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?

  • $\begingroup$ 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

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)

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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.