Time-Consistent Solutions for Two-Stage Network Games with Pairwise Interactions

Petrosyan, Leon A.; Bulgakova, Maria A.; Sedakov, Artem A.

doi:10.1007/s11036-018-1127-7

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…Two-stage network games and the mechanism of network formation also was considered in (Petrosyan et al, 2013). The paper (Bulgakova et al, 2018) is devoted to finding the basic solutions of two-stage cooperative games with pairwise interaction and also to the investigation of the supermodularity of the characteristic function is the special class of network, namely, the star-network. This property significantly increases the value of such a solution as the Shapley value, since in the case of a convex game it always belongs to the core.…”

Section: Introductionmentioning

confidence: 99%

The τ-value in Multistage Games with Pairwise Interactions

Bulgakova¹

2022

Contributions to Game Theory and Management

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We consider multistage bimatrix games with pairwise interactions. On the first stage players chose their neighbours and formed a network. On the later stages bimatrix games between neighbours by network take places. As a solution consider the τ-value (Tijs, 1987). Earlier we calculated coefficient λ of τ-value in case of two-stage game. Now we consider a general case of one-stage game with any players and any number of links. We assumed followings: N is set of players, N ≥ 2 and any type of network g. It is also assumed, that there are not necessarily paths between every pair of vertices. We will consider conditions for time-consistency of τ-value in two-stage game.

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Section: Introductionmentioning

confidence: 99%

The τ-value in Multistage Games with Pairwise Interactions

Bulgakova¹

2022

Contributions to Game Theory and Management

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“…In this paper, we will examine the time consistency problem for two models with network externalities represented by a two-stage network game. The theoretical fundamentals of cooperative two-stage network games including time consistency were introduced in [2][3][4]. Is it supposed that players create a network at the first game stage by announcing potential partners they wish to be connected with, and at the second stage players choose actions.…”

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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“…To the best of the author's knowledge, the research related to cooperative games with pairwise interaction is done in [4][5][6][7][8]. For the first time, in a cooperative form, a multistage network game with pairwise interaction is considered, when players play bimatrix games with their neighbors by network structure, and sufficient conditions for strong time consistency of the core are formulated [4].…”

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confidence: 99%

“…For the first time, in a cooperative form, a multistage network game with pairwise interaction is considered, when players play bimatrix games with their neighbors by network structure, and sufficient conditions for strong time consistency of the core are formulated [4]. Also, in [5], for a particular class of symmetric networks (star-network), a simplified formula for calculating the components of the Shapley value is obtained, and conditions for strong time consistency of the core are derived. In [6], considering multistage cooperative games with pairwise interaction, an analogue of the core is constructed and its strong time consistency proved.…”

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A note on cooperative differential games with pairwise interactions

He,

Petrosyan

2024

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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In this paper, a differential game with pairwise interaction in a network is proposed. For explicitly, the vertices are players, and the edges are connections between them. Meanwhile, we consider the cooperative case. One special characteristic function is introduced and its convexity is proved. The core is used as a cooperative optimality principle. The characteristic function allows the construction of a time-consistent (dynamically stable) solutions, such as the Shapley value and the core. Finally, the results are illustrated by an example.

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Time-Consistent Solutions for Two-Stage Network Games with Pairwise Interactions

Cited by 6 publications

References 19 publications

The τ-value in Multistage Games with Pairwise Interactions

The τ-value in Multistage Games with Pairwise Interactions

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

A note on cooperative differential games with pairwise interactions

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