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I read that a two-person constant-sum game is a two-player game in which, for any choice of both players strategies, the row player's reward and the column player's reward add up to a constant value c. However I am not sure how to use this definition to determine whether a game is constant-sum. Can anyone explain please?

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  • $\begingroup$ Apply the definiton of a constant sum game to the payoff matrices? $\endgroup$ – Batman Apr 28 '15 at 14:58
  • $\begingroup$ @Batman So suppose I have two matrices where the first matrix shows the payoffs for player 1 and the second matrix shows the payoffs for player 2. Is this a constant sum game if I add all the payoffs in the first matrix and it equals the sum of the playoffs in the second matrix. $\endgroup$ – Jnyeboah93 Apr 28 '15 at 15:04
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Add the matrix payoff of player 1 and matrix payoff of player 2 if the resulting matrix has all entries equal then this is a constant sum game.

Example 1 (constant-sum game)

$$ \underbrace{\left(\begin{array}{cc}1 & 0.5 \\0 & 0.2\end{array}\right)}_{\text{payoffs of 1}}+\underbrace{\left(\begin{array}{cc}0 & 0.5 \\1 & 0.8\end{array}\right)}_{\text{payoffs of 2}}=\underbrace{\left(\begin{array}{cc}1 & 1 \\1 & 1\end{array}\right)}_{\text{sum of payoffs}} $$

Example 2 (not a constant-sum game)

$$ \underbrace{\left(\begin{array}{cc}1 & 0.5 \\0 & 0.2\end{array}\right)}_{\text{payoffs of 1}}+\underbrace{\left(\begin{array}{cc}1 & 0.5 \\1 & 0.8\end{array}\right)}_{\text{payoffs of 2}}=\underbrace{\left(\begin{array}{cc}2 & 1 \\1 & 1\end{array}\right)}_{\text{sum of payoffs}} $$

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