Game theory

The study of what happens when decision-makers whose outcomes depend on each other choose. In Osborne & Rubinstein‘s words it is “a bag of analytical tools designed to help us understand the phenomena that we observe when decision-makers interact,” resting on two assumptions: players pursue well-defined exogenous objectives (they are rational) and take into account their expectations of other players’ behavior (they reason strategically).

Rests on a single source so far.

The dividing line that organizes the subject

Game theory is not one model but a family, and the text sorts them along three cuts:

Noncooperative vs cooperative. Whether the unit of analysis is the individual player or the coalition, and whether binding agreements can be made. The book covers both and refuses to call either more basic.
Strategic vs extensive. A strategic (normal-form) game has every player choose a plan once and for all, simultaneously. An extensive game specifies the order of events, so a player can plan at every point where they must decide.
Perfect vs imperfect information. Whether players observe each other’s moves. Perfect-information models are older and, in the authors’ judgment, have “firmer foundations”; imperfect-information models were developed intensively only in the 1980s.

The primitives

A strategic game is (N, (Aᵢ), (≿ᵢ)): players, an action set per player, and each player’s preference over profiles of everyone’s actions. Preferring over profiles rather than over one’s own actions is what makes it a game instead of a decision problem — the interaction lives entirely in that one modelling choice.

Behind the preference relation sits the standard model of rational choice — action set, consequence set, consequence function, complete transitive reflexive preference — and, under uncertainty, von Neumann–Morgenstern expected utility with Savage’s subjective probabilities where the odds aren’t given. Game theory inherits all of decision theory’s assumptions before it adds any of its own.

Solution concepts are the output side: a solution is “a systematic description of the outcomes that may emerge in a family of games.” Nash equilibrium, its mixed and correlated variants, rationalizability, subgame perfection, sequential equilibrium, the core, the Shapley value, the Nash bargaining solution — the subject is largely the study of which of these to believe when, and the source text treats choosing among them as an interpretive question rather than a technical one.

What is under dispute inside the subject

What an equilibrium means. The steady-state reading (a regularity that emerges once players have learned the game) and the deductive reading (what rational players deduce from the rules on a single play) support the same equilibria and different conclusions.
Whether the rationality assumption survives contact with people. The source concedes the assumptions are “under perpetual attack by experimental psychologists” and declines to defend them. Bounded rationality is the internal response — model the player as a finite machine and charge for complexity, as Chapter 9 does.
Whether it is mathematics at all. Osborne and Rubinstein say it is a social science, and that a book with the same content could in principle be written without mathematics. It is filed here anyway, under this spoke’s boundary rule: a text teaching a body of theory from first principles belongs to the subject, whatever field the examples come from.

Reach

The book’s own examples of where these models get used: Nash equilibrium in oligopoly and political competition; mixed-strategy equilibrium in the distribution of tongue length in bees and tube length in flowers; repeated games for threats and promises; the core as a sense in which price-system trading is stable in a large economy. Implementation theory (ch. 10) runs the subject backwards — given a desired outcome, design the game that produces it — which is the mechanism-design half and the one that touches auctions, voting and protocol design.

Nothing in the corpus yet connects to this: the spoke has no page on decision theory or utility theory, which sit directly beneath it, and no source on mechanism design or on experimental/behavioral game theory. All are open edges.

Sources

osborne-rubinstein-course-in-game-theory — graduate text, MIT Press 1994 · T1

mathematics · probability-theory · martin-j-osborne · ariel-rubinstein