04662nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172050001600186072001600202072002300218072001500241100008700256245019000343250001800533264006900551300006700620336002600687337002600713338003600739347002400775490006400799505045600863520214501319650003603464650003403500650002103534650003103555650006103586650003803647650003603685700008803721710003403809773002603843776003603869776003603905776003603941830006403977856004604041912001404087912001404101999001704115978-3-031-43575-1DE-He21320251030110852.0cr nn 008mamaa231213s2024    sz |    s    |||| 0|eng d  a97830314357519978-3-031-43575-17 a10.1007/978-3-031-43575-12doi 4aTA329-348 4aTA345-345.5 7aTBJ2bicssc 7aTEC0090002bisacsh 7aTBJ2thema1 aClempner, Julio B.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut96817010aOptimization and Games for Controllable Markov Chainsh[electronic resource] :bNumerical Methods with Application to Finance and Engineering /cby Julio B. Clempner, Alexander Poznyak.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVIII, 332 p. 99 illus., 94 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aStudies in Systems, Decision and Control,x2198-4190 ;v5040 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.  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. 0aEngineering mathematics.964145 0aEngineeringxData processing. 0aDynamics.965524 0aNonlinear theories.96552514aMathematical and Computational Engineering Applications.24aApplied Dynamical Systems.96553024aEngineering Mathematics.9641451 aPoznyak, Alexander.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9681712 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303143574408iPrinted edition:z978303143576808iPrinted edition:z9783031435775 0aStudies in Systems, Decision and Control,x2198-4190 ;v50440uhttps://doi.org/10.1007/978-3-031-43575-1  aZDB-2-ENG  aZDB-2-SXE  c56796d56796