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Is there such a thing as a theory of cooperative zero-sum two-player games (that do not trivially correspond to a non-cooperative one)? The players can never both be benefited by a cooperation, so it seems that rational agents can never have any reason to cooperate on such situation, so the answer seems to be negative.

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  • $\begingroup$ Are you familiar with the meaning of zero-sum in the phrase "zero-sum game?" Certainly if you were to remove that phrase then the answer is yes. Cooperative zero-sum games however... the combined result is always the same, zero, so no... there is nothing that makes one set of choices any different than another set of choices... $\endgroup$
    – JMoravitz
    May 30, 2018 at 18:19
  • $\begingroup$ Do you have an example of the phrase "cooperative game" being defined in game theory? $\endgroup$ May 30, 2018 at 18:21
  • $\begingroup$ @Jmoravitz Zero-sum cooperative games exist if there are more than 2 players. Consider the game Bridge. It can be regarded as a game of 2 players that do not have perfect recall, or a game of 4 players each of which has perfect recall, but where teammates always get the same payoff. A cooperative consideration is where the teammates may discuss their strategy before the game is started. Thereby, signalling is possible: A player may make a (public) move simply to tell his teammate that he holds a particular card, while the other team doesn't know what he is communicating to his teammate. $\endgroup$ Jun 1, 2018 at 5:07
  • $\begingroup$ Okay, sure., but in the case of a two-player cooperative game... what are they trying to maximize if it is zero-sum? Their combined total number of "points"? Their combined total number of points is always zero, so what makes one outcome "better" or "worse" than another? $\endgroup$
    – JMoravitz
    Jun 1, 2018 at 5:25

1 Answer 1

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P.S. not an expert on game theory. If this is incorrect please point that out.

If the game is iterative with high reward for winning and low risk for losing it makes sense to cooperate across iterations.

Also, for the sake of argument, there could be a reason for players to cooperate even in a strictly competitive zero sum game like chess, so long as they share a motivation for doing so. Say you have two impatient chess players who just want to get to the end game, they could just sacrifice pieces in a tit-for-tat strategy until they reach a point where one of them wants to compete

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