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Constrained Games with Convexity–Concavity Assumptions

In: Discrete-Time Optimal Control and Games on Large Intervals

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  • Alexander J. Zaslavski

    (The Technion – Israel Institute of Technology)

Abstract

In this chapter we study the existence and turnpike properties of approximate solutions for a class of dynamic constrained discrete-time two-player zero-sum games which satisfy convexity–concavity assumptions. We describe the structure of approximate solutions which is independent of the length of the interval, for all sufficiently large intervals and show that approximate solutions are determined mainly by the objective function, and are essentially independent of the choice of intervals and endpoint conditions. We show that the turnpike phenomenon is stable under small perturbations of objective functions and analyze the structure of approximate solutions in regions closed to the endpoints of domains.

Suggested Citation

  • Alexander J. Zaslavski, 2017. "Constrained Games with Convexity–Concavity Assumptions," Springer Optimization and Its Applications, in: Discrete-Time Optimal Control and Games on Large Intervals, chapter 8, pages 303-389, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-52932-5_8
    DOI: 10.1007/978-3-319-52932-5_8
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