Strictly determined game
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In game theory, a strictly determined game is a
two-player A multiplayer video game is a video game in which more than one person can play in the same game environment at the same time, either locally on the same computing system ( couch co-op), on different computing systems via a local area network, or ...
zero-sum Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is e ...
game that has at least one Nash equilibrium with both players using pure strategies. The value of a strictly determined game is equal to the value of the equilibrium outcome. Most
finite Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...
combinatorial games, like
tic-tac-toe Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ...
,
chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...
,
draughts Checkers (American English), also known as draughts (; British English), is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers ...
, and go, are strictly determined games.


Notes

The study and classification of strictly determined games is distinct from the study of Determinacy, which is a subfield of
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
.


See also

*
Solved game 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 inform ...


References

Game theory game classes {{Mathapplied-stub