Vladimir Mazalov

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• PhD, DSci
• Professor at St Petersburg University

A game-theoretic model of pricing in an urban public transport market is considered. It is assumed that the players in the model are transport companies serving urban public transport routes, and the distribution of passengers over the routes is subject to the Hotelling specification. The study focuses on the Nash equilibrium in the pricing game in...

The problem of dividing a pie between two persons is considered. An arbitration procedure for dividing the pie is proposed, in which the arbitrator is a random number generator. In this procedure, the arbitrator makes an offer to the players at each step, and the players can either accept or reject the arbitrator’s offer. If there is no consensus,...

Heterogeneous congestion games make it possible to simulate traffic situations involving multiple classes of vehicles with different preferences in choosing routes. In the presented work, we prove the existence of a potential in a discrete congestion game with $n$ classes of players. Examples are given of calculating equilibria and the emergence of...

Cooperation plays an important role in dynamic games related to resource management problems. To construct the cooperative behavior in asymmetric (when players possess different discount factors) and multicriteria (when players have vector payoff functions) dynamic games the standard approaches are not applicable. The paper presents the methods bas...

The paper considers a game theory approach to calculating the centrality value of the vertices in a directed graph, based on the number of vertex occurrences in fixed length paths. It is proposed to define vertex centrality as a solution of a cooperative game, where the characteristic function is given as the number of simple paths of fixed length...

The paper considers a game theory approach to calculating the centrality value of the vertices in a directed graph, based on the number of vertex occurrences in fixed length paths. It is proposed to define vertex centrality as a solution of a cooperative game, where the characteristic function is given as the number of simple paths of fixed length...

This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. In addition, each customer entering the system uses a strategy and must...

Dynamic game related to resource management problem is considered. The planning horizon is assumed to be divided into the periods of exploitation where many players use a common resource and the periods of recovery where the resource stock is evolving according to the natural growth rule. Both noncooperative and coordinated players’ behaviors are i...

The gambler’s ruin problem is studied. At each of n steps, the probability that the player wins at the next step depends on the win/lose ratio in previous steps. The player’s payoff and the asymptotic formula for large game durations were determined. The numerical results of payoff simulation for different n values are reported.KeywordsRandom walkG...

A single-server queueing system with preemptive access is considered. Each customer has one attempt to enter the system at its working interval [0, T]. As soon as the customer request enters the system, the server immediately starts the service. But when the next request arrives in the system, the previous one leaves the system even he has not fini...

A method for ranking the vertices of a graph based on Kirchhoff’s laws for determining the potentials of an electrical network is proposed. The graph is represented as an electrical network, where the edge weights are interpreted as electrical conductivities. Next, the current is supplied to one of the vertices, and the absolute potentials of all v...

We propose a method for estimating the complexity of texts based on the methods of cooperative game theory. The players in this game are the lengths of words in the text. The game itself is represented as a voting game in which the value of a player is determined by the number of coalitions in which the player is key. The ranks of the players are f...

Network models are widely employed in many areas of science and technology. Mathematical analysis of their properties includes various methods to characterize, rank and compare network nodes. A key concept here is centrality, a numerical value of node importance in the whole network. As the links in a network represent interactions between the node...

We consider the Wardrop model with splittable traffic and externalities applied to the parallel transportation network. These externalities are introduced into the players’ latency functions as a tool of the system’s influence on the equilibrium distribution of traffic flows and also on the PoA values. In the general case, the externalities can be...

1 Preface This special issue contains 11 papers submitted by the participants of the International Conference “Mathematical Optimization Theory and Operations Research” (MOTOR 2020) which was held online from July 6 to July 10, 2020. Like previous MOTOR conferences, this event was intended to bring together researchers and practitioners working in...

This paper considers a single-server queueing system with strategic users in which customers (players) enter the system with preemptive access. As soon as the customer request enters the system, the server immediately starts the service. But when the next request arrives in the system, the previous one leaves the system even he has not finished his...

We find an equilibrium in a single-server queueing system with retrials and strategic timing of the customers. We consider a set of customers, each of which must decide when to arrive to a queueing system during a fixed period of time. In this system, after completion of service, the server seeks a customer blocked in a virtual orbit (orbital custo...

A method of ranking the corpus of texts of a news portal, based on measures of graph centrality, is proposed. Each text is assigned a vertex of a certain graph, and its structure is determined based on the semantic connectivity of the texts. As a measure of centrality, the Myerson value is used in a cooperative game on a graph, where the number of...

A game-theoretic model of competitive decision on a meet time is considered. There are n players who are negotiating the meeting time. The objective is to find a meet time that satisfies all participants. The players' utilities are represented by linear unimodal functions ui(x), x∈ [0, 1], i=1,2,...,n. The maximum values of the utility functions ar...

The paper presents the results of modeling of the city's transport network. The effectiveness of the game-theoretic method for estimating the centrality of graph vertices using the Myerson value is demonstrated on the transport graph. Correspondences in the given graph are found with gravitational and entropy approaches, using the information about...

This paper considers a game-theoretic model of external control influence on opinion dynamics and reached consensus in a social network. The network participants are linked through an arbitrary communication graph. The goal of control is to keep the opinions of all network participants in the neighborhood of a given value. If there are several play...

We consider a cooperative packing game in which the characteristic function is defined as the maximum number of independent simple paths of a fixed length included in a given coalition. The conditions under which the core exists in this game are established, and its form is obtained. For several particular graphs, the explicit form of the core is p...

We consider a model of renewable resource extraction described by a differential game with infinite horizon. The environmental problems are often considered from cooperative prospective as selfish behavior of the players may negatively affects not only on other players’ profits, but also on the environment. The reason is the joint stock of resource...

We consider a game-theoretic model of the influence of players on the dynamics of opinions and the consensus achieved in a social network. The control problem is to maintain the opinions of all participants in the vicinity of a predetermined value. If there are several players, then these target values may differ. The considered dynamic game belong...

This paper is devoted to the study of multicriteria cooperative games with vector payoffs and coalition partition. An imputation based on the concept of the Owen value is proposed. The definition of a stable coalition partition for bi-criteria games is formulated. A three-player cooperative game with the 0-1 characteristic function is considered an...

To analyze the structure of social networks, the methods of cooperative game theory can be adopted. One of such methods is based on the calculation of the Myerson values as a centrality measure of the vertices in a graph. In this case, the number of paths of a certain length in the subgraphs corresponding to the coalitions is used as the characteri...

FOREWORD: SPECIAL ISSUE “EURO 2019: GAMES IN ECONOMICS, FINANCE AND BIOLOGY” Game theory is a mathematical framework developed to address problems with conflicting or cooperating parties who are able to make rational decisions. The theory primarily deals with the finding the optimal rational decision in various scenarios. Game theory is a relativel...

A game-theoretic model of the influence of players on the dynamics of opinions and the achieved consensus in the social network is considered. The goal of a player is to maintain the opinion of all participants in the vicinity of a predetermined value. If there are several players, then these target values are they can be different. The dynamic gam...

This paper considers a game-theoretic model of a competition in which experts (players) seek to enroll two contestants into their own teams. The quality of the contestants is characterized by two random parameters, the first corresponding to the vocal talent of a contestant and the second to his appearance. The first quality parameter is known to t...

We consider a cooperative game based on a network in which nodes represent players and the characteristic function is defined using a maximal covering by the pairs of connected nodes. Problems of this form arise in many applications such as mobile communications, patrolling, logistics and sociology. The Owen value, which describes the significance...

In a transportation network comprised of parallel routes with linear latency functions, we study how externalities among different routes affect the socially optimal allocation and the equilibrium allocation of traffic flows. Assuming that the externalities are not too severe, we analytically derive a system of equations that define the optimal dis...

Equilibrium in a two-sided market represented by network platforms on the plane and heterogeneous agents is investigated. The advocated approach is based on the duopoly model which implies a continuum of agents of limited size on each side of the market and examines the agents’ heterogeneous utility with the Hotelling specification. The exact value...

The problem of choosing the optimal parameters of service by carriers in public transport passenger flows is considered. This problem is modeled as a two-stage game. At the first stage, the players (carriers) select the parameters of their service (the number and schedule of vehicles, etc.). At the second stage, the players announce the prices of s...

We consider the models of average-oriented opinion dynamics. An opinion about an event is distributed among the agents of a social network. There are an optimization problem and two game-theoretical models when players as centers of influence aim to make the opinions of the agents closer to the target ones in a finite time horizon minimizing their...

The paper examines a multi-stage game-theoretic model of an auction where the participants (players) set minimum threshold price levels above which they are ready to sell. Price offerings are a sequence of independent and identically distributed random variables. A two-person game in which each player is interested in selling at a price higher than...

A tournament can be represented as a set of candidates and the results from pairwise comparisons of the candidates. In our setting, candidates may form coalitions. The candidates can choose to fix who wins the pairwise comparisons within their coalition. A coalition is winning if it can guarantee that a candidate from this coalition will win each p...

This book includes papers presented at the ISDG12-GTM2019 International Meeting on Game Theory, as a joint meeting of the 12th International ISDG Workshop and the 13th "International Conference on Game Theory and Management”, held in St. Petersburg in July 2019. The topics cover a wide range of game-theoretic models and include both theory and app...

We examine the influence of management of the opinion of a group members, while the group of agents are considered with different communication structures. We consider the optimization problem in dynamics with feedback information structure. In the model, the communication structure plays an important role since not all agents are directly connecte...

The popular TV show “The Price Is Right” is an attractive source of modeling the strategic behavior in a competitive environment for a specific reward. In this study, the structure of the show is used as a basis for several game-theoretic settings. We consider a noncooperative optimal stopping game for a finite number of players. Each player earns...

The existence of a Nash-stable coalition structure in cooperative games with the Aumann–Dreze value is investigated. Using the framework of potential functions, it is proved that such a coalition structure exists in any cooperative game. In addition, a similar result is established for some linear values of the game, in particular, the Banzhaf valu...

This paper studies equilibrium in a two-sided market represented by network platforms and heterogeneous agents. The setup below is based on the Armstrong monopoly model suggested in 2006 under the following assumptions: (1) a continuum of agents of limited size on each side of the market and (2) the heterogeneous utility of agents with the Hotellin...

The paper considers the model of opinion dynamics in the network having a star structure. An opinion about an event is distributed among network agents restricted by the network structure. The agent in the center of the star is influenced by all other agents with equal intensity. The agents located in non-center nodes are influenced only by the age...

Commuting to work by shared bicycle is an increasingly popular transportation option. We examine the trip data from Citibike, the shared bicycle program of New York City, restricting the analysis to morning rides into the Wall Street area, a destination for which workers are likely to be sensitive to their arrival time. Among the frequent commute o...

We study a two-sided market represented by network platforms and heterogeneous agents. Our setup departs from Armstrong (2006)’s monopoly model by assuming both (1) a continuum of agents of limited size on each side of the market and (2) heterogeneous utility of agents with Hotelling specification. We show that the monopoly’s optimal pricing strate...

The paper is devoted to the study of multicriteria cooperative games with vector payoffs and coalition partition. The imputation which is based on the concept of the Owen value is proposed. We use it for the definition of stable coalition partition for bicriteria games. In three person cooperative game with 0-1 characteristic function the condition...

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on “Game Theory and Management” 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

We study the problem of determining the rating among members of educational groups of different levels: secondary schools, colleges, universities. Models of ratings of teachers and students are described. The method is based on the De Groot model using an influence matrix calculated for different types of educational groups are represented by princ...

ABSTRACT Mazalov V. V., Dorofeeva J. A., Konovalchikova E. N. // Vestnik St.Petersburg University. Ser. 4. 2019. Iss. 3. P. 1–14. We study the problem of determining the rating among members of educational groups of different levels: secondary schools, colleges, universities. Models of ratings of teachers and students are described. The method is b...

We study Wardrop equilibrium in a transportation system with profit-maximizing firms and heterogeneous commuters. Standard commuters minimize the sum of monetary costs and equi- librium travel time in their route choice, while ”oblivious” commuters choose the route with minimal idle time. Three possible scenarios can arise in equilibrium: A pooling...

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation...

In this paper, we propose a game-theoretic model of the mobile network market. The market is presented by three sides: primary mobile network operators (MNO), mobile virtual network operators (MVNO) and consumers of the services. MVNO are mobile operators without their own infrastructure. They buy resources from MNO and compete with other MVNO for...

This paper considers a market where two large companies provide services to the population through “cloud” virtual operators buying companies’ services and reselling them to clients. Each large company assigns a price for selling its services to virtual operators. Also the number of its clients and its resource (a characteristic of company’s attrac...

The community detection in social and communication networks is an important problem in many applied fields: biology, sociology, social networks. This is especially true for networks that are represented by large graphs. In this paper, we propose a method for community detection based on the maximum likelihood method for the random formation of a n...

The purpose of this article is to show the relationship between the game-theoretic approach and the maximum likelihood method in the problem of community detection in networks. We formulate a cooperative game related with network structure where the nodes are players in a hedonic game and then we find the stable partition of the network into coalit...

In this paper we propose a mathematical model and implement an algorithm to detect commu�nities structure in networks presented by either non-oriented simple graphs or multigraphs and belonging to various subject areas. The base of the mathematical model is the maximum likelihood method for random generation of a network with given parameters of li...

This volume collects contributions from the talks given at the Game Theory and Management Conference held in St. Petersburg, Russia, in June 2017. It covers a wide spectrum of topics, among which are: game theory and management applications in fields such as: strategic management, industrial organization, marketing, operations and supply chain mana...

We consider the problem of community detection for the graph which is a fragment of the academic Web. The nodes of the graph are the sites of the scientific organizations, and its arcs are hyperlinks. We propose a new approach based on the methods of coalition game theory to derive the Nash-stable coalition partition. This is determined by a functi...

Discrete-time game-theoretic models of resource exploitation are treated as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim of the paper is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadra...

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting denser subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation....

Final version: Kondratev, A. Y., & Mazalov, V. V. (2020). Tournament solutions based on cooperative game theory. International Journal of Game Theory, 49(1), 119-145. https://www.researchgate.net/publication/333085593_Tournament_solutions_based_on_cooperative_game_theory

This paper considers a network comprised of parallel routes with the Bureau of Public Road (BPR) latency function and suggests an optimal distribution method for incoming traffic flow. The authors analytically derive a system of equations defining the optimal distribution of the incoming flow with minimum social costs, as well as a corresponding sy...

The betweenness centrality is one of the basic concepts in the analysis of the social networks. Initial definition for the betweenness of a node in the graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This metho...

This paper extends the concept of betweenness centrality based on Kirchhoff’s law for electric circuits from centrality of nodes to centrality of edges. It is shown that this new measure admits analytical definition for some classes of networks such as bipartite graphs, with computation for larger networks. This measure is applied for detecting com...

This paper proposes a game-theoretic model of the two-player best-choice problem with incomplete information. The players (experts) choose between objects by observing their quality in the form of two components forming a sequence of random variables (x i , y i ), i = 1,..., n. By assumption, the first quality component x i is known to the players...

This paper studies a game-theoretic model of best choice with incomplete information. In this model, players observe a sequence of incoming objects each described by two random quality components. The first component is announced to players and the other one is hidden. Players choose an object based on known information about it. The winner is the...

This paper considers a noncooperative transport game of (Formula presented.) players on a communication graph. Here players are passenger transportation companies (carriers). Service requests form a Poisson process with an intensity rate matrix (Formula presented.). Players announce prices for their services and passengers choose an appropriate ser...

We consider a market where the consumers are distributed in the vertexes of a transportation graph. The edges of the graph are the transportation links. The vertexes are the hubs. The consumers are the passengers who use this kind of transportation. The demand is determined by the flow of passengers. There are n companies (players) who make a servi...

This paper considers a best-choice game with incomplete information associated with the job search problem. Players (experts) observe a sequence of independent identically distributed random variables (xi, yi), i = 1. . ., n, which represent the quality of incoming objects. The first component is announced to the players and the other one is hidden...

This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to construct a characteristic function via the filled ballot paper profile of voters. The Shapley value serves as the r...

We propose a new method for determining betweenness centraity for weighted graphs based on Kirchhoff's law. This method has low computational complexity. The results of numerical experiments are presented for the coauthors graph from the math portal Math -Net. ru . A comparison is drawn with the PageRank method

This paper considers a statistical model of passenger flows between bus stops. By assumption, the intensities of incoming and outcoming passenger flows are known. We propose an estimation technique for the distribution of incoming passengers at a certain bus stop with respect to all successive bus stops. The simulation results based on natural expe...

Desktop Grids utilize computational resources of desktop computers in their idle time. The BOINC middleware for organizing Desktop Grids has an architecture developed to unite a large number of computing nodes. However, a large flow of server requests may limit the Desktop Grid performance. In the paper we present a game-theoretical model of task s...

Betweenness centrality is one of the basic concepts in the analysis of social networks. Initial definition for the betweenness of a node in a graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This method has quad...

Abstract The emerging market of public and private cloud infrastructure benefits the end users, as it reduces their costs, introduces new efficient services and provides variety of products. End-users primary deal with private clouds or brokers, which serve all the users needs, and if needed, buy extra capacity from public cloud. In this paper we s...