Mathematics & Statistics
Probability, statistics, game theory and the mathematics behind machine learning, with worked examples.
Game Theory: A Complete Learning Path
A self-contained textbook covering game theory from beginner to advanced level, written in LaTeX and compiled to PDF.
Read article →Mathematical Background
This appendix collects the mathematical prerequisites, stated for reference rather than developed from scratch.
Read article →Bibliography and Further Reading
An Introduction to Game Theory. Oxford University Press. The most complete rigorous undergraduate text; the natural companion to Parts I–II of this book. Game Theory for Applied Economists. Princeton University Press. Co
Read article →What Is Game Theory?
Consider the following situations: What do they have in common? In each case, the best choice for one participant depends on what the others do. This interdependence is the defining feature of a game in the technical sen
Read article →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 game theory rests. Readers eager for games may skim it a
Read article →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.
Read article →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 game theory adds one more
Read article →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.
Read article →Extensive-Form Games and Backward Induction
So far, players moved simultaneously. Most real interactions unfold over time—entry then retaliation, offer then counteroffer—and timing changes everything: threats must be credible to matter.
Read article →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 industrial organization and public economics.
Read article →Bargaining
How is a surplus divided when two parties must agree to realize it? Bargaining theory has two complementary traditions: Nash's axiomatic approach (what properties should a solution have?) and Rubinstein's strategic appro
Read article →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 treaties, strangers leave tips at restaurants they'll revisit.
Read article →Bayesian Games: Incomplete Information
Until now, everyone knew everyone's payoffs. In reality, a bidder doesn't know rivals' valuations; an insurer doesn't know the applicant's risk; a poker player doesn't see opponents' cards. Modeling such incomplete infor
Read article →Dynamic Games with Incomplete Information: Signaling and Screening
When informed players move first, their actions speak: choices reveal, conceal, or distort private information. This chapter develops perfect Bayesian equilibrium and its two flagship applications—signaling and cheap tal
Read article →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 (linear programming) and to machine learning (advers
Read article →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.
Read article →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 theory behind spectrum auctions, ad exchanges, sc
Read article →Cooperative Game Theory
Cooperative (coalitional) theory abstracts from individual moves and asks two questions: which coalitions form, and how are the gains divided? Its solution concepts—the core and the Shapley value—are now everyday tools f
Read article →Evolutionary Game Theory
Maynard Smith's export of game theory to biology replaced rationality with selection: strategies that earn higher payoffs (fitness) reproduce faster. The resulting theory illuminates animal conflict, the evolution of coo
Read article →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–Roughgarden–Tardos–Vazirani): Can e
Read article →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, the leading models, and pointers into the literature.
Read article →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 from the
Read article →Solutions Part1
(a) Two players, three actions each, simultaneous, complete information. (b) Seller and buyer; seller moves first (set price / describe car), buyer accepts or not; sequential with incomplete information (quality is the s
Read article →Solutions Part2
If the rival bids v_j/2, bidding b wins with probability (v_j/2 < b) = 2b (for b 12); expected profit (v - b) 2b is maximized at b = v/2. Revenue: = 12 · 23 = 13 = , the second-price revenue—revenue equivalence verified.
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