Definition:Zero-Sum Game/Non-Zero
Definition
A non-zero-sum game is a game in which the total of the payoffs to all players is dependent upon the moves made to reach those payoffs.
Examples
Trade
Consider two parties trading: both may simultaneously gain by a transaction.
It can be assumed that the buyer attaches a value to goods purchased which is higher than the price paid.
At the same time, the price paid to the vendor can also be assumed to be higher than the value, to the vendor, of those goods.
Thus, at the end of this transaction, both parties have a positive payoff.
The loss of a particular ship may cause a setback of considerably greater value to the enemy than the cost of the materiel used by the attacker to destroy it.
Hence naval warfare can often be considered as a non-zero-sum game.
Casino
The players in a casino are operating in a non-zero-sum game.
That is because there is significant leakage to the banker.
Also known as
A non-zero-sum game can also be seen presented as nonzero-sum game.
Also see
- Results about non-zero-sum games can be found here.
Sources
- 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $2$
- 1983: Morton D. Davis: Game Theory (revised ed.) ... (previous) ... (next): $\S 2$: The Two-Person, Zero-Sum Game with Equilibrium Points
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): game theory
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): game theory
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): zero-sum game