Download PDF by David González-Sánchez, Onésimo Hernández-Lerma: Discrete–Time Stochastic Control and Dynamic Potential

By David González-Sánchez, Onésimo Hernández-Lerma

ISBN-10: 3319010581

ISBN-13: 9783319010588

ISBN-10: 331901059X

ISBN-13: 9783319010595

​There are a number of ideas to review noncooperative dynamic video games, corresponding to dynamic programming and the utmost precept (also known as the Lagrange method). It seems, even though, that a technique to symbolize dynamic power video games calls for to research inverse optimum regulate difficulties, and it truly is the following the place the Euler equation method is available in since it is especially well–suited to unravel inverse difficulties. regardless of the significance of dynamic capability video games, there's no systematic research approximately them. This monograph is the 1st try and offer a scientific, self–contained presentation of stochastic dynamic capability games.

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Additional info for Discrete–Time Stochastic Control and Dynamic Potential Games: The Euler–Equation Approach

Example text

Suppose that the investor wishes to maximize 24 2 Direct Problem: The Euler Equation Approach ∞ ∑ β t (st xt )1−γ , t=0 subject to the dynamics of the assets xt+1 = R(1 − st )xt , t = 0, 1, 2, . . , where x0 > 0 is given. In this case the functions gt (t = 0, 1, . ) are of the form gt (x, y) = β t (x − y/R)1−γ . 14) becomes the nonlinear equation − xˆt 1−γ xˆt−1 − R R −γ + β (1 − γ ) xˆt − −γ xˆt+1 R = 0, t = 1, 2, . . , but it can be rewritten as a linear one: xˆt+1 − [R + (Rβ )1/γ ]xˆt + R(Rβ )1/γ xˆt−1 = 0, t = 1, 2, .

See, for instance, Kelley and Peterson [45] or Elaydi [28]. In particular, given the difference equation with constant coefficients xt+1 + axt + bxt−1 = 0, t = 1, 2, . . 20) we consider its characteristic equation λ 2 + aλ + b = 0. 20) is of the form xt = c1 λ1t + c2 λ2t , t = 1, 2, . . , where c1 , c2 are arbitrary constants. 18) and the initial condition x0 to determine the constants c1 , c2 . 3. 15) with ϕ = ϕˆ . 4 holds for examples in Sects. 2 can be used. However, for the example in Sect.

N ). Therefore, for each j = 1, . . 52). 5. 8) where J = {1, . , n} is the set of players. 8) satisfies the following for each j = 1, . . , n and t = 0, 1, .

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Discrete–Time Stochastic Control and Dynamic Potential Games: The Euler–Equation Approach by David González-Sánchez, Onésimo Hernández-Lerma


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