Game of Cheating

Leave the money on the table.

Posted Sep 07, 2017

J. Krueger
Source: J. Krueger

Top bankers have shown no shame for their bad behavior and have made no apologies to the public. ~Bernie Sanders

That ain't workin', that's the way you do it / Money for nothin' and chicks for free. ~Dire Straits

People don’t trust bankers very much, particularly since the great recession of 2008 and the publicity of high-stake fraudsters. In an intriguing study, Cohn et al. (2014) asked whether bankers’ professional identity, when salient in their minds, might loosen their ethical standards. Indeed, the authors found that bankers, but not other professionals, were more likely to cheat in a simple money game when their identities as bankers had been invoked than were bankers in a control group, where these identities were not invoked. Indeed, there was no evidence of cheating at the group level (when cheating was so easy) among bankers in the control condition (identity not salient) or among other professionals (e.g., managers in the pharmaceutical industry).

The finding that there was little cheating overall is encouraging, but it is oddly dispiriting to see that bankers as bankers surrendered to the temptation to cheat but not bankers as people. One might ask for a difference of the opposite kind.

The money game, introduced by other authors before Cohn et al., is simple and elegant. Each person, sitting unobserved in a cubicle, gets to toss a coin 10 times, knowing that there are other participants doing the same. The person is told that each ‘head’ is worth $20, but that the cumulative amount will be paid out only to those participants who do better than the median. (Incidentally, this is a lot of money. Cohn et al. do not comment on this aspect, but it seems that bankers must be paid handsomely to participate in research studies.) In the money game, each individual has an incentive to cheat—that is, to report more heads than obtained. More heads means more money and a higher probability of receiving it. Cohn et al.’s main result is that bankers whose identity was not primed reported 51.6% heads on average, whereas the primed bankers reported 58.2%.

J. Krueger
Source: J. Krueger

Lying for personal profit is immoral. In the context of the Swiss money game, it also produces monetary harm to the researchers and their funding agencies as more money is paid out overall than would be if there were no cheating. There is a second-order moral dilemma for the researchers, who know that they are rewarding cheaters. Cohn et al. only discuss their results in terms of temptation, ethics, and identity. Although they are game theorists, they say little on the strategic aspect of the game. So let’s do this here.

In order to open a game-theoretic window into the strategic context of the game, let’s simplify a few things. First, let us note that the best outcome goes to those participants who cheat while others are honest. If all cheat to the maximum, no one can beat the median; if no one cheats, no one realizes extra profits. To model this arrangement in simplified form, imagine two players, where each as a choice between cheating and being honest. There is only one reward available, $20, and it goes to the cheater who plays with an honest person. In this game—see payoff matrix—cheating ‘weakly dominates’ being honest, which means that the payoff for cheating is equal to or higher than the payoff for being honest. Hard-boiled game theorists conclude from this that everyone should and will cheat. There are no enforceable negative consequences (as in the Cohn study) and internalized norms are, in game theoretic parlance, “cheap thought” (as in “cheap talk”). As game theorists, Cohn et al. might have been surprised at the low incidence of cheating.

J. Krueger
Source: J. Krueger

Let’s thicken the plot and assume that players have a conscience. They feel bad about cheating. It’s like paying $10 out of pocket. The revised payoff matrix shows that cheating no longer dominates. Players still hope to the singular cheaters, but they worry about being in the company of another cheater. In other words, they feel the pull of greed ($10 > 0), while also feeling the sting of fear (-$10 < 0). If they knew what they other player will do, they would choose to do the opposite: cheat an honest person and be honest to a cheater. But they don’t know, hence the dilemma. Game theorists have nothing better to offer than the advice to flip a mental coin (or the physical one, since they have one in the money game) and cheat with a probability of .5.

This game has a name. It is known as the volunteer’s dilemma. There is more you can read, e.g., here: Krueger, Ullrich, & Chen, 2016. And there is more you may want to think about, e.g., how you treat and how you are treated by significant people in your life, where other pains and pleasures besides money are at stake.   

Cohn, A., Fehr, E., Maréchal, M. A. (2014). Business culture and dishonesty in the banking industry. Nature, 516, 86-89.

Krueger, J. I., Ullrich, J., & Chen, L. J. (2016). Expectations and decisions in the volunteer’s dilemma: effects of social distance and social projection. Frontiers in Psychology: Cognition, 7, article 1909.