In game theory, the core is the set of feasible allocations that cannot be improved upon by a subset (a coalition) of the economy's consumers. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first except that every member of the coalition has a different consumption bundle that is part of an aggregate consumption bundle that can be constructed from publicly available technology and the initial endowments of each consumer in the coalition.

An allocation is said to have the core property if there is no coalition that can improve upon it. The core is the set of all feasible allocations with the core property.

The idea of the core already appeared in the writings of Edgeworth (1881), at the time referred to as the contract curve (Kannai 1992). Even if von Neumann and Morgenstern considered it an interesting concept, they only worked with zero-sum games where the core is always empty. The modern definition of the core is due to (Gillies 1959).

Core may refer to:

Game theory is the study of strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide range of class relations, and has developed into an umbrella term for the logical side of science, to include both human and non-humans, like computers. Classic uses include a sense of balance in numerous games, where each person has found or developed a tactic that cannot successfully better his results, given the other approach.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by his 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

A game is structured playing, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements. However, the distinction is not clear-cut, and many games are also considered to be work (such as professional players of spectator sports/games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games).

Key components of games are goals, rules, challenge, and interaction. Games generally involve mental or physical stimulation, and often both. Many games help develop practical skills, serve as a form of exercise, or otherwise perform an educational, simulational, or psychological role.

Attested as early as 2600 BC, games are a universal part of human experience and present in all cultures. The Royal Game of Ur, Senet, and Mancala are some of the oldest known games.

The English word theory was derived from a technical term in philosophy in Ancient Greek. The word theoria, θεωρία, meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action. Theory is especially often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because theory involved no doing apart from itself.

A classical example of the distinction between theoretical and practical uses the discipline of medicine: Medical theory and theorizing involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.

By extension of the philosophical meaning, "theoria" is also a word still used in theological contexts.