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The Game That Keeps On Giving

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Mar 21, 2017

In this article, we shed some light on the following burning question:

How can we distinguish between altruistic donors that give without any expectation of reciprocation versus ‘warm-glow’ donors who give to receive rewards (e.g., social recognition, tax breaks) or avoid punishments (e.g., ostracism, damaged reputation)?

Game theory provides a method to morally differentiate ‘warm-glow’ givers from pure altruists. As a field of study, game theory offers a theoretical framework based on mathematical models to analyze social interactions. As such, it serves as a useful tool to study conflict and cooperation between rational decision-makers (Myerson, 1991). In a cooperation game, the payoff to each player depends on their actions. One particular game, The Prisoner’s Dilemma (see Table 1), has reliably held its own as an illustration of a novel finding. That is, what is best for one individual can be disastrous for the group.

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The Prisoner’s Dilemma

Table 1. Both Prisoner A and B are suspects of a murder. They received the same offers from the public prosecutor. If both Prisoner A and Prisoner B confess to manslaughter, then they will each serve ten years in jail. If one remains quiet while the other confesses, then the snitch will get to go free, while the other will face lifetime imprisonment. If both keep quiet, then they will each face only one year in jail.

Each of the two players in the Prisoner’s Dilemma can choose to either cooperate by keeping quiet, or defect by confessing. Collectively, it would be best for both to keep quiet as they would only face one year behind bars.,  However, a key concept of game theory is that of the Nash equilibrium, which states that each individual player within a game will maximize her own utility (or make the best decision for herself) based on what he believes the other players will do. Thus, if Prisoner A believes Prisoner B will defect and confess to the authorities, he will also defect, so as to not face life imprisonment. In the Nash equilibrium, nobody can do better by unilaterally changing her strategy, as every group member is doing as well as she possibly can. Therefore, both players will defect, and the Nash equilibrium is found in the top left corner of Figure 1, confess x confess.

The Nash equilibrium was simply explained in the 2001 film A Beautiful Mind. In one scene, Nash and his friends are looking to score dates with a group of women at their Princeton campus bar. Among these women, there are a handful of brunettes and a single blonde. After each setting their sights on the blonde, one of Nash’s friends suggests that they should each go at it alone, recounting Adam Smith’s famous dictum, “in competition, individual ambition serves the common good.” Following a flash of inspiration, Nash says Adam Smith needs revision (Rey, 2008).

He continues, “If we all go for the blonde, we block each other and not a single one of us is going to get her. So then we go for her friends, but they will all give us the cold shoulder because nobody likes to be second choice. But what if no one goes to the blonde? We don’t get in each other’s way and we don’t insult the other girls. That’s the only way we win.”

In this example, the ‘no one go for the blonde’ strategy is effective because all of the players (no pun intended) end up winning. Outside the idealism of Hollywood, events are much less predictable. Without certain knowledge of agents’ preferences, we tend to hesitate in accepting the common good because the cost of cooperation can be too high or unpredictable. For this reason, we tend to strategize by prioritizing our own vested self-interests. In the case of the Prisoners’ Dilemma, keeping quiet is never a good option no matter what the other criminal chooses as there is a looming possibility that the other suspect might have talked. As such, snitching invariably avoids lifetime imprisonment.

In practice, economists use the Nash equilibrium to predict how companies respond to competitors’ prices. At the microeconomic level, this tragedy of the commons explains why we overfish seas and deplete fish stocks. A related concept is the tragedy of the commons, in which there is a scarce collective resource that must be allocated between individual actors. In the classic example, there is a “commons” on which members of a local community can let their cows graze. The issue, however, is that overgrazing will cause the land to be less productive, and thus reduce total output for the entire community. Because there is no regulation to share the benefits of the “optimal” outcome with the entire community, each individual will pursue his own personal interest at the expense of the collective good. This explains why, for example, in absence of a centralized authority, we deplete fish stocks by overfishing. Employees competitively overwork themselves to the point of exhaustion to impress their managers. We emit too much carbon into atmosphere at the expense of our collective well-being. We vehemently bicker about the space allotted to us in the work refrigerator. In cases where the commodity is unregulated and there are no clear winners, the tragedy of the commons comes into effect. Most of us may consider ourselves as altruistic persons, yet we get in each other’s way to reap individual rewards as a direct result of the formal incongruence between the singular and plural.

The Envelope Game

Hoffman, Yoeli & Navarette (2016) from Harvard University recently created the “Envelope Game,” as a modification to the well-known Prisoner’s Dilemma (Chammah & Rapoport, 1965). This game elegantly embodies a method of differentiating warm-glow donors from pure altruists. In the Prisoner’s Dilemma and other cooperation games we only know whether players choose to cooperate or defect. This is not sufficient because we are not only concerned with whether or not players cooperate but also about how they decide. We place more trust in players that never even considered defecting. The Envelope Game makes collecting this valuable information possible.

In this game, Player 1 has two choices. He can open a sealed envelope containing the information of the cost of helping, or he may simply choose not to open it. Player 2 has to observe whether Player 1 opens the envelope (i.e., whether he weighs the personal risks to benefits) or if Player 1 instinctively helps. Following this, Player 2 decides whether to continue this relationship (strong or weak tie). Theoretically, a purely altruistic person will give without ever opening the envelope, whereas a warm-glow donor will need this information to weigh risks and benefits.

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Key Takeaways for Charities

As an object of scientific inquiry, human interaction with probabilistic events is complex.

The interplay between these factors mounts up the complexity. Predicting behavior at an individual level is challenging feat in it of itself. Introducing multiple decision-makers into the mix renders prediction all the more volatile. Along a similar vein, prosocial behavior is just as nuanced. At least with advancements in game theory we know that altruists do not just to good, they do good instinctively. Charitable organizations can use this insight to segment pure altruists from warm-glow givers. If we accept this assumption, targeted marketing would become a crucial undertaking as warm-glow givers and pure altruists would necessarily respond to distinct strategies.It is likely that warm-glow givers are less concerned with the cost of cooperation if they are properly engaged. This would mean that the requests for donations should be framed to focus on empathy and social impact rather than statistical financing. Similarly, it is likely that using tactics that would be effective for warm-glow givers (e.g., publicizing donor contributions) could be detrimental to pure altruists.


Hoffman, M., Yoeli, E., & Navarrete, C. D. (2016). Game Theory and Morality. In The Evolution of Morality (pp. 289-316). Springer International Publishing.

Myerson, Roger B. (1991). Game Theory: Analysis of Conflict, Harvard University Press, p. 1.

Rey, J. (2008, June 1). If we all go for the blonde. Retrieved March 17, 2017, from

About the Author

Arash Sharma portrait

Arash Sharma

Government of Canada · Behavioral Economics

Arash is a Behavioural Scientist at the Government of Canada.

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