In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw,...
Ernst Friedrich Ferdinand Zermelo (; German: [tsɛɐ̯ˈmeːlo]; 27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing...
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated...
Game theory is the field of applied mathematics that models interactions between multiple agents as "games" of strategy between "players". It is a scientific method of describing, predicting, evaluating, and selecting choices (or "actions"), often...
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full...
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making procedure based on ordinal utilities (citizens' orderings of different alternatives) can...
In game theory, a focal point (or Schelling point) is a solution that people tend to choose by default in the absence of communication in order to avoid coordination failure. The concept was introduced by the American economist Thomas Schelling in...
Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if their individual beliefs are common knowledge. In other words, if it is commonly known what each...
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence (as defined below) eventually terminates at 0. Laurence Kirby and Jeff Paris showed...
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of nim. It can therefore be represented as a natural...