Cooperative Differential Games with Transferable Payoffs

Petrosyan, Leon A.; Zaccour, Georges

doi:10.1007/978-3-319-44374-4_12

Cited by 22 publications

(21 citation statements)

References 78 publications

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“…Following the continuous time analysis of Yeung and Petrosyan [34] for cooperative differential games, we formulate a discrete time version of the imputation distribution procedure [8] so that the agreed upon imputations will be time consistent. By B k i (x * ,k i ), denote the payment that firm i receives in stage k under the cooperative agreement along the cooperative trajectory…”

Section: Resulting Cooperative Solution and Theoremertiesmentioning

confidence: 99%

“…The notion of time consistency was formalized mathematically by Petrosyan in the paper [7]. In the next paper on time consistency [8], L. Petrosyan defined the notion of the Imputation Distribution Procedure (IDP), which is used to compose a time consistent cooperative solution or single imputation. Later on, L. Petrosyan defined the notion of strong time consistency in the paper [9].…”

Section: Introductionmentioning

confidence: 99%

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Moving Information Horizon Approach for Dynamic Game Models

et al. 2019

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In the paper, a new class of dynamic game models with a moving information horizon or dynamic updating is studied. In this class of games, players do not have full information about the game structure (motion equations, payoff functions) on the interval on which the game is defined. It is supposed that the players at each stage of the dynamic game have only truncated information about the game structure defined by the information horizon. Cooperative and noncooperative settings are considered in the paper. Results are illustrated using the oligopoly advertising game model, and comparison between the solution in the initial game model and in the game model with moving information horizon is presented. Simulation results are presented.

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Section: Resulting Cooperative Solution and Theoremertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Moving Information Horizon Approach for Dynamic Game Models

et al. 2019

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“…From Propositions 2 and 3, we conclude that characteristic functions v 1 (S) and v 2 (ḡ, S) may not coincide, which implies that a cooperative solution may not be time consistent (see [1,4,17] for more details). However, in some instances, these functions coincide.…”

Section: Positive Externalities: Public Goods Provisionmentioning

confidence: 99%

Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities

Sedakov

2020

Mathematics

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Time consistency is a property of the solution to a cooperative dynamic game which guarantees that this solution remains stable with respect to its revision by players over time. The fulfillment of this property is directly related to the characteristic function and its behavior with the course of the game as any solution is based on this function. In this paper, we will examine the characteristic functions for two economic models with network externalities represented by a two-stage network game using the theory developed for this class of games. For a network game with positive externalities represented by a public goods provision model, we demonstrate a sufficient condition for time consistency. For a network game with negative externalities represented by a market competition model, we show that the cooperative solution is always time consistent.

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“…The evolution of the resource over time is described by the following differential equation: 3 There is a sizeable literature in applied cooperative dynamic games on time consistency, a concept that was initially proposed in Petrosjan (1977). The concept and its ramifications are covered in the books by Petrosjan (2005, 2012) and in the recent contributions by Yeung and Petrosjan (2018) and Petrosjan and Zaccour (2018). For tutorials on time consistency in differential games and in games played over event trees, see Zaccour (2008Zaccour ( , 2017.…”

Section: The Modelmentioning

confidence: 99%

A fair and time‐consistent sharing of the joint exploitation payoff of a fishery

Dahmouni

Vardar

Zaccour

2019

Natural Resource Modeling

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We consider the problem of efficiently managing a fishery where pollution externalities are present. The open‐access bionomic model is analyzed in an n‐player differential game framework with two‐state variables, that is, the fish stock and the pollution stock. We characterize the noncooperative feedback‐Nash equilibrium and cooperative solution, and define an egalitarian sharing rule to allocate the joint welfare maximizing payoff over an infinite time horizon, and show that this rule is time consistent. Recommendations for Resource Managers Cooperation in management of a fishery where pollution externalities are present yields a higher payoff over time as compared to the noncooperative behavior. The dividend of cooperation can be allocated among the fisherpersons according to an egalitarian sharing rule. This allocation is time‐consistent, that is, no player will be tempted to deviate from cooperation as time goes by, and the initial agreement is sustainable.

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Cooperative Differential Games with Transferable Payoffs

Cited by 22 publications

References 78 publications

Moving Information Horizon Approach for Dynamic Game Models

Moving Information Horizon Approach for Dynamic Game Models

Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities

A fair and time‐consistent sharing of the joint exploitation payoff of a fishery

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