Toán học và Thống kê
Xác suất, thống kê, lý thuyết trò chơi và toán học đằng sau học máy, kèm ví dụ giải chi tiết.
Game Theory Complete Learning Path
Game Theory A Complete Learning Path From Beginner to Advanced Player 1 Player 2 Player 2 (3, 1) (0, 0) (1, 3) (2, 2) A B a b a b Strategic Form Games · Nash Equilibrium· Dynamic Games Bayesian Games· Mechanism Design· C
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Appendix A Mathematical Background This appendix collects the mathematical prerequisites, stated for reference rather than developed from scratch. A.1 Sets, functions, correspondences A correspondenceF :X ⇒Y assigns to e
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Appendix B Solutions to Exercises Solutions are deliberately compact: they give the key steps and answers, leaving routine algebra to the reader. Attempt each exercise seriously before reading. Chapter 1 Exercise 1.1. (a
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Bibliography and Further Reading Textbooks Osborne, M. J. (2004).An Introduction to Game Theory. Oxford University Press. The most complete rigorous undergraduate text; the natural companion to Parts I–II of this book. G
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Chapter 1 What Is Game Theory? 1.1 Strategic interaction everywhere Consider the following situations: • Two firms decide simultaneously how to price a similar product. • Countries negotiate a climate treaty, each tempte
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Chapter 2 Rationality, Preferences, and Expected Utility Before analyzing games we must be precise about what a “payoff” is and what “rational” means. This chapter builds the decision-theoretic foundation on which all of
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Chapter 3 Games in Normal Form and Dominance We now formalize simultaneous-move games and develop the most conservative solution concepts: those that rely only on rationality and common knowledge of rationality. 3.1 The
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Chapter 4 Nash Equilibrium Dominance arguments are compelling but often silent: in the Battle of the Sexes or the Stag Hunt, nothing is dominated, and rationalizability permits everything. The central solution concept of
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Chapter 5 Mixed Strategies Matching Pennies has no pure Nash equilibrium: any deterministic play can be exploited. The way out, foreshadowed by the practice of every poker player and penalty-kick taker, is to randomize.
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Chapter 6 Extensive-Form Games and Backward Induction So far, players moved simultaneously. Most real interactions unfold overtime—entry then retaliation, offer then counteroffer—and timing changes everything: threats mu
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Chapter 7 Economic Applications: Markets and Strategy The concepts of Part I earn their keep in applications. This chapter analyzes the canonical models of imperfect competition and collective action—workhorses of indust
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Chapter 8 Bargaining How is a surplus divided when two parties must agree to realize it? Bargaining theory has two complementary traditions: Nash’saxiomatic approach (what properties should a solution have?) and Rubinste
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Chapter 9 Repeated Games and the Emergence of Cooperation The Prisoner’s Dilemma predicts defection—yet cooperation among self-interested parties is everywhere: cartels hold, merchants extend credit, countries honor trea
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Chapter 10 Bayesian Games: Incomplete Information Until now, everyone knew everyone’s payoffs. In reality, a bidder doesn’t know rivals’ valu- ations; an insurer doesn’t know the applicant’s risk; a poker player doesn’t
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Chapter 11 Dynamic Games with Incomplete Information: Signaling and Screening When informed players move first, theiractions speak: choices reveal, conceal, or distort private information. This chapter develops perfect B
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Chapter 12 Zero-Sum Games and the Minimax Theorem Pure conflict—what one wins, the other loses—is where game theory began, and where its theory is most complete. Zero-sum games also connect game theory to optimization (l
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Chapter 13 Existence of Equilibrium and Refinements This chapter supplies the rigorous core of non-cooperative theory: why equilibria exist, and how to discipline the multiplicity of equilibria in dynamic games. 13.1 Fix
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Chapter 14 Mechanism Design and Auction Theory Mechanism design inverts game theory: instead of analyzing a given game,design the game so that self-interested equilibrium play produces the outcome you want. It is the the
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Chapter 15 Cooperative Game Theory Cooperative (coalitional) theory abstracts from individual moves and asks two questions:which coalitions form, andhow are the gains divided? Its solution concepts—the core and the Shapl
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Chapter 16 Evolutionary Game Theory Maynard Smith’s export of game theory to biology replaced rationality withselection: strategies that earn higher payoffs (fitness) reproduce faster. The resulting theory illuminates an
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Chapter 17 Algorithmic Game Theory Computer science met game theory when the internet became a system of interacting selfish agents—routers, bidders, miners, platforms. Three founding questions organize the field (Nisan–
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Chapter 18 Frontiers: Behavioral, Experimental, and Modern Directions The final chapter surveys where game theory is being tested, revised, and extended. Each section states the core departure from the classical theory,
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Preface Game theory is the mathematical study of strategic interaction: situations in which the outcome for each participant depends not only on their own decisions but also on the decisions of others. Born in the 1940s
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Game Theory A Complete Learning Path From Beginner to Advanced Player 1 Player 2 Player 2 (3, 1) (0, 0) (1, 3) (2, 2) A B a b a b Strategic Form Games · Nash Equilibrium· Dynamic Games Bayesian Games· Mechanism Design· C
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