Game Theoretic Study of Moral Behavior
In the article ‘Interaction between games give rise to the evolution of moral norms of cooperation’ sourced from the Max Planck Institute, the authors use game theory to explain how individuals exuding moral behavior benefit more than those who set their self-interests first. The theory aims to answer the question – why must one act morally? Mathematician Mohammad Salahshour uses two famous game theory models – Prisoner’s Dilemma and Coordination Game – to present and solve the social dilemma of one acting morally.
The Prisoner’s Dilemma is an apt portrayal of the difficulty to coordinate when individuals are faced with the choice between coordination for a better social outcome (one where all players receive a fair payoff) and non-coordination for a better individual outcome (one where some players benefit more than others since they act on their self-interest). To understand this better, let us consider the following payoff matrix:
Here, we can find the equilibrium outcome using the following method:
- If player 2 chooses strategy 1, then player 1 would choose strategy 1 to maximize payoffs.
- If player 2 chooses strategy 2, then player 1 would choose strategy 1 to maximize payoffs.
- If player 1 chooses strategy 1, player 2 would choose strategy 1 to maximize payoffs.
- If player 1 chooses strategy 2, then player 2 would choose strategy 1 to maximize payoffs.
- Thus, the mutually agreeable outcome would be for both players to choose strategy 1.
Hence, given that both the players maximize their payoffs, the nash outcome would give a lesser payoff for both players as compared to their ‘ideal’ self-interest outcome.
On the other hand, the coordination game depicts how players can achieve a higher payoff if they coordinate while playing a game. To understand this better, let us consider the following payoff matrix:
Here, we can find the equilibrium outcome using the following method:
- If player 2 chooses strategy 1, then player 1 would choose strategy 1 to maximize payoffs.
- If player 2 chooses strategy 2, then player 2 would choose strategy 1 to maximize payoffs.
- If player 1 chooses strategy 1, player 2 would choose strategy 1 to maximize payoffs.
- If player 1 chooses strategy 2, then player 2 would choose strategy 2 to maximize payoffs.
- Thus, the mutually agreeable outcome would be either for both players to choose strategy 1 or for both players to choose strategy 2.
Hence, given that both the players maximize their payoffs, the nash outcome would be a coordinated outcome such the players choose the same strategies that other players in the game choose.
Combining the two games, we can develop an evolutionary model for moral systems that behaves like a Trojan horse: “once established out of the individuals’ self-interest to promote order and organization, it also brings self-sacrificing behavior”. The Prisoner’s Dilemma game shows that cooperation does not pay-off if one is selfish. In this case, self-interested behavior yields a higher payoff if the other individuals are selfless. However, in a society where everyone wishes to maximize their individual payoffs, that is they act selfishly, people fail to reach a mutually agreeable outcome without coordination. When the Prisoner’s Dilemma is coupled with the coordination game and moral norms favor cooperation, people tend to cooperate since the gain they receive from the cooperation game by choosing to cooperate makes up for the loss from the Prisoner’s Dilemma game.
Thus, in an evolutionary model where the Prisoner’s Dilemma is played first and the coordination game is played second, selfish people tend to cooperate which leads to the emergence of moral norms.
Citation: “Interaction between games give rise to the evolution of moral norms of cooperation” by Mohammad Salahshour. PLOS Computational Biology