Artem Sedakov

Two-stage network games

In the paper, two-stage network games are studied. At the first stage of the game, the players form a network, while at the second stage they choose strategies according to the network realized at the first stage. Both noncooperative and cooperative settings are considered. In the noncooperative case, the Nash equilibrium is used as a solution concept, whereas the cooperative setting involves an allocation (the Shapley value) as a solution concept. It is demonstrated that the Shapley value does not satisfy the time consistency property.

Multistage network games with perfect information

We consider multistage network games with perfect information. At each time instant, a current network structure connecting the players is specified. It is assumed that each edge has some utility value (player’s benefit from being linked to another player), and players can change the network structure at each stage. We propose a method for finding optimal behavior for players in games of this type.

Cooperation in two-stage games on undirected networks

In the paper, cooperative two-stage network games are studied. At the first stage of the game, players form a network, while at the second stage players choose their behaviors according to the network realized at the first stage. As a cooperative solution concept in the game, the core is considered. It is proved that some imputations from the core are time inconsistent, whereas one can design for them a time-consistent imputation distribution procedure. Moreover, the strong time consistency problem is also investigated.

The Subgame-Consistent Shapley Value for Dynamic Network Games with Shock

In the paper, cooperative repeated network games containing network formation stages are studied. After the first network formation stage, a particular player with a given probability may stop influencing other players by removing all her links and receiving zero payoffs. This effect is called “shock.” The effect of shock may appear only once, and the stage number, at which shock appears, is chosen at random. In the cooperative scenario of the game, subgame consistency of the Shapley value, based on a characteristic function, which is constructed in a special way, is investigated. To prevent players from breaking the cooperative agreement, a mechanism of stage payments—so-called imputation distribution procedure—is designed.

Transformation of Characteristic Function in Dynamic Games

Abstract The problem of transformation of characteristic function, using a transformation matrix and connected with associated consistency of a solution concept, was investigated for the class of so-called “one-shot” games. The same problem also arises in dynamic games when players move step by step along the cooperative trajectory. In this case the evolution of characteristic function is, in general, unpredictable and may lead to time-inconsistency of a fixed cooperative solution concept. There are different approaches to overcome this problem based on transformation of characteristic function. In this paper, the step-wise transformation is used, which is a generalization of similar transformation of characteristic function for dynamic games with perfect information, and it leads to the time-consistent solution. The general form of such transformation is proposed.

On the Strong Time Consistency of the Core

Time consistency is one of desirable properties for any solution of a cooperative dynamic game. If a solution is time-consistent, the players do not need to break a cooperative agreement. In this paper, we consider the core as the solution and establish conditions for its strong time consistency. When the core is not strongly time-consistent, we show that in some cases its elements can be yielded using a strongly time-consistent imputation distribution procedure. An explicit form of the procedure is given.

Consensus in a social network with two principals

This paper considers a model of opinion dynamics in a social network with two principals, in which the members may affect the opinions of each other and their opinions evolve according to a time-homogeneous Markov chain. We study the existence of a consensus in this network for two types of influence models, namely, when the principals may or may not affect the opinions of each other directly. In addition, we find the values of social network parameters under which a consensus is reached. For the cases without a consensus in its standard definition, we introduce the notion of a consensus of the majority and find the parameter values under which it is reached. Two numerical examples illustrate the obtained theoretical results.

A Dynamic Formation Procedure of Information Flow Networks

Abstract A characterization of the equilibrium of information flow networks and the dynamics of network formation are studied under the premise of local information flow. The main result of this paper is that it gives the dynamic formation procedure in the local information flow network. The research shows that core-periphery structure is the most representative equilibrium network in the case of the local information flow without information decay whatever the cost of information is homogeneous or heterogeneous. If the profits and link costs of local information flow networks with information decay are homogeneous empty network and complete network are typical equilibrium networks, which are related to the costs of linking.

The Time-Consistent Shapley Value for Two-Stage Network Games with Pairwise Interactions

In this paper, cooperative network games with pairwise interactions are considered. The cooperative version of games is investigated. For a particular type of networks, a simplified formula for the Shapley value based on a constructed characteristic function is derived. The time inconsistency of the Shapley value is shown.

Characteristic Functions in a Linear Oligopoly TU Game

We consider a linear oligopoly TU game without transferable technologies in which the characteristic function is determined from different perspectives. In so-called γ-, δ-, and ζ-games, we study the properties of characteristic functions such as monotonicity, superadditivity, and supermodularity. We also show that these games have nonempty cores of a nested structure when the δ-characteristic function is supermodular.