Game theory, Duopoly supergame, Asymmetric Cournot duopoly

The authors examine core convergence for economies with a large finite number of agents and an infinite number of commodities. They find a serious disconnection between economies with a large finite number of agents and economies with a continuum of agents: the authors provide examples of nonconvergence of the core for large finite economies in L[superscript 1], a commodity space for which core equivalence holds for continuum economies. In addition, they show that, if preferences exhibit uniformly vanishing marginal utility of consumption at infinity, core convergence is restored.

The authors consider a family of rank tests based on the regression rank score process introduced by C. Gutenbrunner and J. Jureckova (1992) to test the unit root hypothesis in economic time series. In contrast to tests based on least-squares methods, the rank tests are asymptotically Gaussian under the null hypothesis, and have excellent power--particularly under innovation exhibiting heavy tails. These regression rank scores arise as a vector of solutions of the dual form of the linear program required to compute the regression quantile statistics of R. W. Koenker and G. Bassett (1978). For location model, they are simple ranks of the sample observations.