Most Popular Books by Barry Nalebuff

In Cournot''s model of complements, the producers of A and B are both monopolists. This paper extends Cournot''s model to allow for competition between complements on one side of the market. Consider two complements, A and B, where the A + B bundle is valuable only when purchased together. Good A is supplied by a monopolist (e.g., Microsoft) and there is competition in the B goods from vertically differentiated suppliers (e.g., Intel and AMD). In this simple game, there may not be a pure-strategy equilibrium. With constant marginal costs, there is never a pure-strategy solution where the lower-quality B firm obtains positive market share. We also consider the case where A obtains revenue from follow-on sales, as might arise when A expects to make upgrade sales to an installed base. If profits from the installed base are sufficiently large, a pure-strategy equilibrium exists where both B firms are active in the market. Although there is competition in the complement market, the monopoly Firm A may earn lower profits in this environment. Consequently, A may prefer to accept lower future profits in order to interact with a monopolist complement in B.

Pensions influence retirement decisions. The analysis provides a framework for assessing the phenomenon. The qualitative features of most defined benefit pension plans in the United States, as the first section demonstrates, can be used to induce optimal retirement choices. Pensions are viewed as a form of forced savings; their purposeis to enable the worker to "commit himself" by making it in his own self-interest to retire at an appropriate age. The remaining sections examine the use of pensions in populations that are heterogeneous with respect to such features as disutility of work or expected lifespan.Given heterogeneity, a major policy concern is whether pensions are actuarially fair to different groups, retirement cohorts, etc. It is proven that optimal pension plans cannot be actuarially more than fair, in the sense that someone who retires later must impose a smaller cost on the pension pool than he would were he to retire earlier. However, there are differences in life expectancy among cohorts defined by retirement age: late retirees generallyl ive longer. Late retirees may thus impose a greater expected cost on the pension fund under an optimal plan; interestingly, they do impose a higher cost than those retiring earlier under most common pension funds.In a first-best world, a separate pension plan would be designed for each group of workers. But, government-mandated retirement programs and legislation regulating private pensions require common treatment of different workers. Such homogenization is shown to work to the possible detriment of workers as a whole. Pensions are a workhorse compensation mechanism. They provide an additional instrument beyond wages for attracting, motivating, sorting, and retaining workers, while facilitating appropriate retirement decisions

We present a model of the labor market with asymmetric information in which the equilibrium of the'' market generates unemployment and job queues so that wages may serve as an effective screening device. This happens because more productive workers -- within any group of individuals with a given set of observable characteristics -- are more willing to accept the risk of being unemployed than less productive workers. The model is consistent with cyclical movements in average real wages as well as with differences in unemployment rates across different groups in the population. We also show that the market equilibrium is not, in general. constrained Pareto efficient Moreover. we identify a new category of nonexistence problems, different in several essential ways from those earlier discussed by Rothschild-Stiglitz [1976J and Wilson [1977]. We also extend the analysis to incorporate the possibility of renegotiation, showing that a separating-renegotiation-proof-equilibrium exists for certain parameters and that a renegotiation-proof equilibrium is always constrained Pareto efficient Finally, we present a version of the model in which firms enter sequentially, as in Guash and Weiss [1980]. But contrary to the main result in that paper, we show that there is no advantage of being late, provided workers have rational expectations.