The idea of a theory of games arises in the middle of the twentieth century. What the science promised was a way to model and predict economic and political behavior that was assumed to follow the rational choices of individual actors. Homo economicus had a more or less adequate understanding of their own interests–and the relation of those interests to all possible actions.
Economistic assumptions and preoccupations predominate in the typologies and structures of games as understood within the theory. Games are mapped according to a possible "pay-off." The "strategy" played by each participant is indexed to the strategy played by the others, and associated with a particular pay-off for each permutation. In a "zero-sum" game, any gain by one player is accompanied by an equivalent loss for another.
Positivist tendencies aside, the modeling of behavior as games has the benefit of revealing a panoply of game structures which broaden the way that social interaction might be understood. And some of these models cannot be neatly solved by the application of a rationality based on individual interest. The exercise of schematizing behavior in games has the perverse consequence of suggesting problematic games that violate assumptions about rational behavior. These end up providing both compelling representations of human predicaments and delivering a rebuke to rational choice theory.
The Prisoner's Dilemma is perhaps one of the most well known of these games that defy the application of rational choice. In the game, two imprisoned suspects are separately given the opportunity to betray the other or to remain silent. If they are both silent, they each receive a short sentence. If they betray each other they both serve a moderate time. If only one betrays the other, the betrayer is set free while the betrayed serves a long sentence.
The decision made out of rational self interest is always to betray. Not knowing what the other will do, a player reasons that in either case, they benefit most by betraying the other. The fourth case, where each is silent and together they serve less time is excluded. Cooperation is seemingly incompatible with rational choice in this scenario.
An important aspect of the game is that that players cannot know each other's minds, and because of that, have to use reason as compensation. Reason substitutes for collaboration, as it excludes it. The variants of these games, as found in Poe's "Purloined Letter," or as proposed by Lacan in "Logical Time," emphasize the problem of uncertainty, and the logic of putting oneself in the place of the other as a method for solving it. In Poe's story, the detective must find the missing letter; he does so by imagining the reasoning of his adversary. 
The knowledge of the other that these games require is purely aggressive since that knowledge brings victory at the other's expense, which makes them zero-sum games through a kind of truncation. Either by bracketing cooperation within the operations of self-interested rationality, or by definition, there is a refusal of communitas. All these games are contests; there are winners and losers, and therefore, it seems, no community. Is a game without winners and losers still a game? And would such a game allow for a consideration of some notion of community?
The contestatory character of the game is based on two economistic presumptions: that there ought to be a particular goal defined in terms of maximization; and, that the criteria of success be applied at the level of the individual player. To alter either of these presumptions would result in a very different field of play. A change from individual criteria to communal criteria is obvious. Imagining a replacement to maximization that wouldn't simply be its equivalent (like minimization would) is more difficult; one possibility might be to endeavor to play in such a way that the game will not end–because if the play stops, then the community of players, as a whole, would be let down. The difference here introduced is significant since such play proceeds without the introduction of an external and quantitative system of reward and punishment–i.e. no pay-offs. Participation would be its own reward.
The paradigms of game theory have a symmetrical blindness in regard to questions of community since the defining impossibility of cooperation inside them is matched, on the outside, by the exclusion from consideration of questions of participation and constitution. Games are abstractions whose relation to the world is representational. The test of a game's validity is empirical: how well does the model predict actual data. But if the game bears any relation to real social scenarios, questions about the genealogy of the rules and the conditions of participation become crucial. In the hypotheticals of game theory, the participants find themselves Kafkaesquely in the game–possessed of an agency that is circumscribed by the moves the existing rules allow. This is at once our actual situation and not our situation at all. There is another field of contest that overlaps any game, and that is the game of the rules.
 Richard Serra videotaped an enactment of the game in his 1974, "Prisoner's Dilemma," which he said was a comment on the role of TV in the contemporaneous Watergate scandal. See Jonathan Jones, "Caught on Tape," The Guardian, July 28, 2003, <http://arts.guardian.co.uk/features/story/0,11710,1007084,00.html>.
 It is not strictly accurate to present game theory as incapable of treating cooperation since some games, like "Stag and Rabbit Hunt" (and "Prisoner's Dilemma" too), explicitly deal with the problematics of cooperation; but they do so using the same economistic presumptions.
 Lacan's three prisoners each wear one of five hats, two white and three black, that can only be seen by the others; the one who can determine his color will be set free. To solve the problem requires a reasoning that includes imagining what the others see. The Turing Test, where a person must guess if an unseen interlocutor is human or a machine by asking questions, is also a variant of the prisoner's dilemma. In that game of identification and dissimulation, the contestants must navigate asymmetrically the expectations that correspond to the identity of the other: machine to human and vice versa. To win is to out think the other in its own terms: the computer must answer as if it were human, or as if it were a human impersonating a machine, and so on, iteratively. The questioner must reason in a way that accommodates this regress. It has been remarked that this situation bears a striking similarity to that of the closeted homosexual–which Turing was, and for which he suffered tragically.