Equilibrium Points in Game Theory

2020 ◽

Author(s):

Zahra VEISI ◽

Heydar KHADEM ◽

Samin RAVANSHADI

Keyword(s):

Game Theory ◽

Stem Cells ◽

Stem Cell ◽

Evolutionary Game Theory ◽

Equilibrium Points ◽

Evolutionary Game ◽

Mathematical Framework ◽

Replicator Equations ◽

Different Types ◽

Cancerous Cells

Background: Immunotherapy is a recently developed method of cancer therapy, aiming to strengthen a patient’s immune system in different ways to fight cancer. One of these ways is to add stem cells into the patient’s body. Methods: The study was conducted in Kermanshah, western Iran, 2016-2017. We first modeled the interaction between cancerous and healthy cells using the concept of evolutionary game theory. System dynamics were analyzed employing replicator equations and control theory notions. We categorized the system into separate cases based on the value of the parameters. For cases in which the system converged to undesired equilibrium points, “stem-cell injection” was employed as a therapeutic suggestion. The effect of stem cells on the model was considered by reforming the replicator equations as well as adding some new parameters to the system. Results: By adjusting stem cell-related parameters, the system converged to desired equilibrium points, i.e., points with no or a scanty level of cancerous cells. In addition to the theoretical analysis, our simulation results suggested solutions were effective in eliminating cancerous cells. Conclusion: This model could be applicable to different types of cancer, so we did not restrict it to a specific type of cancer. In fact, we were seeking a flexible mathematical framework that could cover different types of cancer by adjusting the system parameters.

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Game Theory

10.1017/9781108636049 ◽

2020 ◽

Author(s):

Michael Maschler ◽

Eilon Solan ◽

Shmuel Zamir

Keyword(s):

Game Theory ◽

Stochastic Games ◽

Equilibrium Points ◽

Worked Examples ◽

Graduate Courses ◽

Bargaining Set ◽

Incomplete Information Games ◽

Games With Incomplete Information ◽

New Material ◽

Games With Vector Payoffs

Now in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reference for researchers.

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