Setting Nash Versus Kalai–Smorodinsky Bargaining Approach: Computing the Continuous-Time Controllable Markov Game

2017 ◽  
pp. 335-369 ◽  
Author(s):  
Kristal K. Trejo ◽  
Julio B. Clempner
Keyword(s):  
Continuous Time ◽  
Markov Game ◽  
Bargaining Approach

Computing the Bargaining Approach for Equalizing the Ratios of Maximal Gains in Continuous-Time Markov Chains Games

2018 ◽  
Vol 54 (3) ◽  
pp. 933-955 ◽  
Author(s):  
Kristal K. Trejo ◽  
Julio B. Clempner ◽  
Alexander S. Poznyak
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Continuous Time Markov Chains ◽  
Bargaining Approach

scholarly journals Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs

2005 ◽  
Vol 42 (2) ◽  
pp. 303-320 ◽  
Author(s):  
Xianping Guo ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Queueing System ◽  
Transition Rates ◽  
Markov Game ◽  
Continuous Time Markov Chains ◽  
Payoff Functions ◽  
Zero Sum ◽  
Action Spaces ◽  
Uniformly Bounded

In this paper, we study two-person nonzero-sum games for continuous-time Markov chains with discounted payoff criteria and Borel action spaces. The transition rates are possibly unbounded, and the payoff functions might have neither upper nor lower bounds. We give conditions that ensure the existence of Nash equilibria in stationary strategies. For the zero-sum case, we prove the existence of the value of the game, and also provide arecursiveway to compute it, or at least to approximate it. Our results are applied to a controlled queueing system. We also show that if the transition rates areuniformly bounded, then a continuous-time game is equivalent, in a suitable sense, to a discrete-time Markov game.

scholarly journals Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs

2005 ◽  
Vol 42 (02) ◽  
pp. 303-320 ◽  
Author(s):  
Xianping Guo ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Queueing System ◽  
Transition Rates ◽  
Markov Game ◽  
Continuous Time Markov Chains ◽  
Payoff Functions ◽  
Zero Sum ◽  
Action Spaces ◽  
Uniformly Bounded

In this paper, we study two-person nonzero-sum games for continuous-time Markov chains with discounted payoff criteria and Borel action spaces. The transition rates are possibly unbounded, and the payoff functions might have neither upper nor lower bounds. We give conditions that ensure the existence of Nash equilibria in stationary strategies. For the zero-sum case, we prove the existence of the value of the game, and also provide arecursiveway to compute it, or at least to approximate it. Our results are applied to a controlled queueing system. We also show that if the transition rates areuniformly bounded, then a continuous-time game is equivalent, in a suitable sense, to a discrete-time Markov game.

scholarly journals Markov approximations of nonzero-sum differential games

2020 ◽  
Vol 30 (1) ◽  
pp. 3-17
Author(s):  
Yu.V. Averboukh
Keyword(s):  
Differential Games ◽  
Differential Inclusion ◽  
Continuous Time ◽  
Value Function ◽  
Dynamic Game ◽  
Approximate Solutions ◽  
Time Dynamic ◽  
Markov Game ◽  
Approximate Nash Equilibrium ◽  
The Value Function

The paper is concerned with approximate solutions of nonzero-sum differential games. An approximate Nash equilibrium can be designed by a given solution of an auxiliary continuous-time dynamic game. We consider the case when dynamics is determined by a Markov chain. For this game the value function is determined by an ordinary differential inclusion. Thus, we obtain a construction of approximate equilibria with the players' outcome close to the solution of the differential inclusion. Additionally, we propose a way of designing a continuous-time Markov game approximating the original dynamics.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Hierarchical Bayesian continuous time dynamic modeling.

2018 ◽  
Vol 23 (4) ◽  
pp. 774-799 ◽  
Author(s):  
Charles C. Driver ◽  
Manuel C. Voelkle
Keyword(s):  
Dynamic Modeling ◽  
Continuous Time ◽  
Hierarchical Bayesian ◽  
Time Dynamic

Continuous Time Controller Design

IEE Review ◽  
1991 ◽  
Vol 37 (6) ◽  
pp. 228
Author(s):  
Stephen Barnett
Keyword(s):  
Continuous Time ◽  
Controller Design
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