A Course in Game Theory (Osborne & Rubinstein, 1994)

martin-j-osborne and ariel-rubinstein‘s graduate text on game-theory, mit-press 1994 (ISBN 0-262-15041-7; the copy held is the third printing, 1996, 372pp scanned). Read from a PDF the curator sent; the Internet Archive scan carries OCR errors in the mathematics, so formulas quoted below were checked against the surrounding prose rather than lifted verbatim.

The authors state the target precisely: one semester, about 28 meetings of 90 minutes, graduate level. They also state what they left out — experimental game theory, and learning and evolution, two chapters they say they would add if starting over. This is the corpus’s first text that names its own omissions as a dated choice.

What kind of book it is

Two commitments run through the preface and Chapter 1, and they set this text apart from the applied game-theory literature:

Pure theory, not applications. “We stay almost entirely in the territory of ‘pure’ theory. The art of applying an abstract model to a real-life situation should be the subject of another tome.”
Foundations and interpretation over generality. “Our style is to give precise definitions and full proofs of results, sacrificing generality and limiting the scope of the material when necessary to most easily achieve these goals.”

And a claim that decides where this book belongs: the authors treat game theory not as a branch of mathematics but as a social science, mathematics being the notation. “The game theoretical ideas that we discuss are not inherently mathematical; in principle a book could be written that had essentially the same content as this one and was devoid of mathematics.” They add that they find the mathematical results “interesting only if they are confirmed by intuition.”

That is the first time a text in this corpus argues its own subject is not mathematics while proving theorems throughout. It sits beside mari-measurement-across-sciences, the other page here whose subject is not mathematics, but for a different reason — Mari’s book is about measurement, this one is mathematics used by a discipline that disclaims it.

Structure — four parts, and the six-chapter core

The book is built as four families of models, with an explicit dependency chart in the preface. A basic course is Chapters 2, 3, 6, 11, 12, 13; the rest hang off those.

Part I — Strategic games (ch. 2–5). Nash equilibrium and Bayesian games; mixed, correlated and evolutionary equilibrium; rationalizability and iterated elimination of dominated actions; knowledge and common knowledge, ending at the electronic mail game.
Part II — Extensive games with perfect information (ch. 6–10). Subgame perfect equilibrium; bargaining with alternating offers; repeated games and four folk theorems; complexity considerations (strategies as finite machines); implementation theory — dominant-strategy, Nash, and subgame-perfect implementation.
Part III — Extensive games with imperfect information (ch. 11–12). Behavioral vs mixed strategies, equivalence of extensive games and framing effects, sequential equilibrium, perfect Bayesian equilibrium, trembling-hand perfection.
Part IV — Coalitional games (ch. 13–15). The core and its nonemptiness, markets and exchange economies; von Neumann–Morgenstern stable sets, the bargaining set, kernel and nucleolus, the Shapley value; the Nash bargaining solution, its axiomatic characterization, and its link back to the alternating-offers game of Chapter 7.

The authors refuse the usual ranking of the two branches: the book is mostly noncooperative, but “we do not share the view of some authors that noncooperative models are more ‘basic’ than cooperative ones.” The imperfect-information material gets less weight for a stated reason — it “was developed intensively only in the 1980s” and is “less mature”, not less important.

Definitions actually read

Strategic game (Def. 11.1): a finite set N of players; for each player i a nonempty action set Aᵢ; and for each i a preference relation ≿ᵢ over the set A = ×ⱼ∈ₙ Aⱼ of action profiles. The load-bearing detail is spelled out: preferences are over profiles, not over one’s own action — “the feature that distinguishes a strategic game from a decision problem.” Where preferences admit a payoff function uᵢ: A → ℝ, the game is written (N, (Aᵢ), (uᵢ)).

Mixed extension (Def. 32.1): replace each Aᵢ by Δ(Aᵢ), the probability distributions over it, and each payoff by its expected value under independent randomization. Each Uᵢ is then linear in the mixed profile — the property that makes the existence proof work.

Rational choice (§1.4), stated before any game appears: an action set A, a consequence set C, a consequence function g: A → C, and a complete transitive reflexive preference relation over C. Under uncertainty the book adopts von Neumann–Morgenstern and Savage wholesale. The authors decline to defend those assumptions and say so plainly — they note the assumptions are “under perpetual attack by experimental psychologists, who constantly point out severe limits to its application.” That is a live cross-spoke tension, not a settled point: the heuristics-and-biases tradition is exactly the attack being referred to.

Two interpretations of a solution

§1.5 separates the steady state (evolutive) reading — an equilibrium is a regularity observed after players have learned the game by playing it — from the deductive reading, in which a single play is analyzed by rational players reasoning from the rules alone. The two readings license different conclusions from the same equilibrium, and the book keeps returning to which one a chapter is using. §1.6 flags bounded rationality as the standing exception; Chapters 5, 8 and 9 draw on Rubinstein’s draft book on bounded-rationality models, and Chapter 9 makes complexity of a strategy an explicit cost.

Level and rigour

Graduate, proof-complete, and terse — nearer trench-real-analysis than corral-vector-calculus on the rigour axis. Exercises carry theory: “many of the exercises are challenging; we often use exercises to state subsidiary results,” and instructors are told to add easier problems themselves. There is a List of Results appendix (pp. 313–320), so the theorem inventory is checkable without reading the chapters. No solutions in the book — instructors requested them from MIT Press.

The preface also contains an unusual signed disagreement between the authors about generic pronouns, printed at length with both positions and the compromise they call “highly unsatisfactory.” It is a small thing, but it is the same instinct as the rest of the book: state the disagreement rather than paper it over.

Assessment

T1. A canonical graduate text from a major press by two authors who work in the field, held in full as a scanned PDF and read directly. The caveats are age and OCR: the mathematics is 1994 vintage — nothing after it, and the authors themselves name learning-and-evolution and experimental work as the gaps — and the scan mangles symbols, so this page quotes prose and paraphrases formulas.

game-theory · martin-j-osborne · ariel-rubinstein · mit-press · mathematics · probability-theory · mari-measurement-across-sciences