Game Theory and Post-Mortal Existence

Game theory is the study of strategic interaction between two individuals. Take two people playing rock-paper-scissors as an example. Two players have three choices each: rock, paper, or scissors. The objective of one player is to choose the option which dominates the option of their opponent  Example: Paper beats Rock, Rock beats Scissors, Scissors beats Paper. There is no best option for a given player because the best option is relative to their opponent's choice.

A classic example is the Prisoner's Dilemma. Two men are arrested, but the police do not have enough information for a conviction. The police separate the two men, and offer both the same deal: if one testifies against his partner (defects/betrays), and the other remains silent (cooperates with/assists his partner), the betrayer goes free and the one that remains silent gets a one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept secret from his partner. What should they do? If it is assumed that each player is only concerned with lessening his own time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. The sole concern of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the optimal decision for each is to betray the other, even though they would be better off if they both cooperated. (wikipedia, prisoner's dilemma)

The Prisoner's dilemma shows us that the option which offers the most overall benefit is not chosen due to selfish desire for more personal benefits. This pattern of choice can be seen in the world around us. A child chooses to not do the dishes. Both benefit if they take turns. Both lose if no one does the dishes. One wins more if one does the dishes every time. Taking turns is the best overall option, but the second the child refuses to do them, the parent is forced to do so, or live with worse consequences with the dirty dishes.

This example of game theory is very difficult to overcome in the real world, but not impossible. One of the best ways to over come the lose-lose option (which in this example is called Nash Equilibrium) is to make the game repetitive. What this means is that the actor will answer for his actions. If a prisoner confesses, and they happen to be in the same situation sometime in the future, his accomplice will not likely trust that he will remain silent. Knowing that they might replay this scenario in the future or that one prisoner will be held accountable for his choice, he is more likely to choose the option with the most collective benefits (Socially optimal outcome)

Why do people keep commandments? Certainly not because it is easy or most rewarding to our egos. Easy is Nash Equilibrium. Nash Equilibrium is what we might call the default option or the "natural man" option. It's where the water will pool if left unaltered. Our choices pool to certain positions. Sin is easy. If we are left unattended, our choices collect in the pool of the natural man.

Believing in a post-mortal existence and judgement is key to making "socially optimal" choices in this life. Knowing that I will answer for each choice, I will choose options with the most benefits and least eternal consequences. A life after this one denotes a "repeated game." Thus, our knowledge and belief change our actions. “And now, as the preaching of the word had a great tendency to lead the people to do that which was just—yea, it had had more powerful effect upon the minds of the people than the sword, or anything else, which had happened unto them—therefore Alma thought it was expedient that they should try the virtue of the word of God” (Alma 31:5). Teaching others to believe changes incentive more that coercion.

“We live in perilous times when many believe we are not accountable to God and that we do not have personal responsibility or stewardship for ourselves or others. Many in the world are focused on self-gratification, put themselves first, and love pleasure more than they love righteousness. They do not believe they are their brother’s keeper. In the Church, however, we believe that these stewardships are a sacred trust.” Quentin L. Cook, “Stewardship—a Sacred Trust,” Ensign, Nov. 2009, 91