Game Theory

Game theory studies strategic and combinatorial interaction, equilibria, winning conditions, and optimal play.

Almost all of the subject is combinatorial games, most of them impartial. The Sprague–Grundy theorem makes every impartial game equivalent to a Nim heap, and the field works out P-positions and Grundy values game by game, from Wythoff's game, whose P-positions are the pairs \((\lfloor n\varphi \rfloor, \lfloor n\varphi \rfloor + n)\) and their reflections, to variants of Nim, chocolate bar games and Sylver Coinage, where opening with a prime greater than \(3\) wins. The partizan game Snort is a second-player win on opposable graphs. Social choice has the theorems of Arrow and of Gibbard and Satterthwaite, and cooperative games the Bondareva–Shapley theorem: a game with transferable utility has a nonempty core exactly when it is balanced.

• Combinatorial game theory
• Cooperative game theory
• Social choice theory

The dependency explorer needs JavaScript and its graph data.

Download the complete graph data.