More lecture notes. These describe a particular sticky price model, and indicate the basic Klein-Krusell-Rios Rull strategy for finding a differentiable Markov equilibrium for that model. The basic model is described here and the equations needed for the details of the strategy are discussed in section 3.1 of that paper. That section is actually devoted to describing a global nonlinear strategy for finding a differentiable Markov equilibrium. The equations derived for that purpose in section 3.1 are straightforward to adapt so that they can used to implement the Klein-Krusell-Rios-Rull perturbation strategy.
Albanesi, Chari and Christiano, Expectation Traps and Monetary Policy.
Albanesi, Chari and Christiano, How Severe is the Time Consistency Problem in Monetary Policy?
Ireland, Does the Time Consistency Problem Explain the Behavior of Inflation in the United States?
Christiano and Gust, The Expectation Trap Hypothesis.
Papers that work with the type of ideas discussed here, but apply them in different contexts:
Bargaining: Albanesi, Inflation and Inequality.
Political Economy: Krusell, Quadrini, Rios-Rull, Politico-Economic Equilibrium and Economic Growth.
Taxation: Klein, Krusell, and Rios-Rull, Time-Consistent Policy.
Perturbation methods are used in the Klein-Krusell-Rios Rull paper. For a discussion of these methods, see Judd's textbook and also
Schmitt-Grohe and Uribe, Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function.
Christopher Sims, Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models.