Maria Nastych

Bio: Maria Nastych is an academic researcher from National Research University – Higher School of Economics. The author has contributed to research in topics: Oligopoly & Differential game. The author has an hindex of 2, co-authored 6 publications receiving 24 citations. Previous affiliations of Maria Nastych include Saint Petersburg State University.

Non-cooperative Differential Game Model of Oil Market with Looking Forward Approach

Abstract: The paper applies Looking Forward Approach to analyze the world oil market with the framework of a differential game model of quantity competition oligopoly Namely Looking Forward Approach is used to take into account dynamically updating information Under the information we understand the forecast of the oil demand dynamics We focus on the period from December 2015 to November 2016 and suppose that during this time interval countries did not cooperate officially on the amounts of oil to be produced Therefore, their behavior can be modeled using the non-cooperative game model As a solution concept for this conflict-controlled process we use feedback Nash equilibrium In order to define the parameters of model open source data is used, results of numerical simulations and comparison with the historical data are presented

Differential game of oil market with moving informational horizon and non-transferable utility

Abstract: Non-transferable utility game of oil market is considered. Special approach for defining solution is used. This approach enables to construct a real time models of conflicting processes. Connection between the solution in the game with moving information horizon and solutions on the truncated time intervals is shown.

The Looking Forward Approach in a Differential Game Model of the Oil Market with Non-transferable Utility

Abstract: The paper applies the Looking Forward Approach to analyze the world oil market within the framework of a differential game model of a quantity competition oligopoly. More precisely, the Looking Forward Approach is used to take into account dynamically updating information. Under information we understand the forecast of oil demand dynamics. We use a non-cooperative game modeling for the period from December 2015 to November 2016, because over this period the countries did not cooperate officially in what concerns the amounts of oil to be produced. For the period from December 2016 to May 2017, a non-transferable utility cooperative game modeling is adapted due to the agreement to reduce oil extraction signed by the largest oil exporters at the end of November 2016. We use both solutions, which correspond to the historical cooperative solution and the sub-game consistent solution proposed developed in the field of dynamic games. In order to define the parameters of the model, open source data is used, with the results of numerical simulations and comparison between the historical data and model data for both periods also presented.

Mergers and Acquisitions Stochastic Cooperative Games

Abstract: Study of the formation and subsequent behavior of the companies’ coalitions are becoming increasingly important in today's economy. In the elementary case, the process of collaboration may be represented as a classical cooperative game with transferable utility. However, the assumption of the possibility of describing the potential winnings of coalitions using deterministic values seems very controversial. Hypothesis of their random nature is much more realistic. The paper presents the conversion from classical cooperative game theory with side-payments to stochastic analog. Game theory modeling of mergers and acquisitions processes is based on this class of games here.

Coordination within a Supply Chain with a Profit Sharing Contract

Abstract: We analyze an equilibrium choice of a product quality within a supply chain consisting of a manufacturer and a supplier. A quality of an intermediate good is private information of the supplier and determines the quality of a final product. The manufacturer holds all bargaining power and proposes a profit sharing contract to the supplier. We show that (i) such the contract may serve as the efficient mechanism of within-chain coordination in special cases and (ii) tougher market competition may lead to a higher profit of both supplier and manufacturer.

The Economic Institutions of Capitalism

Abstract: The 2008 crash has left all the established economic doctrines - equilibrium models, real business cycles, disequilibria models - in disarray. Part of the problem is due to Smith’s "veil of ignorance": individuals unknowingly pursue society’s interest and, as a result, have no clue as to the macroeconomic effects of their actions: witness the Keynes and Leontief multipliers, the concept of value added, fiat money, Engel’s law and technical progress, to name but a few of the macrofoundations of microeconomics. A good viewpoint to take bearings anew lies in comparing the post-Great Depression institutions with those emerging from Thatcher and Reagan’s economic policies: deregulation, exogenous vs. endoge- nous money, shadow banking vs. Volcker’s Rule. Very simply, the banks, whose lending determined deposits after Roosevelt, and were a public service became private enterprises whose deposits determine lending. These underlay the great moderation preceding 2006, and the subsequent crash.

On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating

Abstract: The subject of this paper is a linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new, there it is assumed that at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. As time goes on, information about the game structure updates. Under the information about the game structure we understand information about motion equations and payoff functions of players. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. The notion of Nash equilibrium as an optimality principle is defined and the explicit form of Nash equilibrium for the linear quadratic case is presented. Also, the case of dynamic updating for the linear quadratic differential game is studied and uniform convergence of Nash equilibrium strategies and corresponding trajectory for a case of continuous updating and dynamic updating is demonstrated.

Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating

Abstract: This paper is devoted to a new class of differential games with continuous updating. It is assumed that at each time instant, players have or use information about the game defined on a closed time interval. However, as the time evolves, information about the game updates, namely, there is a continuous shift of time interval, which determines the information available to players. Information about the game is the information about motion equations and payoff functions of players. For this class of games, the direct application of classical approaches to the determination of optimality principles such as Nash equilibrium is not possible. The subject of the current paper is the construction of solution concept similar to Nash equilibrium for this class of differential games and corresponding optimality conditions, in particular, modernized Hamilton-Jacobi-Bellman equations.

Moving Information Horizon Approach for Dynamic Game Models

Abstract: 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.

Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle

Abstract: We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval of a fixed duration. Over time, information about the game structure will be updated. The subject of the current paper is to construct players’ cooperative strategies, their cooperative trajectory, the characteristic function, and the cooperative solution for this class of differential games with continuous updating, particularly by using Pontryagin’s maximum principle as the optimality conditions. In order to demonstrate this method’s novelty, we propose to compare cooperative strategies, trajectories, characteristic functions, and corresponding Shapley values for a classic (initial) differential game and a differential game with continuous updating. Our approach provides a means of more profound modeling of conflict controlled processes. In a particular example, we demonstrate that players’ behavior is braver at the beginning of the game with continuous updating because they lack the information for the whole game, and they are “intrinsically time-inconsistent”. In contrast, in the initial model, the players are more cautious, which implies they dare not emit too much pollution at first.