Interactions, including cooperative ones, can be intra-organismal (that is, within organisms), intraspecific (between conspecifics), or interspecific (between different species). It is simplifying to consider cooperation only in terms of intraspecific interactions, and that will be the focus in this chapter (see "Symbioses, the following chapter, for greater emphasis on the interspecific cases, and the previous chapter, "Genomes, for some consideration in the other direction). It is also simplifying to view interactions in terms of "games", that is, interactions in which there are both rules and specific payoffs associated with different behaviors. For games employed in the study of cooperation, those payoffs are not just for specific behaviors, but for specific combinations of behaviors between individuals: players and their opponents. An additional simplifying measure is to limit the range of possible behaviors to two, which one describes either as cooperation or as defection, that is, potentially increasing the fitness of one's opponent versus not (or, at least, cooperation can be viewed as not negatively impacting the other's fitness). Finally, many games of cooperation and defection are most easily envisaged as they occur between only two individuals. That is, games that can occur between two interacting individuals, each of which is capable of only two possible behaviors, cooperation and defection. I will begin with this two-player simplification before generalizing to the n-player case.
The Prisoner's Dilemma is a game with a 2×2 payoff matrix. That is, in a two-player game, where each player has to choose from only two possible individual behaviors, the total number of behavior combinations possible is four (i.e., 2×2). If the first player's behavior choices are D1 and C1 (e.g., such as defection and cooperation, respectively), while the second player's behavior choices are D2 and C2, then the possible behavioral combinations are D1C2, C1C2, D1D2, and C1D2", which (mathematically) is simply a list of the products of (D1 + C1) × (D2 + C2). We can assign payoff values, such as gains or losses in Darwinian fitness, to each of these combinations. Note that arbitrarily payoffs are assigned as experienced by player 1 rather than as experienced by player 2 (indeed, which player is player 1 and which is player 2 also often are arbitrarily assigned). The two players do not necessarily receive the same payoff in these games, and that is particularly true if they choose different behaviors (C for one, D for the other) rather than the same behavior (C and C or D and D). An additional rule in these games is that the players cannot know what the other player will do prior to a given interaction. That is, behavioral choices have to be made in ignorance of the behavioral choice of the other player.
It is further simplifying to view payoffs using a relative scale rather than an absolute scale. That is, we can consider that a given combination of behaviors can benefit player 1 more than some other combination of behaviors without worrying about the absolute magnitude of that benefit (this perspective is equivalent to considering relative fitness values rather than absolute ones). If we consider only inequalities, that is, no two combinations of behaviors are considered to have the same payoff, then D1C2, C1C2, D1D2, and C1D2 can be arranged into 24 different combinations (i.e., 4!, which is read, "Four factorial"). Dropping the subscript, but retaining positional information such that the first behavior is the first player's, then these combinations are DC > CC > DD > CD, CC > DC > DD > CD, DC > DD > CC > CD, DC > CC > CD > DD, and so on (Rapoport et al., 1976). One of these combinations in particular has been singled out for extensive study, and this is the DC > CC > DD > CD payoff combination, which has been dubbed the Prisoner's Dilemma (PD).
The salient feature of the Prisoner's Dilemma is that no matter what player 2 does (i.e., behaviorally), player 1 is always better off defecting. That is, in terms of payoff values, DC > CC and DD > CD (T > R and P > S). Also key is the order of the inequality of these two inequalities. That is, also in terms of payoff values, (DC > CC) > (DD > CD) (that is, T > R > P > S), rather than (DD > CD) > (DC > CC). What this latter point implies is that player 1 is always better off when player 2 cooperates and always less well off when player 2 defects. Stating these two points together: player 1 is always better off when player 1 defects and is always better off when player 2 cooperates. As noted, the designations "player 1" and "player 2" are arbitrary and it is just as reasonable to view payoffs from the perspective of player 2 than from that of player 1, which is to say that for player 2, just as for player 1, it is always preferable to defect and it is always preferable to player 2 for its opponent to cooperate. Obviously the preferences of these two players are incompatible, since they cannot both defect while both having their opponent cooperate. This incompatibility is the Prisoner's Dilemma. Put yet another way, how can one achieve mutual cooperation (CC) in a world in which a behavior of defection inevitably provides a better payoff?
The Tragedy of the Commons is similar to what is known as an n-player Prisoner's Dilemma. That is, rather than 2 players interacting, more than 2 players interact. The commons in the Tragedy of the Commons is the source of the payoff. A behavior of defection (D) removes more resource from the commons, resulting in less resource available for other players. A behavior of cooperation (C), by contrast, removes less resource from the commons, resulting in more resource for other players. Key is that available resources are finite. Another, more implicit component is time. That is, over-exploitation of the commons (too much defection) can result in declines in resource availability over time, such as in the future. In other words, D is a selfish behavior that benefits the player in the short term but messes things up for everybody in the long term. The rational behavior, in a commons populated with defectors (a.k.a., cheaters) is defection since even though the future is bleak, by acquiring more resources in the near term, the present for the defector is better than it is for the cooperator.
The Tragedy of the Commons is similar to the Prisoner's Dilemma because a behavior of defection still provides a bigger payoff than one of cooperation, and it similarly is preferable that one's opponents cooperate. It is a more complicated than a Prisoner's Dilemma as considered above, at least in part because it no longer is a question of how one achieves mutual cooperation among only two players but instead how one achieves mutual cooperation among more than two players. The two basic solutions to either game – that is, routes toward mutational cooperation – are for individual players either to display restraint in their actions or for that restraint to be externally imposed. The problem with internally imposed restraint is that a population of cooperators is always ripe for exploitation by defectors. Stable, long-term solutions thus require one of the following scenarios: (i) exclusion of defectors from interactions (such as of defectors coming from the external environment), (ii) blocks that make it difficult for would-be defectors to achieve the defection behavior, or (iii) for defectors to be punished for defecting, thereby lowering the defection payoff to below that of the cooperation payoff. I've purposefully listed these solutions in order of increasing difficulty to achieve, at least by microorganisms. That is, avoiding defectors is easier than creating an environment in which it is difficult to defect. In turn, making it difficult for would-be defectors to defect (the second scenario) may be at least behaviorally less complicated than identifying defectors in order to selectively punish them (the third scenario).