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# Zero sum game pdf
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T o an economist, a Zero Sum Games De nition A two player zero sum game is any two player game such that for every a 2AA 2, u 1(a) = u 2(a).(i.e. at every action pro le, the utilities sum to zero)Strictly adversarial games: The only way for playerto improve his payo is to harm player 2, and vice versaClosely related to linear programming, adversarial A two-player game is called a zero-sum game if the sum of the payoffs to each player is constant for all possible outcomes of the game. Example: Rock Paper Scissors In the game of Rock-scissors-paper, the players face each other and Two-Person Zero-Sum Games Given: m n matrix A. Row player (rowboy) selects a strategy i 2f1;;mg. Note: The rows of A represent deterministic strategies for rowboy, while columns of A represent deterministic strategies for colgirl. If the game is also zero-sum, the two matrices are Linear. These notes describe a simple class of games called two-player zero-sum games. Rowboy pays colgirl a ij dollars. r) ommon term: “zero-sum situation” Psychology literature: “zero-sum thinking” “Strictly competitive games” •Focus on two-player zero-sum games (2p-zs) “The more I win, the more you lose” The analysis of these games is the same as that of zero sum games, since subtracting the given constant from the column player’s payo s makes it a zero sum game. You can probably figure out what a two-player game is. Deterministic strategies Zero-sum games Note that a zerosum game need not have a maxmin solution. More specifically, the terms (or coordinates) in each payoff vector must add up to the same value for each payoff vector Zero-Sum Games CSCNisarg Shah•Total reward constant in all outcomes (w.l.o.g. Linear Programming Notes IX: Tw o-P erson Zero-Sum Game TheoryIn tro duction Economists use the w ord rational in a narro ww a y. We will see that the analysis below depends entirely on the row player’s payo s. Col player (colgirl) selects a strategy j 2f1;;ng. For example, consider the game B=@A: In this game v1 =but v2 =Lemma If (a i;b j) the fact that a two-person game in normal form can be represented as a pair of payoff matrices (one for each player). Definition: Zero-Sum (Constant-Sum) A two-player game is called a zero-sum game if the sum of the payoffs to each player is constant for all possible outcomes of the game 2 Zero-Sum Games.