What is a two person constant sum game?

Question

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?

Answer 1

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)

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