Degenerate Feedback and Time Consistency in Dynamic Games

This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as `perfect uncontrollable' and provide two examples based on (i) a model where firms invest so as to increase consumers' reservation prices, based upon Cellini and Lambertini (CEJOR, 2003); and (ii) a model where firms compete to increase their respective market shares, based upon Leit- mann and Schmitendorf (IEEE Transactions on Automatic Control, 1978).