Multistage Games

The following sections are included:Multistage control systemsSystem description in a state spaceOpen-loop and closed-loop control structuresLinear systemsOptimal controlAn optimal economic-growth modelDescription of multistage games in a state-spaceInformation structureStrategies and equilibrium solutionsOpen-loop Nash equilibria in multistage gamesFeedback-Nash equilibria (FNE) in multistage gamesDynamic programming for multistage gamesOpen-loop versus feedback in deterministic gamesA feedback-Nash equilibrium solution to a fishery-management modelIntuitionIdentifying a solution to the dynamic-programming equationsEconomic interpretationFeedback-Nash equilibrium in infinite-horizon multistage games with discounted payoffsVerification theoremAn application: An infinite-horizon feedback-Nash equilibrium solution to the fishery’s problemLinear-quadratic gamesGeneral presentationInfinite-horizon LQ gameAn example of a linear-quadratic gameTwo-person zero-sum linear-quadratic game and robust controller designProblem formulationOpen-loop saddle-point solutionFeedback saddle-point solutionEquilibria in a class of memory strategies for infinite-horizon gamesOther equilibriaExample: Self-enforcing climate treatiesMemory-strategy equilibria in a non-discounted infinite-horizon multistage gameWhat have we learned in this chapter?Exercises𝔾𝔼 illustration: Growth-rate divergence between countries with the same fundamentalsA macroeconomic problemAn endogenous growth modelGame solutions