How Game Theory Promotes Moral Behaviour

Introduction

Society is governed by morals. For humans to live together in an orderly and peaceful manner, morals form a set of ‘rules’ that promote the wellbeing of the collective over the interests of the individual. For example, behaviour like theft is widely considered immoral, even though it is self-benefiting for the thief. But what causes these common morals to form? What incentivizes humans to choose moral behaviour over purely self-beneficial behaviour? 

There have been various approaches in attempting to answer this question in the past, such as through the lenses of biology or psychology. But mathematician Mohammad Salahshour, in his study Interaction between games give rise to the evolution of moral norms of cooperation, proposes a new explanation: game theory.

Applying Game Theory

For this study, most collective decision making scenarios can be modelled using game theory in one of two ways: a prisoner’s dilemma, or a coordination game. The latter represents decisions when choosing what benefits the group is rewarded with the higher individual payoff, while in the former, choosing to be selfish gives the higher individual payoff. We can ignore the zero sum game model for this discussion, as it represents two direct opponents rather than potential collaborators.

Let us first take a deeper look at a coordination game model:

We can see in this game that there are two Nash equilibriums: either both players choose the group’s interest, or both choose their own self-interest.

Given that the individual payoff is greater in the Nash equilibrium where both players choose group interest, the reasoning behind the ‘moral’ choice of choosing the group’s interests is fairly obvious. The individual gains the most when choosing the option that benefits the group.

However, the reasoning behind moral behaviour is not so clear when dealing with the prisoner’s dilemma.

If the other player chooses self-interest, the payoff would be the same no matter what move the player chooses. But if the other player chooses the group’s interest, the greater payoff would be to choose self-interest. So here, the dominant strategy for both participants is to choose the selfish move.

So doesn’t this model show that there is no incentive for the individual to choose moral behaviour in this scenario?

In a vacuum, that may be the case. But we can introduce new elements to these models to explain moral behaviour: what if the players in both the coordination and prisoner’s dilemma games were the same two players both times? Additionally, what if the prisoner’s dilemma game preceded the coordination one? If you knew that the other player chose their self-interest in the last game, would you still trust them to choose group interest next time?

A Revised Model

To account for these new elements, let us also introduce probability into these games. Additionally, let us adjust the payouts for the games as follows:

Game 1

Game 2

Suppose in the prisoner’s dilemma game (game 1), player 1 chooses self-interest. In the best case, their opponent will choose group interest, resulting in a payoff of 3 for player 1.

However, this decision makes player 2 lose trust in player 1. So let’s say in the second game, player 2 only has a 10% chance of choosing group interest, as they think player 1 is likely to choose self-interest.  So if player 1 chooses group interest in game 2, their expected payoff is 0.1(10) + 0.9(0), or 1. If they choose self-interest instead,  their expected payoff is 0.1(2) + 0.9(1), or 1.1.

So overall, the best possible total expected payout for player 1 is 3 + 1.1 = 4.1.

Alternatively, suppose player 1 chooses group interest in game 1. In the best case, their opponent will choose group interest, resulting in a payoff of 2 for player 1.

Because player 1 chose group interest in game 1, player 2 trusts player 1, believing that will likely choose group interest in game 2 as well. So let’s say in the second game, player 2 now has a 90% chance of choosing group interest. So if player 1 chooses group interest in game 2, their expected payoff is 0.9(10) + 0.1(0), or 9. If they choose self-interest instead, their expected payoff is 0.9(2) + 0.1(1), or 1.9.

So overall, the best possible total expected payout for player 1 is 2 + 9 = 11. Even if player 2 did not choose group interest in game 1, at worst player 1 will have a total expected payout of 1 + 9 = 10. This is still greater than the best total expected payout of choosing self-interest in game 1, which was only 4.1.

This demonstrates why individuals may be incentivized to act morally by game theory. Though choosing group interest may not seem to have the best payoffs in an isolated scenario, in the long term, they can gain more than they may have lost out on in that initial game.

---

References

Max Planck Society. “Study Shows How Moral Behavior Pays off in the End.” Phys.org, Phys.org, 18 Nov. 2022, https://phys.org/news/2022-11-moral-behavior-pays.html?fbclid=IwAR1LzcSJm0Jkgdz9S88roNjr3XyjEWl6zDgPHYpKwP5eRAFDOwAp24g7WVA.

Salahshour, Mohammad. “Interaction between Games Give Rise to the Evolution of Moral Norms of Cooperation.” PLOS Computational Biology, vol. 18, no. 9, 2022, https://doi.org/10.1371/journal.pcbi.1010429.