Incombinatorial game theory, the zero game is the game where neither player has any legal options. Therefore, the first player automatically loses, and it is a second-player win. The combinatorial notation of the zero game is Combinatorial game theory (CGT) is a mathematical theory that studies a certain kind of game. ...
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Simple examples of zero games include Nim with no piles or a Hackenbush diagram with nothing drawn on it. Nim is a two-player game of strategy in which players take turns removing objects from heaps, one or more objects at a time but only from a single heap. ... Hackenbush is a two-player partisan mathematical game that consists of several colored line segments connected to the ground. ...
Other games can have values of zero, and in fact, all second-player win games have exactly that value, though they may not be the zero game.
For example, Nim with two identical piles (of any size) is a fuzzy game, but has value 0, since it can be a second-player winning situation if the first player plays imperfectly. This article may be too technical for most readers to understand. ...
A zero game is the opposite of the star (game) {0|0}, which is a first-player win since either player must (if first to move in the game) move to a zero game, and therefore win.
Other non-zero-sum games are games in which the sum of gains and losses by the players are always more or less than what they began with.
For example, a game of poker played in a casino is a zero-sum game unless the pleasure of gambling or the cost of operating a casino is taken into account, making it a non-zero-sum game.
The concept was first developed in game theory and consequently zero-sum situations are often called zero-sum games though this does not imply that the concept, or game theory itself, applies only to what are commonly referred to as games.
Game theory is a hybrid branch of applied mathematics and economics that studies strategic situations where players choose different actions in an attempt to maximize their returns.
Game theorists may assume players always act rationally to maximize their wins (the Homo economicus model), but real humans often act either irrationally, or act rationally to maximize the wins of some larger group of people (altruism).
Game theory experienced a flurry of activity in the 1950s, during which time the concepts of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed.
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