scholarly journals Game theoretic modeling of AIMD network equilibrium

2016 ◽  
pp. 116-128
Author(s):  
O.P. Ignatenko ◽  
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Existence And Uniqueness ◽  
Denial Of Service ◽  
Payoff Matrix ◽  
Network Equilibrium ◽  
Theory Approach ◽  
Equilibrium Existence ◽  
Network Game ◽  
Game Theoretic

This paper deals with modeling of network’s dynamic using game theory approach. The process of interaction among players (network users), trying to maximize their payoffs (e.g. throughput) could be analyzed using game-based concepts (Nash equilibrium, Pareto efficiency, evolution stability etc.). In this work we presented the model of TCP network’s dynamic and proved existence and uniqueness of solution, formulated payoff matrix for a network game and found conditions of equilibrium existence depending of loss sensitivity parameter. We consider influence if denial of service attacks on the equilibrium characteristics and illustrate results by simulations.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

scholarly journals New Directions for Modelling Strategic Behavior: Game-Theoretic Models of Communication, Coordination, and Cooperation in Economic Relationships

2016 ◽  
Vol 30 (4) ◽  
pp. 131-150 ◽  
Author(s):  
Vincent P. Crawford
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Strategic Behavior ◽  
Economic Problem ◽  
Noncooperative Game ◽  
Economic Relationships ◽  
Future Developments ◽  
New Directions ◽  
Game Theoretic

In this paper, I discuss the state of progress in applications of game theory in economics and try to identify possible future developments that are likely to yield further progress. To keep the topic manageable, I focus on a canonical economic problem that is inherently game-theoretic, that of fostering efficient coordination and cooperation in relationships, with particular attention to the role of communication. I begin with an overview of noncooperative game theory's principal model of behavior, Nash equilibrium. I next discuss the alternative “thinking” and “learning” rationales for how real-world actors might reach equilibrium decisions. I then review how Nash equilibrium has been used to model coordination, communication, and cooperation in relationships, and discuss possible developments

A game theory approach to selecting marketing-mix strategies

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mansour Abedian ◽  
Atefeh Amindoust ◽  
Reza Maddahi ◽  
Javid Jouzdani
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Marketing Strategy ◽  
Equilibrium Model ◽  
Marketing Mix ◽  
Marketing Strategies ◽  
Theory Approach ◽  
Market Place ◽  
Content Type ◽  
The Game Theory

PurposeAdopting efficient marketing strategies is a challenging task in a competitive market place involving complex marketing planning, techniques and mechanisms to identify the best course of action under these circumstances and finding optimal solutions or stable outcomes. Decisions and strategies of competitors in the market influence the selection of the appropriate marketing strategy. The main purpose of this paper is to develop a mathematical methodology based on the game theory approach for planning optimal marketing-mix strategies in dynamic competitive markets, taking into account strategic foresight and interaction effects.Design/methodology/approachThe game theory approach, as a decision-making tool in conflict situations, is suggested for planning and adopting optimal marketing strategy. The main intellectual attraction of the game theory is essentially a question of how to act in gaming situations against highly rational opponents A kind of static, finite and non-cooperative game analytics approach has been developed for this issue, and the proposed model has been implemented to design optimal marketing strategies for two top brands of the automotive parts market in Iran.FindingsThe findings of this study show that the optimal marketing-mix strategy for brand A is pricing and for brand B is the product strategy.Practical implicationsGame theory and the Nash equilibrium model can provide a practical approach to find and adopt the right strategy, know competitors' movements and strategies and get more profit.Originality/valueThe integration of the game theory approach into the marketing mix framework has been adopted as a generalized model for marketing strategy planning and analysis as well as to resolve some shortcomings of the marketing mix framework. The Nash equilibrium model has been used to analyze the results. The incorporation of game theory into marketing models has the potential to enrich the scope of marketing modeling.

scholarly journals Game-theory models of binary collective behavior

2020 ◽  
Vol 12 (2) ◽  
pp. 3-19
Author(s):  
Владимир Валетинович Бреер ◽  
Vladimir Breer
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Collective Behavior ◽  
General Model ◽  
Nash Equilibria ◽  
Dynamic Models ◽  
Utility Functions ◽  
Point Of View ◽  
Algebraic Equations ◽  
Game Theoretic

Game-theoretic models were investigated not from the point of view of the maxima of the players' utility functions, as is usually done, but by solving algebraic equations that characterize the Nash equilibrium. This characterization is obtained for models of binary collective behavior, in which players choose one of two possible strategies. Based on the results for the general model, game-theoretic models of conformal threshold Binary Collective Behavior (BCB) are studied, provided the collective is divided into L groups. The conditions for the existence of Nash equilibria is proved. For each Nash equilibrium, its structure is defined. The results obtained are illustrated by two examples of conformal threshold BCB when the group coincides with the whole team and when the latter is divided into two groups. It is shown that the Nash equilibria in the first and second examples are analogues of the equilibria in the dynamic models of M. Granovetter and T. Schelling, respectively.

scholarly journals The contribution of evolutionary game theory to understanding and treating cancer

2020 ◽  
Author(s):  
Benjamin Wölfl ◽  
Hedy te Rietmole ◽  
Monica Salvioli ◽  
Frank Thuijsman ◽  
Joel S. Brown ◽  
...  
Keyword(s):  
Game Theory ◽  
Cancer Progression ◽  
Evolutionary Game Theory ◽  
Cancer Biology ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Great Promise ◽  
Full Potential ◽  
Theory Approach ◽  
Game Theoretic

AbstractEvolutionary game theory mathematically conceptualizes and analyzes biological interactions where one’s fitness not only depends on one’s own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather, inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer’s eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. We discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with an evolutionary game theory approach has medically useful implications that can inform and create a lockstep between empirical findings, and mathematical modeling. We suggest that cancer progression is an evolutionary game and needs to be viewed as such.

Dilemmas of Interaction

2018 ◽  
Author(s):  
Peter Vanderschraaf
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Incomplete Information ◽  
Mathematical Theory ◽  
Free Rider ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Free Rider Problem ◽  
Game Theoretic ◽  
Principles Of Justice

Problems of interaction, which give rise to justice, are structurally problems of game theory, the mathematical theory of interactive decisions. Five problems of interaction are introduced that are all intrinsically important and that help motivate important parts of the discussions in subsequent chapters: the Farmer’s Dilemma, impure coordination, the Stag Hunt, the free-rider problem, and the choice for a powerless party to acquiesce or resist. Elements of noncooperative game theory essential to analyzing problems of justice are reviewed, including especially games in the strategic and extensive forms, the Nash equilibrium, the Prisoner’s Dilemma, and games of incomplete information. Each of the five motivating problems is reformulated game-theoretically. These game-theoretic reformulations reveal precisely why the agents involved would have difficulty arriving at mutually satisfactory resolutions, and why “solutions” for these problems call for principles of justice to guide the agents’ conduct.

scholarly journals Comparative Study on Game-Theoretic Optimum Sizing and Economical Analysis of a Networked Microgrid

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 4004 ◽  
Author(s):  
Ali ◽  
Muyeen ◽  
Bizhani ◽  
Ghosh
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
System Optimization ◽  
Electrical Load ◽  
Economical Analysis ◽  
The Game Theory ◽  
Shapley Values ◽  
Game Theoretic ◽  
The Impact ◽  
Theory Technique

In this paper, two techniques of game theory are considered for sizing and comparative analysis of a grid-connected networked microgrid, based on a multi-objective imperialistic competition algorithm (ICA) for system optimization. The selected networked microgrid, which consists of two different grid-connected microgrids with common electrical load and main grid, might have different combinations of generation resources including wind turbine, photovoltaic panels, and batteries. The game theory technique of Nash equilibrium is developed to perform the effective sizing of the networked microgrid in which capacities of the generation resources and batteries are considered as players and annual profit as payoff. In order to meet the equilibrium point and the optimum sizes of generation resources, all possible coalitions between the players are considered; ICA, which is frequently used in optimization applications, is implemented using MATLAB software. Both techniques of game theory, Shapley values and Nash equilibrium, are used to find the annual profit of each microgrid, and results are compared based on optimum sizing, and maximum values of annual profit are identified. Finally, in order to validate the results of the networked microgrid, the sensitivity analysis is studied to examine the impact of electricity price and discount rates on maximum values of profit for both game theory techniques.

Applications to Game Theory

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Incomplete Information ◽  
Private Information ◽  
Quantal Response ◽  
Feedback Effects ◽  
Symmetric Game ◽  
Wide Range ◽  
The World ◽  
Game Theoretic

This chapter explores several applications of quantal response equilibrium (QRE) to specific games in order to illustrate and expand on the wide range of game-theoretic principles and phenomena associated with QRE that have been highlighted in the previous chapters. The first application considered belongs to the class of continuous games. With a continuum of decisions, QRE predicts a choice distribution that is not merely a (possibly asymmetric) spread to each side of a Nash equilibrium, since “feedback effects” from deviations by one player alter others' expected payoff profiles, which would induce further changes. The second application is a symmetric game with binary actions where players have continuously distributed private information about an unknown state of the world that affects both players' payoffs. The remainder of the chapter looks at three applications to extensive-form games, all of which are games of incomplete information.

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