Game Theory

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.

scholarly journals Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective

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.

Rationalization and Incomplete Information

2003 ◽  
Vol 3 (1) ◽  
Author(s):  
Pierpaolo Battigalli ◽  
Marciano Siniscalchi
Keyword(s):  
Incomplete Information ◽  
Dynamic Games ◽  
Form Solution ◽  
Forward Induction ◽  
First Order ◽  
Bayesian Equilibrium ◽  
Incomplete Information Games ◽  
Games With Incomplete Information ◽  
Intuitive Criterion ◽  
Signalling Games

We analyze a family of extensive-form solution procedures for games with incomplete information that do not require the specification of an epistemic type space a la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions D on first-order beliefs. For any fixed D we obtain a solution called D-rationalizability.In static games, D-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibrium model consistent with D; these are precisely the outcomes consistent with common certainty of rationality and of the restrictions D. Hence, our approach to the analysis of incomplete-information games is consistent with Harsanyi's, and it may be viewed as capturing the robust implications of Bayesian equilibrium analysis.In dynamic games, D-rationalizability yields a forward-induction refinement of this set of Bayesian equilibrium outcomes. Focusing on the restriction that first-order beliefs be consistent with a given distribution on terminal nodes, we obtain a refinement of self-confirming equilibrium. In signalling games, this refinement coincides with the Iterated Intuitive Criterion.

Formal Models of Domestic Politics

2021 ◽  
Author(s):  
Scott Gehlbach
Keyword(s):  
Game Theory ◽  
Mathematical Knowledge ◽  
Domestic Politics ◽  
The Political ◽  
Formal Models ◽  
Legislative Bargaining ◽  
Economics Students ◽  
New Models ◽  
New Material ◽  
Basic Calculus

Formal Models of Domestic Politics offers a unified and accessible approach to canonical and important new models of politics. Intended for political science and economics students who have already taken a course in game theory, this new edition retains the widely appreciated pedagogic approach of the first edition. Coverage has been expanded to include a new chapter on nondemocracy; new material on valance and issue ownership, dynamic veto and legislative bargaining, delegation to leaders by imperfectly informed politicians, and voter competence; and numerous additional exercises. Political economists, comparativists, and Americanists will all find models in the text central to their research interests. This leading graduate textbook assumes no mathematical knowledge beyond basic calculus, with an emphasis placed on clarity of presentation. Political scientists will appreciate the simplification of economic environments to focus on the political logic of models; economists will discover many important models published outside of their discipline; and both instructors and students will value the classroom-tested exercises. This is a vital update to a classic text.

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