12.26.10

Welcome back! It's time for Part 2 of:

Satan, Discount Factors, and Mortality's Grim Trigger: The Garden of Eden Game

Here we will be exploring the next Adam and Eve model which I have called the Latter-day Saint model (or LDS). This game has several differences from the OS model that I think you'll find interesting. And so, without further ado, here is it:

Model 2: Adam and Eve’s Forbidden Assurance Game

Again, this game has two players, but no exogenous players. We consider the following game.

		ADAM
		Eat	Don’t Eat
EVE	Eat	Ω, Ω	Ωε, βε
	Don’t Eat	βε, Ωε	β, β

Where Ω is the payoff for making covenants with the Lord, β, as before, is the payoff for staying in the Garden, and ε is the penalty to each player for leaving the Garden alone (Ωε) or failing to coordinate (βε). This is an assurance game and is also infinitely repeated. This means there is a discount factor δ here as well which, again, measures Adam and Eve’s knowledge of mortality. The principle payoff assumption is that Ω > β > Ω/β(ε) in the n-th game. That is, the eventual benefits of mortality outweigh the benefits to staying in the Garden, and that both these are preferred over any action with a coordination error term ε. This game also has an iteration where Adam and Eve become indifferent between equilibria as follows:

Ωε + Ωδ/1-δ ≥ β + βδ/1-δ

Where they, due to their understanding of mortality, realize that the payoff of making covenants outweighs the payoff of staying in the Garden combined with the penalty of leaving. Notice that there is no exogenous actor here and that the mortal stage of the game can be (was built to be) superior to the Garden of Eden stage—I discuss these assumptions and characteristics below.

A man after His own heart: The Plan of Salvation

The most obvious difference in the LDS game is that the payoff for making covenants in the mortal stage (Ω) is strictly preferred to the payoff for staying in the Garden (β), even in pure strategies. This traces to the fact that Adam and Eve’s understanding of covenants and the purposes of the second stage actually caused them to eat the fruit and leave the Garden. This is due to God’s intricate and complete outlining of the Plan of Salvation before the Garden of Eden or anything else was created. God did not intend for the Garden to be a permanent state of being for Adam or Eve; He therefore made it possible for them to learn the importance of mortality and thereby make the choice to suffer a small penalty (leaving the Garden) in order to receive the eventual payoff of mortal purpose.

Man does not live by bread alone: Complete Agency

Secondly, Satan has little power in this game except (perhaps counter-intuitively) to aid in Adam and Eve’s learning principles for themselves. Satan’s temptation of Eve actually sparked her contemplation of the purpose of the Tree of Knowledge of Good and Evil and she began to realize, as mentioned, the value of mortality. This implies the doctrine that Adam and Eve were subject to opposition in the Garden, but that their agency remained perfectly balanced. It also implies that Satan was actually the least knowledgeable actor in the narrative since he did not understand God’s purposes for mortality.

Time and tide wait for no man: Celestial Purposes

This leads to the last characteristic which is that of a complete agency. This type of agency allows the human family to have a progressive purpose which is not inferior to the divine. That is, because we have greater agency, our eternal potential is boundless. This traces to the doctrine of becoming like our Heavenly Father through the learning of a perfect application of our agency. 

Consider the following table which summarizes the characteristics and doctrinal principles discussed above:

GAME ASSUMPTION

1. The payoff Ω strictly dominates the payoff β in pure strategies

2. The discount factor δ is only manipulable endogenously

3. The grim trigger strategy is strictly preferred (Ωε outweighs β eventually)

CHARACTERISTIC

1. The eventual benefit of the second stage outweighs the Garden payoff, causing movement to mortality

2. Satan has no exogenous power over decision making

3. No inherent agency constraints meaning a more complete divine value

DOCTRINE

1. Plan of Salvation before the creation

2. Opposition to facilitate learning, but no agency constraints

3. Man’s agency and Celestial purpose and potential

Which, again, is pretty cool stuff. Again, this may not completely reflect the LDS point of view, but it does add some insight into a vastly different way of viewing the Garden of Eden. Interesting to think that such (seemingly) small actions by our first parents could trace to such important doctrines; this I will discuss a bit more in my next post. Hoped you enjoyed this one; stay tuned for the final post in this three-part adventure!

Part 3: Game Assumptions and Moving Mountains

Have a wonderful Christmas weekend! :)