On an approach to constructing a characteristic function in cooperative differential games

Gromova, Ekaterina; Petrosyan, Leon A.

doi:10.1134/s0005117917090120

Cited by 41 publications

(23 citation statements)

References 9 publications

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“…While this result does not need to hold in general, it shows that there is a certain interconnection between different types of charateristic functions that is yet to be studied. This paper extends and generalizes a number of results scattered through the series of works by the first author, [14,12,13]. See also [25,28] for related results.…”

Section: Introductionsupporting

confidence: 75%

“…The ζ-characteristic function was initially proposed in [25] and later developed in [14]. Its construction is carried out in two steps.…”

Section: ζ-Characteristic Functionmentioning

confidence: 99%

“…For the game (13), (14), the distance of the characteristic functions V α and V η to the respective upper and lower bounds are given by…”

Section: Analysis and Comparison Of The Obtained Characteristic Functmentioning

confidence: 99%

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A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

Gromova¹,

Марова²,

Gromov³

2020

Journal of Dynamics &Amp; Games

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In this paper, we present a systematic overview of different endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, η-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effort and has a reasonable economic interpretation. In particular, the new characteristic function can be seen as a reduced version of the classical Neumann-Morgenstern characteristic function, where the players both from the coalition and from the complementary coalition use their previously computed strategies instead of solving respective optimization problems. Our finding are illustrated by a pollution control game with n non-identical players. For the considered game, we compute all characteristic functions and compare their properties. Quite surprisingly, it turns out that both the characteristic functions and the resulting cooperative solutions satisfy some symmetry relations.

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Section: Introductionsupporting

confidence: 75%

“…The ζ-characteristic function was initially proposed in [25] and later developed in [14]. Its construction is carried out in two steps.…”

Section: ζ-Characteristic Functionmentioning

confidence: 99%

See 1 more Smart Citation

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

Gromova¹,

Марова²,

Gromov³

2020

Journal of Dynamics &Amp; Games

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“…In this case, we assume that such a group is the grand coalition, i.e., the totality of the involved players. Clearly, any dynamic model in which players form coalitions that are subgroups of the grand coalition deserves a special attention as well, but it is outside the scope of this paper (for the construction of the value functions in cooperative games, see, for example, [27,28] for cooperative differential games).…”

Section: Main Results In the Cooperative Setupmentioning

confidence: 99%

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

2018

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A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively.

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“…We will also draw on it in our analysis. As for determining the characteristic function, we will use the maximin approach [11], although there are other approaches [10,[12][13][14][15][16] in the same context of the model under consideration. Since the characteristic function is key in sustaining the cooperative agreement during its implementation, we study when this function does not change over time under the two economic models as cooperative two-stage games with network externalities.…”

Section: Introductionmentioning

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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On an approach to constructing a characteristic function in cooperative differential games

Cited by 41 publications

References 9 publications

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

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

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