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Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order ...
The number of vertebrae in a region can vary but overall the number remains the same. In a human spinal column, there are normally 33 vertebrae. [3] The upper 24 pre-sacral vertebrae are articulating and separated from each other by intervertebral discs, and the lower nine are fused in adults, five in the sacrum and four in the coccyx, or tailbone.
Let be the number of players, the set of action profiles over the action sets of each player and : be the payoff function for player .. Given a game = (, = …,:), we say that is a potential game with an exact (weighted, ordinal, generalized ordinal, best response) potential function if : is an exact (weighted, ordinal, generalized ordinal, best response, respectively) potential function for .
A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
The Grundy value or nim-value of any impartial game is the unique nimber that the game is equivalent to. In the case of a game whose positions are indexed by the natural numbers (like nim itself, which is indexed by its heap sizes), the sequence of nimbers for successive positions of the game is called the nim-sequence of the game.
In game theory, an information set represents all possible points (or decision nodes) in a game that a given player might be at during their turn, based on their current knowledge and observations. These nodes are indistinguishable to the player due to incomplete information about previous actions or the state of the game .
In game theory and related fields, a game form, game frame, ruleset, or outcome function is the set of rules that govern a game and determine its outcome based on each player's choices. A game form differs from a game in that it does not stipulate the utilities or payoffs for each agent.