Important as it is, the negative-sum violence game just described is, one hopes, less common than positive-sum games such as trading or hunting in which the players are likely though not certain to achieve a positive payoff of some kind.
Below is a hunting game in which both players face a choice between cooperating and finagling, and the payoffs follow the PD:
Other
Cooperate Finagle
Cooperate 5, 5 0, 10
Self
Finagle 10, 0 2, 2
As always in a PD, you are better off finagling no matter what the other player does.
Now, the hunting game with Trust payoffs:
Other
Cooperate Finagle
Cooperate 10, 10 0, 5
Self
Finagle 5, 0 2, 2
Here, as in Trust games in general, both of you do best by cooperating; you have a reason to finagle only if the other player is going to finagle.
Compared to the violence game with its relatively clear picture of aggression, the meaning of finagling or cheating in a hunt is open to interpretation. If finagling is outright theft of the killed animal, the PD payoffs work in immediate material terms. But in that case, I would suggest that the future-discounted payoff for the thief may well be lower than the payoff when both players cooperate, given the likelihood that the hunters know one another very well. In that case, the game is a Trust game, not a PD. In any case, in the hunting game as in the violence game, the players are unlikely to see themselves as having PD payoffs. They are likely instead to see themselves as having Trust payoffs, and as feeling pressure to finagle not because they can get their best outcome from doing so but from concern the other player will do so and leave them with their worst outcome. (Obviously, both players cannot successfully finagle by stealing the captured animal; one way to interpret the situation in which both finagle is that they abandon cooperation in favor of pursuing lower-value game individually, which makes the game a Stag Hunt, one of the variants of Trust.)
Instead of outright thievery, finagling in the hunt game can be interpreted instead in terms of harder to detect "cover your ass" or CYA behavior that minimizes the risks for the CYA player, who, say, does not take the same chance of getting gored by the tusked boar that the cooperator does and in doing so makes the hunt more dangerous for the cooperator and less likely to result in success. If finagling is CYA behavior rather than outright thievery, the immediate material payoffs for the players as well as the future-discounted ones are likely to follow Trust rather than the PD. The finagler lowers the probability of success to a degree that hurts him as well as the cooperator; that means his payoff for taking advantage of the cooperator is less than his payoff for mutual cooperation; that in turn means the game is Trust and not the PD.
My intuition is that hunts by our ancient ancestors and by ourselves are more likely to feature finagling in the form of CYA behavior than finagling in the form of outright thievery. Accordingly, it seems to me that the immediate material payoffs associated with cooperating versus finagling in a hunt are usually better described as Trust games than as PDs. Further, even if the immediate material payoffs of cheating are accurately described by a PD, the future-discounted payoffs seem likely to be better described by Trust than by the PD.
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