LEADER 04792nam 22006255 450 001 9910770257303321 005 20240322031216.0 010 $a9783031435751 010 $a3031435753 024 7 $a10.1007/978-3-031-43575-1 035 $a(MiAaPQ)EBC31018123 035 $a(Au-PeEL)EBL31018123 035 $a(DE-He213)978-3-031-43575-1 035 $a(CKB)29364121700041 035 $a(OCoLC)1414523057 035 $a(EXLCZ)9929364121700041 100 $a20231213d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimization and Games for Controllable Markov Chains $eNumerical Methods with Application to Finance and Engineering /$fby Julio B. Clempner, Alexander Poznyak 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (340 pages) 225 1 $aStudies in Systems, Decision and Control,$x2198-4190 ;$v504 311 08$aPrint version: Clempner, Julio B. Optimization and Games for Controllable Markov Chains Cham : Springer,c2024 9783031435744 327 $aControllable Markov Chains -- Multiobjective Control -- Partially Observable Markov Chains -- Continuous-Time Markov Chains -- Nash and Stackelberg Equilibrium -- Best-Reply Strategies in Repeated Games -- Mechanism design -- Joint Observer and Mechanism Design -- Bargaining Games or How to Negotiate -- Multi-Traffic Signal-Control Synchronization -- Non-cooperative bargaining with unsophisticated agents -- Transfer Pricing as Bargaining -- Index. 330 $aThis book considers a class of ergodic finite controllable Markov's chains. The main idea behind the method, described in this book, is to develop the original discrete optimization problems (or game models) in the space of randomized formulations, where the variables stand in for the distributions (mixed strategies or preferences) of the original discrete (pure) strategies in the use. The following suppositions are made: a finite state space, a limited action space, continuity of the probabilities and rewards associated with the actions, and a necessity for accessibility. These hypotheses lead to the existence of an optimal policy. The best course of action is always stationary. It is either simple (i.e., nonrandomized stationary) or composed of two nonrandomized policies, which is equivalent to randomly selecting one of two simple policies throughout each epoch by tossing a biased coin. As a bonus, the optimization procedure just has to repeatedly solve the time-average dynamic programming equation, making it theoretically feasible to choose the optimum course of action under the global restriction. In the ergodic cases the state distributions, generated by the corresponding transition equations, exponentially quickly converge to their stationary (final) values. This makes it possible to employ all widely used optimization methods (such as Gradient-like procedures, Extra-proximal method, Lagrange's multipliers, Tikhonov's regularization), including the related numerical techniques. In the book we tackle different problems and theoretical Markov models like controllable and ergodic Markov chains, multi-objective Pareto front solutions, partially observable Markov chains, continuous-time Markov chains, Nash equilibrium and Stackelberg equilibrium, Lyapunov-like function in Markov chains, Best-reply strategy, Bayesian incentive-compatible mechanisms, Bayesian Partially Observable Markov Games, bargaining solutions for Nash and Kalai-Smorodinsky formulations, multi-traffic signal-control synchronization problem, Rubinstein's non-cooperative bargaining solutions, the transfer pricing problem as bargaining. 410 0$aStudies in Systems, Decision and Control,$x2198-4190 ;$v504 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aDynamics 606 $aNonlinear theories 606 $aMathematical and Computational Engineering Applications 606 $aApplied Dynamical Systems 606 $aEngineering Mathematics 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aDynamics. 615 0$aNonlinear theories. 615 14$aMathematical and Computational Engineering Applications. 615 24$aApplied Dynamical Systems. 615 24$aEngineering Mathematics. 676 $a519.233 700 $aClempner$b Julio B$01460460 701 $aPoznyak$b Alexander$0721769 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910770257303321 996 $aOptimization and Games for Controllable Markov Chains$93660307 997 $aUNINA