A more solid foundation might, however be built on the ongoing relationship of an individual with society at large rather than any single other. The basic idea is that anyone cheating on a relationship will be punished by ostracism--a transgression against one is treated as a transgression against all, with exclusion from future trust games serving as the punishment. Provided society is large, such a threat acts as a far more powerful deterrent and hence much more trust may be sustained.
Implementing this, of course, requires that an aggrieved party communicate her case to the rest of society. After all, if only Ann knows that Bob cheated her, society will be in no position to punish Bob. Clearly, Bob has little interest in telling the world he is a fink or cad (to use two delightfully archaic terms), so the job falls to Ann, who might be thought to relish the prospect of dragging Bob's name through the mud.
There are, however, several difficulties with this arrangement. The first is that Ann might lack the means of communicating to the rest of society all by herself. She may need others to propagate the message for her. But what social scientists antiseptically call "propagation" is, in lay terms, nothing more than gossip:
Did you hear what Bob did to Ann? He should be ashamed of himself. I'll never think of him the same way again...And so society won't think of Bob in the same way. According to the logic of cooperation, he is now an outcast, "dead" to the society in which he once happily played trust games.
I previously wrote about how morality might help us solve certain social dilemmas, but here it clearly does not. Suppose that Ann's best (and only) friend, who, in a remarkable coincidence, happens to be named Carole, was brought up to believe that "a lady does not gossip." Now, Bob's misdeeds sadly go unpunished since the communication trail ends with Carole, who never speaks ill of others based on second-hand reports. But Carole's moral stance now redounds to the detriment of society. Bob, anticipating that there are enough Caroles in the population, now feels he can get away with his foul deeds. Strictly speaking, Carole is being irrational--her unwillingness to "spread the word" about Bob leaves her (and society) worse off.
This is all a bit unfair to Carole for, in this world, we assumed that individuals could only destroy the reputation of those who actually deserved it. The possibility of a "vicious rumor," a totally unfounded attack on someone, simply cannot arise. Indeed, even more weirdly, we don't really have to assume this. Citizens in game theory land have nothing to gain (and a little to lose, see below) from such actions and so, even if we allowed it, "smear campaigns" would never arise. Thus, Carole would still have nothing about which to be fearful in rumor mongering and her whole ladylike morality comes off as mere prudishness.
Yet, as a devoted follower of reality TV, I can readily report many incidents where false allegations were made, even against such kind and decent folks as Snooki from Jersey Shore. Worse yet, others with less scruples than Carole happily propagated them. Clearly, something important about human nature is missing from our little game theory world in terms of rumors.
A second problem with this social glue, pointed out by Avinash Dixit, is that, even if there are no Caroles in the population, so long news passes sufficiently slowly, a "gossip equilibrium" might still not work. More precisely, he suggested that news is likely to travel slower in larger societies than in smaller ones and showed that, a tipping point arose wherein, despite gains from globalization, well-being could fall suddenly once "society," or rather the community that individuals counted as constituting society, grew too large.
Growing up in a small town, I was all too aware that everyone knew everyone else's business. I longed for the greater privacy (and anonymity) of city life. Rather than despairing at this, Dixit suggests that I had it exactly backwards--those despised small town busybodies are, in fact, the social "glue" necessary for cooperation.
Game Theorists Nageeb Ali and David Miller point out an even more subtle problem: Perhaps Ann herself will choose to stay mum about Bob. They study a world where no one is squeamish about passing gossip and where news, once released, spreads quickly. Their point is that, by throwing Bob under the bus, Ann has, in effect, made society smaller---by exactly one member, Bob. Since cooperation is borne on the back of the threat of ostracism, with the loss of Bob, this threat has now lost a little of its punch. And hence, Like the rest of this literature, they assume that "vicious rumors," unjustified smears on another's character, are impossible, but justified smears are voluntary. by ratting out Bob, Anne has now reduced, by a tiny bit, the amount of cooperation possible. Since this leaves her worse off, she remains silent. Bob, cunning chap that he is, anticipates that Ann will bear her victimhood stoically and silently and hence has nothing to fear from cheating. Taking to its logical end, Ali and Miller show that this implies that the social glue of ostracism is completely worthless, the only sustainable trust is that from a bilateral relationship, regardless of society's size. Paradoxically, allowing victims the apparently worthless option of remaining silent completely destroys the value of society in enforcing trust.
It's a striking result, but I cannot help thinking that it says more about the power of logic than it does about the nature of human behavior. Certainly, in a large society, the effect of "losing" Bob is very small. If, for instance, we granted that Ann gained even an ounce of happiness from unburdening herself of the secret as to what Bob did, then, once society is large enough, this will be enough to overcome her reticence and hence permit society to maintain trust. Personally, I think an ounce of happiness is a vast understatement of the joy that many of us get in ensuring that Bob gets his comeuppance. Here again, irrationality may save us--provided that individuals have an irrational "taste" for justice, the problem of Ann's potential reticence quickly becomes a non-problem.