Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider asymmetric partially observed Shapley-type finite-horizon and infinite-horizon games where the state, a controlled Markov chain $\{X_t\}$, is not observable to one player (minimizer) who observes only a state-dependent signal $\{Y_t\}$. The maximizer observes both. The minimizer is informed of the maximizer's action after (before) choosing his control in the MINMAX (MAXMIN) game. A nontrivial open problem in such situations is how the minimizer can use this knowledge to update his belief about $\{X_t\}$. To address this, the maximizer uses off-line control functions which are known to the minimizer. Using these, novel control-parameterized nonlinear filters are constructed which are proved to characterize the conditional distribution of the full path of $\{X_t\}$. Using these filters, recursive algorithms are developed which show that saddle-points exist in both behavioral and Markov strategies for the finite-horizon case in both games. These algorithms are extended to prove saddle-points in M...
['Arnab K. Basu', 'Lukasz Stettner']
I am writing a research paper on a idea Finite- and Infinite-Horizon Shapley Games with Nonsymmetric Partial Observation
[{"from": "human", "value": "I am writing a research paper on a idea Finite- and Infinite-Horizon Shapley Games with Nonsymmetric Partial Observation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider asymmetric partially observed Shapley-type finite-horizon and infinite-horizon games where the state, a controlled Markov chain $\\{X_t\\}$, is not observable to one player (minimizer) who observes only a state-dependent signal $\\{Y_t\\}$. The maximizer observes both. The minimizer is informed of the maximizer's action after (before) choosing his control in the MINMAX (MAXMIN) game. A nontrivial open problem in such situations is how the minimizer can use this knowledge to update his belief about $\\{X_t\\}$. To address this, the maximizer uses off-line control functions which are known to the minimizer. Using these, novel control-parameterized nonlinear filters are constructed which are proved to characterize the conditional distribution of the full path of $\\{X_t\\}$. Using these filters, recursive algorithms are developed which show that saddle-points exist in both behavioral and Markov strategies for the finite-horizon case in both games. These algorithms are extended to prove saddle-points in M..."}]