The order of play proceeds as follows: The first player (red) chooses in secret one of the two actions 1 or 2; the second player (blue unaware of the first player's choice, chooses in secret one of the three actions A, B.
For the resulting u vector, the inverse of the sum of its elements is the value of the game.Suppose a zero-sum game has a payoff matrix M where element M i, j displaystyle M_i,j is the payoff obtained when the minimizing player chooses pure strategy i and the maximizing player chooses pure strategy j (i.e.Warfare game, Chess) and non-zero-sum games (e.g.Extensions edit In 1944, John canyon bakehouse coupon code 2017 von Neumann and Oskar Morgenstern proved that any non-zero-sum game for n players is equivalent to a zero-sum game with n 1 players; the ( n 1)th player representing the global profit or loss.Red could reason as follows: "With action 2, I could lose up to 20 points and can win only 20, and with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better." With similar reasoning.Wahjong is our online twist to this classic game.Choice 1 -A, A, b, -B, choice.If the game matrix does not have all positive elements, simply add a constant to every element that is large enough to make them all positive.This minimax method can compute probably optimal strategies for all two-player zero-sum games.On the Wahjong battle field, information is the key to victory.Such games are distributive, steam 60 dollar gift card not integrative; the pie cannot be enlarged by good negotiation.If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero."Theory of Games and Economic Behavior".Mahjong is a classic Chinese game in which good memory, observation skills strategy and in some cases extreme luck are required for winning.Microeconomics: Behavior, Institutions, and Evolution.
See also edit References edit a b Ken Binmore (2007).
If both players take these actions, Red will win 20 points.