supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including

win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013.[15] Generous

strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called \[16] to be those for which the player responds to past mutual cooperation with future

cooperation and splits expected payoffs equally if she receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the

[15]

population is very small, defection strategies tend to dominate.

Continuous iterated prisoners' dilemma[edit]

Most work on the iterated prisoners' dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoners' dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd[17] found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoners' dilemma. The basic intuition for this result is straightforward: in a continuous prisoners' dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoners' dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to

non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoners' dilemma may help explain why

real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein[18]) even though tit for tat seems robust in theoretical models.

Emergence of Stable Strategies[edit]

Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.[19] Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This

strategy outperforms a simple Tit-For-Tat strategy - that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.[20]

Real-life examples[edit]

The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.

In environmental studies[edit]

In environmental studies, the PD is evident in crises such as global climate change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb CO

2 emissions. The immediate benefit to an individual country to maintain current behavior is perceived to be greater than the purported eventual benefit to all countries if behavior was changed, therefore explaining the current impasse concerning climate change.[21]

An important difference between climate change politics and the

prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests states will cooperate much less than in a real iterated prisoner's dilemma, so that the

probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.[22]

Osang and Nandy provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.[23]

In animals[edit]

Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors by tit for tat strategy.[citation needed]

Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:[24]

C/C: \I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much.\

? D/C: \You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night.\? C/D: \Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death.\

? D/D: \you on my good nights. But I run a real risk of starving on my poor nights.\

?

In psychology[edit]

In addiction research/behavioral economics, George Ainslie points out[25] that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome, and that defecting both today and in the future is the worst outcome. The case where one abstains today but relapses in the future is clearly a bad outcome—in some sense the discipline and self-sacrifice involved in abstaining today have been \where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). The final case, where one engages in the addictive behavior today while abstaining \familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting \but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.

John Gottman in his research described in \science of trust\defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.

In economics[edit]

Advertising is sometimes cited as a real life example of the prisoner’s dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A’s advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period the advertising cancels out, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the creation of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry.[citation needed][26] This analysis is likely to be pertinent in many other business situations involving advertising.[citation needed]

Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoners' dilemma.[27] 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.

In sport[edit]

Doping in sport has been cited as an example of a prisoner's dilemma.[28] If two competing athletes have the option to use an illegal and dangerous drug to boost their performance, then they must also consider the likely