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Many times you hear Economics is a "non zero sum game" implying that anything that is earnt by one person or group isnt lost by other. This might not be the definition of non zero sum game, but that's how it is used many times. What I believe it happens it's part of what is earnt by a person or group is lost by other and other part isnt.

In the other hand, you have "zero sum game", where everything earnt by someone is lost by other.

Is there a name for a game where part of what a person or group earns is part of what other person or group loses, and other part of what this first person or group earns isnt part of what other person or group loses?

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    $\begingroup$ A zero-sum game is so named because in it, the sum of the players' payoffs is always zero. Unless you provide a specific payoff structure to the players in the game, it's hard to categorize it. From what you've described, I suggest you look up the term constant-sum game and see if it is something you're looking for. $\endgroup$ – Herr K. May 25 '17 at 23:17
  • $\begingroup$ @HerrK. I would vote for this answer. $\endgroup$ – Giskard May 26 '17 at 16:50
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A zero-sum game is so named because in it, the sum of the players' payoffs is always zero. Unless you provide a specific payoff structure to the players in the game, it's hard to categorize it. From what you've described, I suggest you look up the term constant-sum game and see if it is something you're looking for.

An example:

$$ \begin{array}{|r|c|c|} \hline & X & Y \\\hline X&2,-1&-1,2\\\hline Y&-1,2&2,-1\\ \hline \end{array} $$

Suppose the status quo payoff is $0$ for both players. Then in each of the outcomes in the game above, one of the players gets $2$ at the expense of the other player losing $1$. The pair of payoffs in each outcome sums up to the constant $1$, hence the name constant-sum game. Do notice, however, that this is only a very small subset of the possible games due to the heavy restrictions on the payoffs.

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  • $\begingroup$ well it's kind of, but not necessarily a constant amount. Zero sum game, everything that is win by someone is lost by another person. Win-win game, everybody wins, and nobody loses (though I dont know if this name is an informal name or it comes from some mathematics or economics or game theory) . The game I'm looking for, a group or somebody loses, other group or person wins, and the payoffs outcome sums up to a positive number, though not a constant number $\endgroup$ – Pablo May 26 '17 at 19:04
  • $\begingroup$ @Pablo: There's no standard way of calling the class of games you're describing. I suppose you could try to call them "positive-sum competitive games". The word "competitive" indicates that one's gain is always another's loss, but the sum of the payoffs is positive (though not necessarily a constant), so that the loss is only a fraction of the gain. $\endgroup$ – Herr K. May 26 '17 at 19:36
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As far as I know the definition is yet to be extended beyond two person games, but you seem to be looking for some notion of antagonism.

A two player game is antagonistic if given any two outcomes A and B, if player one prefers outcome A then and only then player two prefers outcome B.

Read more here.

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