarchical game in which the rights (or information) of the players can be strictly ordered.

Directors' and Officers' Insurance and Shareholder Protection

Corporate directors are liable for the corporation’s actions as well as their own. Strangely, and by far, the most likely plaintiffs in a lawsuit against corporate directors are the shareholders who appointed them in the first place. As a result, directors often require protection so that their personal wealth is not expropriated in the event of a good faith error. There are three ways to protect a director’s wealth: corporate indemnification plans, limited liability provisions and directors’ and officers’ (D&O) insurance policies. Of the three types of protection, D&O insurance is arguably the strangest not because shareholders purchase it to protect directors in case of a lawsuit, but because it also protects shareholders. Using an original database, I test a set of hypotheses that should determine the demand for D&O insurance. My analysis suggests that D&O insurance protects the shareholders’ wealth more than the directors’.

Centralizing Insurance Fraud Investigation

The study of insurance fraud and its remedy is a hot topic of research, mainly because the problem of insurance fraud is so widespread. In the United States many state governments have setup agencies to combat fraud. These Insurance Fraud Bureaus (IFB) are typically established to gather information about potential fraudulent claims, and to advise prosecuting officers on the nature of each offense. This paper presents the conditions under which more fraud will be observed in an economy where an IFB conducts all audits than in an economy where each insurance company is responsible for its own investigation. Even if fraud increases, policyholders may be better off than in economy lacking an IFB. One unambiguous case where policyholders are always better is when the IFB conducts every investigation at a cost that is equal to the industrys average.

A Dynamic Duopoly Investment Game Without Commitment Under Uncertain Market Expansion

We model capacity-building investments in a homogeneous product duopoly facing uncertain demand growth. Capacity building is achieved through the addition of production units that are durable and lumpy and whose cost is irreversible. While building their capacity over time, firms compete a la Cournot in the product market given their installed capacity. There is no exogenous order of moves, no commitment regarding future decisions, and no finite horizon. We investigate Markov Perfect Equilibrium (MPE) paths of the investment game, which may include episodes during which firms invest at different times, a preemption pattern, and episodes in which firms invest simultaneously, a tacit collusion pattern. These episodes may alternate and are typically several. When firms have yet to invest in capacity, the sole pattern that is MPE-compatible is a preemption episode: firms invest at different times but have equal value. The first such investment may occur earlier and therefore be riskier than socially optimal. When both firms hold capacity, tacit collusion episodes may be MPE-compatible: firms invest simultaneously at a postponed time (hence holding back production in the meantime), thereby generating an investment wave in the industry. Such investment episodes are more likely with higher demand volatility, faster market growth, and lower cost of capital (discount rate).