Competing Vertical Structures: Preconmitment and Renegotiation

The authors present three distinct approaches to perfect and proper equilibria for infinite normal form games. In the first two approaches, players 'tremble' in the infinite game playing full support approximate best responses to others' strategies. In the strong approach, a tremble assigns high probability to the set of pure best responses; in the weak approach, it assigns high probability to a neighborhood of this set. The third, limit-of-finite approach applies traditional refinements to sequences of successively larger finite games. Overall, the strong approach to equilibrium refinement most fully respects the structure of infinite games.

This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript alpha) and Z(subscript t) unit root tests. Two new tests are also introduced. The tests are shown to be asymptotically similar, and simple representations of their limiting distributions are given and asymptotic critical values are tabulated. The ADF and Z(subscript t) tests are asymptotically equivalent. Power properties of the test are also studied. The tests are consistent if suitably constructed, but the ADF and Z(subscript t) tests have slower rates of divergence under cointegration than the other tests.

A new framework for games in continuous time is proposed. The continuous-time model conforms as closely as possible to the conventional discrete-time framework. Indeed, continuous time is viewed as "discrete time, but with a grid that is infinitely fine." The paper presents several examples illustrating the difficulties that arise in continuous-time game theory. Theorems relate the equilibria of continuous time games to the equilibria of approximating discrete time games. A variety of industrial organization applications are studied, yielding sharp predictions. Applications include continuously repeated games, preemption models, and patent races.

This paper uses cross-sectional and longitudinal data to examine differences in pay for equally-skilled workers in different ind ustries. The major finding is that there is substantial dispersion in wages across industries, even after allowing for measured and unmeas ured labor quality, working conditions, fringe benefits, transitory d emand shocks, the threat of union-ization, union bargaining power, fi rm size, and other factors. In addition, evidence is presented demons trating that turnover has a negative relationship with industry wage differentials. These findings suggest that workers in high-wage indus tries receive noncompetitive rents.

Analyse de la structure des preferences intertemporelles, necessaire pour obtenir une planification consistante