Oligopoly theory by Friedman J.W.

By Friedman J.W.

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In the max-min problem, θ ∈ (θ, +∞] is a penalty parameter restraining the minimizing choice of the wt+1 sequence. The lower bound θ is a socalled breakdown point beyond which it is fruitless to seek more robustness because the minimizing agent is sufficiently unconstrained that he can push the criterion function to −∞ despite the best response of the maximizing agent. 8 ) for θ shows how the value of θ depends on the return function, the discount factor, and the transition law. 7. We shall discuss the lower bound θ and an associated upper bound η extensively in chapter 8.

Robust control theory tells him how to make good decisions when his model approximates a correct one. This chapter summarizes methods for computing robust decision rules when the decision maker’s criterion function is quadratic and his approximating model is linear. 1 After describing possible misspecifications as a set of perturbations to an approximating model, we modify the Bellman equation and the Riccati equation associated with the standard linear-quadratic dynamic programming problem to incorporate concerns about misspecification of the transition law.

1. 21 This book describes how he 17 Also see Vuong (1989). 18 See Kreps (1988, chapter 11) for an interesting discussion of the problem of model discovery. 19 In chapter 9, we entertain the hypothesis that the decision maker has estimated his model by maximum likelihood using a data set of length T and use Bayesian detection error probabilities to guide the choice of a set of models against which he wants to be robust. 20 Hansen and Sargent (2005b, 2007a) provide an extensive discussion of reasons for adopting this measure of model misspecification.

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