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If the losses of player A are the game of the player B, then the game is known as

Question

If the losses of player A are the game of the player B, then the game is known as

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Solution

The game is known as a "Zero-Sum Game". In a zero-sum game, the total benefit to all players in the game, for every combination of strategies, always adds up to zero. This means that any gain (or loss) of utility for one player is exactly balanced by the losses (or gains) of the utility of the other player(s).

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In a small football league, teams are awarded 5 points for winning a match, 3 points for a draw and 1 point for losing. The team with the most points after 12 matches wins a prize.Team A win 6 of their matches and have half as many draws. The rest of the matches they lose.Team B win as many matches as Team A lose, but all the rest of their matches are draws and they don’t lose a single game.Team C and D both lose 10 matches, but Team C wins the rest and Team D draws the rest.Team E wins 1 more match than Team A, but draws 2 matches and loses the rest.Which team wins the prize?

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