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equitable
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a fair-division procedure like adjusted winner is said to be equitable if each player believes he or she received the same fractional part of the total value
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last-diminisher method
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a cake-division procedure introduced by Stefan Banach and Bronislaw Knaster. it works for any number of players and produces an allocation that is proportional but not, in general, envy-free.
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saddlepoint
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in a two-person constant-sum game, the payoff that results when a row minimum and a column maximum are the same, which is the value of the game. The saddlepoint has the shape of a saddle-shaped surface and is also a Nash equilibrium.
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selfridge-conway envy-free procedure
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a cakedivision procedure introduced independently by john selfridge and john conway. it works only for three palyers but produces an allocation that is envy free (as well as proportional)
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Nash equilibrium
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strategies associated with an outcome such that no player can benefit by choosing a different strategy, given that the other players do not depart from their strategies.
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stemplot
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display of the distribution of a variable that attaches the final digits of the observations as leaves on steams made up of all but the final digit.
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five-number summary
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the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest. In symbols, the five-number summary is Minimum Q1 M Q3 Maximum
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outlier
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an individual value that falls outside the overall pattern.
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distribution
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tells us what values the variable takes and how often it takes these values.
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taking turns
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a fair-division procedure in which two or more parties alternate selecting objects.
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cake-division procedure
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a fair-division procedure that uses a cake as a metaphor. Such procedures involve finding allocations of a single object that is finely divisible, as opposed to the situation encountered with either the adjusted winner procedure or Knaster's procedure. In a cake-division procedure, each player has a strategy that will guarantee that player a piece with which he or she is "satisfied" even in the face of collusion by the others.
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mixed-strategy value
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a player's expected value is the mixed-strategy value of the game. Unlike the use of this notion in games with a saddlepoint, the value here can be realized only by use of mixed strategies
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mixed strategy
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a strategy that involves the random choice of pure strategies, according to particular probabilities. A mixed strategy of a player is optimal if it guarantees the value of the game.
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maximin strategy
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in a two-person zero-sum game, the pure strategy of the row player corresponding to the maximin in a payoff matrix.
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total-conflict game
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a zero-sum or constant-sum game, in which what one player wins the other player loses
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value
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the best outcome that both players can guarantee in a two-person zero-sum game. If there is a saddlepoint, this is the value. Otherwise, it is the expected payoff resulting when the players choose their optimal mixed strategies.
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symmetric
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right and left sides of the histogram are approximately mirror images of each other.
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rational choice
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a choice that leads to a preferred outcome
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dominated strategy
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a strategy that is sometimes worse and never betterfor a player than some other strategy, whatever strategies the other players choose.
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point ratio
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the fraction in which the numerator is the number of points one party placed on an object and the denominator is the number of points the other party placed on the object.
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theory of moves (TOM)
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a dynamic theory that describes optimal choices in strategic-form games in which players, thinking ahead, can make moves and counter-moves.
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strategy
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one of the courses of action a player can choose in a game; strategies are mixed or pure, depending on whether they are selected in a randomized fashion (mixed) or not (pure).
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normal distribution
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described by a normal curve. the area under the curve above any interval of values tells us what proportion of all values of the variable lie in that interval. The total area under the curve is exactly 1.
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game tree
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a symbolic tree, based on the rules of play in a game, in which the vertices, or nodes, of the tree represent choice points, and the branches represent alternative courses of action that the players can select.
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pure strategy
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a course of action a player can choose in a game that does not involve randomized choices.
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least-squares regression line
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a line drawn on a scatterplot that makes the sum of the squares of the vertical distances of the data points from the line as small as possible. The regression line can be used to predict the response variabley for a given value of the explanatory variable.
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variable-sum game
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a game in which the sum of the payoffs to the players at the different outcomes varies
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constant-sum game
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a game in which the sum of payoffs to the players at each outcome is a constant, which can be converted to a zero-sum game by an appropriate change in the payoffs to the players that does not alter the strategic nature of the game.
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third quartile of a normal distribution
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.67 standard deviation above the mean
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