What are some of the challenges in finding closed-form solutions for differential games?
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Closed-form solutions for differential games present several challenges. Defining closed-loop strategies and determining the value of a differential game is difficult, as there is no "two-sided Maximum Principle" for closed-loop strategies . Additionally, finding closed-form solutions for continuous state zero-sum stochastic games is still an open problem, as closed-form solutions for nonlinear optimization are generally unavailable . Power control in optimization and game frameworks also faces challenges, as the water-filling problem and Nash equilibrium in symmetric Gaussian interference game require solving non-linear equations . Pricing barrier options in discrete-time using lattice techniques also requires closed-form solutions, as the value of a barrier option is highly sensitive to the number of time steps used . Transforming nonlinear control systems into linear controllable systems, known as exact linearization, is another challenge, but it has been used to derive closed-form guidance laws for nonlinear problems of pursuit or evasion in linear differential games .
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07 Dec 1988 | The provided paper does not discuss the challenges in finding closed-form solutions for differential games. |
| The provided paper is about finding closed-form solutions for barrier options, not differential games. Therefore, there is no information in the paper about the challenges in finding closed-form solutions for differential games. | |
Open access•Posted Content | The provided paper does not discuss the challenges in finding closed-form solutions for differential games. |
Open access•Proceedings Article 23 Jul 2014 | The provided paper does not discuss the challenges in finding closed-form solutions for differential games. |
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