On a Simplified Method of Defining Characteristic Function in Stochastic Games

Parilina, Elena; Petrosyan, Leon A.

doi:10.3390/math8071135

Cited by 7 publications

(5 citation statements)

References 22 publications

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“…The natural research question arising in the area of dynamic games is the sustainability and time-consistency of the cooperative solution over time. The problem of stability of a cooperative agreement in stochastic games with mean preferences is discussed by Parilina and Tampieri [19], Parilina [18], Parilina and Petrosyan [21], where conditions of stable cooperation are examined. The other research question is how to determine another cooperative solution like the Shapley value, nucleolus, etc., for stochastic games with mean-variance preferences and how to sustain them over time.…”

Section: Discussionmentioning

confidence: 99%

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Cooperative Stochastic Games with Mean-Variance Preferences

Parilina

Akimochkin

2021

Mathematics

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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.

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Section: Discussionmentioning

confidence: 99%

“…The conditions of node-consistency of the core in dynamic games played over event trees with stochastic nature are obtained by Parilina and Zaccour [20]. Recently, the sufficient conditions of strong subgame consistency of the core are obtained by Parilina and Petrosyan [21].…”

Section: Introductionmentioning

confidence: 99%

Cooperative Stochastic Games with Mean-Variance Preferences

Parilina

Akimochkin

2021

Mathematics

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“…Such setups can occur, for instance, in stochastic games with many players [3] and mean-field games with almost infinitely many players [4]. Additionally, we assume that the external influence W for all its arbitrariness at each moment of time k has a structure s k of finite order.…”

Section: Discretization In System State Spacementioning

confidence: 99%

Dynamic System Identification via Randomized Stochastic Optimization Under Unknown-but-Bounded Noise

Granichin,

Ivanskiy,

Kopylova

2023

Preprint

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Discretization in time and in the state space of the system leads to the necessity to solve the parameter identification problems for dynamic systems in a limited time (at a finite time interval) using observations obtained under the influence of unknown-but-bounded noise. Finding the solution in this case is more difficult compared to traditional identification problem setting which considers random independent zero-mean noise. For system parameter identification problem under unknown-but-bounded noise, a randomized stochastic optimization algorithm is given in the paper, estimates for the mean square values of the residuals for a finite observation interval are obtained. An example of application of the given method to the problem of tuning the parameters of a multi-mirror telescope is considered.

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“…Назовем такой набор стратегий кооперативным и обозначим черезφ, причемφ i (z) =ā z i , i ∈ N , z ∈ Z. Для построения кооперативного варианта игры необходимо определить характеристическую функцию для любой подыгры G(z), z ∈ Z, которую обозначим через (S, z), S ⊂ N . Существует множество подходов к определению характеристических функций в динамических и стохастических играх [1,8,11,23,26,28]. Мы используем так называемый α-подход, согласно которому v(S, z) есть максиминное значение игры с нулевой суммой между коалицией S и N \ S [20].…”

Section: определение характеристической функцииunclassified

Stochastic model of network formation with asymmetric players

Сунь¹,

Sun²,

Parilina³

2020

MGTA

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We propose a model of a network formation using the theory of stochastic games with random terminal time. Initially, the leader proposes a joint project in the form of a network to the players. Then, the players have the opportunities to form new links with each other to update the network proposed by the leader. Any player's payoff at any stage is determined by the network structure. It is also assumed that the formation of links proposed by the players is random. The duration of the game is also random. As a result of the players' actions and the implementation of the random steps of the Nature, a network is formed. We consider a cooperative approach to network formation, and we use the CIS-value as a cooperative solution. In this paper, a recurrent formula for its derivation in any cooperative subgame is obtained. The paper also investigates the dynamic consistency of CIS-value. The theoretical results are demonstrated by a numerical example.

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On a Simplified Method of Defining Characteristic Function in Stochastic Games

Cited by 7 publications

References 22 publications

Cooperative Stochastic Games with Mean-Variance Preferences

Cooperative Stochastic Games with Mean-Variance Preferences

Dynamic System Identification via Randomized Stochastic Optimization Under Unknown-but-Bounded Noise

Stochastic model of network formation with asymmetric players

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