Stability and cooperative solution in stochastic games

Parilina, Elena; Tampieri, Alessandro

doi:10.1007/s11238-017-9619-7

Cited by 10 publications

(4 citation statements)

References 32 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%

“…However, applications of these approaches need corrections, considering the stochastic nature of payoffs and mean-variance utility functions. Cooperative stochastic games with expected payoff as a utility function are introduced by Petrosjan [16] and Petrosjan and Baranova [17], and then extended by Parilina [18] and Parilina and Tampieri [19] by examining the stability of cooperative solutions in stochastic dynamic settings. As proposed by Suijs et al [11], we consider the core as a solution of a cooperative game.…”

Section: Introductionmentioning

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%

Section: Introductionmentioning

confidence: 99%

Cooperative Stochastic Games with Mean-Variance Preferences

Parilina

Akimochkin

2021

Mathematics

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“…To define cooperative game when the non-cooperative stochastic game is given, we use the classical approach and define it in the form of characteristic function v : 2 N → R 1 whose values estimate the "power" of any coalition or the subset of players. In [21], the characteristic function value for coalition S in subgame starting at any state ω is defined in as maxmin value, which is…”

Section: Modelmentioning

confidence: 99%

On a Simplified Method of Defining Characteristic Function in Stochastic Games

Parilina

Petrosyan

2020

Mathematics

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In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of the characteristic function is based on a calculation of the maximin values of zero-sum games between a coalition and its anti-coalition for each state of the game. The proposed characteristic function has some advantages in comparison with previously defined characteristic functions for stochastic games. In particular, the advantages include computation simplicity and strong subgame consistency of the core calculated with the values of the new characteristic function.

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“…Пользуясь методом построения кооперативной стохастической игры, изложенным в [21,22,24], мы определяем специальную стохастическую игру формирования сети со случайной продолжительностью. Хочется отметить, что случайность в формировании сети исходит от двух источников.…”

Section: Introductionunclassified

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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Stability and cooperative solution in stochastic games

Cited by 10 publications

References 32 publications

Cooperative Stochastic Games with Mean-Variance Preferences

Cooperative Stochastic Games with Mean-Variance Preferences

On a Simplified Method of Defining Characteristic Function in Stochastic Games

Stochastic model of network formation with asymmetric players

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