A Third-Party Ultimatum Game

There is great power in doing nothing. —Lao Tzu, paraphrased

The usual narrative arc of this kind of essay begins with a real-life story to illustrate a psychological issue of interest, and then offers a formal description in an effort to capture the essential and generalizable properties of the case. Today, I want to reverse this order.

The Game

The ultimatum game is well known (Güth et al., 1982; Krueger, 2022). There are two players. The proposer, P, has been given a small sum of money, which they can now offer to split with the receiver, R. If R accepts the proposal, the deal is made and the money is transferred. If R rejects P’s offer, no one gets any money. Empirically, many proposers offer a 50-50 split with the average offer lying somewhat below 50%. Proposers are seen as moral to the extent that they make generous offers; receivers are seen as moral to the extent that they reject low offers. Perceptions of rationality tilt the opposite way (Krueger et al., 2020).

Now imagine a third party, T, taking an interest in the proceedings. Suppose T is whoever provided the funds to play the game. Consider a situation in which P offers a 60-40 split and R accepts. Before P transfers 40% of the money to R, however, T decides to keep half of the transfer. In other words, the true end state of the game shapes up to be 60% for P, 20% for R, and 20% for T. R does not know whether P is aware of T’s intervention, and R still has the option of vetoing the deal. What is R to do?

If R now rejects this revised and worsened deal, he might score moral points. This is only so with regard to T, however, whose intervention failed and who is now empty-handed. What about P? P thought their reasonable offer was accepted, and is now astonished at R’s change of heart. Much will depend on P being informed of T’s intervention, which might help P understand R’s reasoning. Still, R might not be free from moral guilt. R could blame T for P now going empty, but it was still R’s option to preserve the benefits for P. R reneged on a promise to P, for good reason it seems, but it was still a reneging.

The Story

True life stories contain additional elements that might be relevant, and so it is in this case. I encourage the reader to ponder whether the game described above captures the story below. Here, Professor Hafiz receives an invitation from Professor Ekmek to serve on a panel to evaluate Rafik’s Ph.D. thesis. Hafiz agrees, waives the honorarium that many universities offer in such cases, and merely notes his expectation that modest travel, accommodation, and food expenses be covered. Ekmek agrees.

Weeks later, the Office of Examinations at Ekmek’s and Rafik’s university sends a letter to Hafiz noting that he is scheduled to serve as a thesis evaluator, and advising him that the Office has no budget to cover expenses. There is no cc information indicating whether the Office copied Ekmek on this correspondence. What is Hafiz to do?

A first instinct suggests Hafiz do nothing (Krueger, 2013). The deal has deteriorated in a bait-and-switch manner (Cialdini & Guadagno, 2004), so no action is required of Hafiz. Being a person of good conscience, however, Hafiz wonders what Ekmek knows. The most plausible inference is that Ekmek is unaware; yet, arguably, he should have been aware of university policy and should have informed Hafiz thereof. Rafik is more likely to be unaware, and he is the one to bear the greatest cost (e.g., a postponed thesis defense, which might compromise career plans). Rafik’s situation would be saved if either Hafiz, or Ekmek, or the Office stepped up. The Office, however, has already made a commitment to do nothing, and has done so in writing. Hafiz could climb the moral high ground and cover the travel expenses himself. Ekmek could see if he might find alternate funds to cover the cost.

The second instinct suggests Hafiz tell Ekmek what he has learned from the Office and see what Ekmek does. This would put Ekmek in Zugzwang (forcing him to make a move). This option seems morally superior than what the first instinct suggests, but it is not without its own inferential underbelly. When Ekmek learns from Hafiz of the situation created by the Office, he must wonder whether he missed his obligation to be informed and to inform other involved parties. This is a burden Hafiz cannot take away from Ekmek. Hence the first instinct retains some appeal (Krueger, 2024).