On a Mixture Class of Stochastic Game with Ordered Field Property

2008 ◽  
pp. 451-477 ◽  
Author(s):  
S. K. Neogy ◽  
A. K. Das ◽  
S. Sinha ◽  
A. Gupta
Keyword(s):  
Stochastic Game ◽  
Ordered Field ◽  
Mixture Class ◽  
Ordered Field Property ◽  
Field Property

ORDERED FIELD PROPERTY IN A SUBCLASS OF FINITE SER-SIT SEMI-MARKOV GAMES

2013 ◽  
Vol 15 (04) ◽  
pp. 1340026 ◽  
Author(s):  
PRASENJIT MONDAL ◽  
SAGNIK SINHA
Keyword(s):  
Stochastic Game ◽  
Transition Probability ◽  
Pollution Tax ◽  
Markov Games ◽  
Ordered Field ◽  
Markov Game ◽  
Ordered Field Property ◽  
Single Matrix ◽  
Zero Sum ◽  
Field Property

In this paper, we deal with a subclass of two-person finite SeR-SIT (Separable Reward-State Independent Transition) semi-Markov games which can be solved by solving a single matrix/bimatrix game under discounted as well as limiting average (undiscounted) payoff criteria. A SeR-SIT semi-Markov game does not satisfy the so-called (Archimedean) ordered field property in general. Besides, the ordered field property does not hold even for a SeR-SIT-PT (Separable Reward-State-Independent Transition Probability and Time) semi-Markov game, which is a natural version of a SeR-SIT stochastic (Markov) game. However by using an additional condition, we have shown that a subclass of finite SeR-SIT-PT semi-Markov games have the ordered field property for both discounted and undiscounted semi-Markov games with both players having state-independent stationary optimals. The ordered field property also holds for the nonzero-sum case under the same assumptions. We find a relation between the values of the discounted and the undiscounted zero-sum semi-Markov games for this modified subclass. We propose a more realistic pollution tax model for this subclass of SeR-SIT semi-Markov games than pollution tax model for SeR-SIT stochastic game. Finite step algorithms are given for the discounted and for the zero-sum undiscounted cases.

DISCOUNTING AND AVERAGING IN GAMES ACROSS TIME SCALES

2012 ◽  
Vol 23 (03) ◽  
pp. 609-625 ◽  
Author(s):  
KRISHNENDU CHATTERJEE ◽  
RUPAK MAJUMDAR
Keyword(s):  
Time Scales ◽  
Stochastic Game ◽  
Optimal Strategies ◽  
Sequential Decision ◽  
Ordered Field ◽  
Markov Decision ◽  
Mean Payoff Games ◽  
Upper Level ◽  
Ordered Field Property ◽  
Mean Payoff

We introduce two-level discounted and mean-payoff games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted or mean-payoff game and the lower level game is a (undiscounted) reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. For both discounted and mean-payoff two-level games, we show the existence of pure memoryless optimal strategies for both players and an ordered field property. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted or mean-payoff games can be decided in NP ∩ coNP . We also give an alternate strategy improvement algorithm to compute the value.

Ordered Field Property for Semi-Markov Games when One Player Controls Transition Probabilities and Transition Times

2015 ◽  
Vol 17 (02) ◽  
pp. 1540022 ◽  
Author(s):  
Prasenjit Mondal ◽  
Sagnik Sinha
Keyword(s):  
Linear Programming ◽  
Transition Probabilities ◽  
Markov Games ◽  
Markov Strategy ◽  
Ordered Field ◽  
Player Game ◽  
Ordered Field Property ◽  
Transition Times ◽  
Zero Sum ◽  
Field Property

Two-person finite semi-Markov games (SMGs) are studied when the transition probabilities and the transition times are controlled by one player at all states. For the discounted games in this class, we prove that the ordered field property holds and there exist optimal/Nash equilibrium stationary strategies for the players. We illustrate that the zero-sum SMGs where only transition probabilities are controlled by one player, do not necessarily satisfy the ordered field property. An algorithm along with a numerical example for the discounted one player control zero-sum SMGs is given via linear programming. For the undiscounted version of such games, we exhibit with an example that if the game ceases to be unichain, an optimal stationary or Markov strategy need not exist, (though in this example of a one-player game we exhibit a semi-stationary optimal strategy/policy). Lastly, we prove that if such games are unichain, then they possess the ordered field property for the undiscounted case as well.

scholarly journals A class of stochastic games with ordered field property

1990 ◽  
Vol 65 (3) ◽  
pp. 519-529 ◽  
Author(s):  
O. J. Vrieze ◽  
S. H. Tijs ◽  
T. Parthasarathy ◽  
C. A. J. M. Dirven
Keyword(s):  
Stochastic Games ◽  
Ordered Field ◽  
Ordered Field Property ◽  
Field Property

scholarly journals Cooperative Stochastic Games with Mean-Variance Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 230
Author(s):  
Elena Parilina ◽  
Stepan Akimochkin
Keyword(s):  
Standard Deviation ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Stochastic Variable ◽  
Expected Payoff ◽  
The Core ◽  
Risk Sensitive ◽  
Payoff Functions ◽  
Cooperative Solutions ◽  
Mean Variance

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.

scholarly journals Distributed Group Location Update Algorithm for Massive Machine Type Communication

Sensors ◽  
2020 ◽  
Vol 20 (24) ◽  
pp. 7336
Author(s):  
Mincheol Paik ◽  
Haneul Ko
Keyword(s):  
Outage Probability ◽  
Stochastic Game ◽  
Location Update ◽  
Response Dynamics ◽  
Small Energy ◽  
Machine Type ◽  
Best Response ◽  
Machine Type Communication ◽  
Iot Devices ◽  
The Individual

Frequent location updates of individual Internet of Things (IoT) devices can cause several problems (e.g., signaling overhead in networks and energy depletion of IoT devices) in massive machine type communication (mMTC) systems. To alleviate these problems, we design a distributed group location update algorithm (DGLU) in which geographically proximate IoT devices determine whether to conduct the location update in a distributed manner. To maximize the accuracy of the locations of IoT devices while maintaining a sufficiently small energy outage probability, we formulate a constrained stochastic game model. We then introduce a best response dynamics-based algorithm to obtain a multi-policy constrained Nash equilibrium. From the evaluation results, it is demonstrated that DGLU can achieve an accuracy of location information that is comparable with that of the individual location update scheme, with a sufficiently small energy outage probability.

scholarly journals A Kinetic Theory Model of the Dynamics of Liquidity Profiles on Interbank Networks

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 363
Author(s):  
Marina Dolfin ◽  
Leone Leonida ◽  
Eleonora Muzzupappa
Keyword(s):  
Kinetic Theory ◽  
Network Formation ◽  
Transition Probabilities ◽  
Stochastic Game ◽  
Theory Model ◽  
Point Of View ◽  
Network Efficiency ◽  
Modelling Framework ◽  
Wide Range ◽  
Complex Adaptive

This paper adopts the Kinetic Theory for Active Particles (KTAP) approach to model the dynamics of liquidity profiles on a complex adaptive network system that mimic a stylized financial market. Individual incentives of investors to form or delete a link is driven, in our modelling framework, by stochastic game-type interactions modelling the phenomenology related to policy rules implemented under Basel III, and it is exogeneously and dynamically influenced by a measure of overnight interest rate. The strategic network formation dynamics that emerges from the introduced transition probabilities modelling individual incentives of investors to form or delete links, provides a wide range of measures using which networks might be considered “best” from the point of view of the overall welfare of the system. We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures.

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