Original Sin: Part 5, A Game Theoretic Summary of Sin in the Malthusian World

In this essay I want to use game theory to summarize how I see Malthusian dynamics operating in human affairs as the locus of "sin."

To do this we need to review a bit about game theory.

Game theory is a branch of applied mathematics where the idea of a "game" is used to isolate critical features of decision-making, particularly when those decisions are social. Simplifying greatly, games from poker to Monopoly to chess have a few common features:

1. Players: People making choices
2. Moves: Choices the people can make
3. Payoffs: The outcome/consequences of the choices

The interest in game theory is that, by using the idea of players making moves leading to payoffs, game theory allows us to create models of real world decision-making scenarios. If we can specify with some degree of realism the actual choices people face along with a realistic appraisal of the consequences attached to those choices then a mathematical/analytical approach to decision-making might be enjoyed.

For our purposes, game theorists speak broadly of two kinds of games. Thus, using game theory as a lens on human behavior, we might also break human interactions into one of two basic types.

The first kind of game (model of human interaction) is called a zero sum game. The name comes from the fact that there are some games where the sum of the player's payoffs at the end of the game sum to zero. Poker is a good example. Imagine you and I play head's up poker. If at the end of the night I'm up $20 then, by definition, you are down $20. Our payoffs, plus $20 and minus $20, sum to zero. The point being that in zero sum games my wins define your losses (and visa versa). Consequently, zero sum games are also called games of "war" or "total conflict." Another way of looking at zero sum games is that the player interests do not overlap. There is no middle ground where we can find a win/win. It is win or lose for either you or me. This slide represents that situation:



The second type of game (human interaction) is called a non-zero sum game. In this game the interests of the players overlap (to some extent). In the space where the interests overlap a win/win outcome is possible:



We can see why the game is called non-zero sum: If we both "win" (positive payoffs to us both) then the sum of our winnings is non-zero. (We should also note the dark side of non-zero sum games: The possibility of lose/lose.)

With these notions of game theory in hand we can now approach some biblical concepts in a novel way. For example, consider the Golden Rule. Using the language of the non-zero sum game we could argue that the Golden Rule is asking us to seek the place where I consider my interests to overlap perfectly with your own. To love you as I love myself. Our interests do not simply overlap to some degree. They form an identity:



I mention the Trinity in the slide because, if one wanted to think of the situation theologically rather than ethically, I think the Trinity--the mutual and loving indwelling of the Father, Son, and Holy Spirit--is another way to consider the identity relationship inherent in love: Distinct persons with fully overlapping interests. This Trinitarian life is to be lived out in the church. Sharing and having all things in common so no one is in need. Weeping with those who weep, rejoicing with those who rejoice.

Okay, we are now ready to use game theory to summarize my notion of Malthusian sin.

Basically, we can see sin and love as forces pulling us in opposite directions. The Malthusian forces of this world are constantly forcing our interests apart. We call this divergence "selfishness." That is, I begin seeing my encounters with others as zero sum interactions. It is me against you. I must "win." I must look out for myself.

As I've argued, I don't think this intense zero sum-ness is innate. I think, as the psychological default, humans approach each other in a non-zero sum manner (to some small degree). Generally, we don't approach people in a state of total suspicion or "war." We are, as a species, open to the possibility of reciprocity, coordination, and cooperation. We know that our personal good is somewhat implicated in the good of others. The point of this observation? Simply this: From a game theoretic perspective humans are not totally depraved.

Depravity comes from the Malthusian pressures that force us away from our non-zero sum default into zero sum war. When we feel vulnerable or in want we begin to grow increasingly "selfish." We start looking at encounters as zero sum affairs. We stop looking for moments of cooperation and start looking for ways to "win."

Conversely, love/salvation/grace/Trinity/church, whatever you want to call it, is constantly trying to fuse our interests in the Golden Rule identity moment. Pushing us toward greater non-zero sum-ness. This is, admittedly, a highly unnatural thing to do, particularly when I'm being attacked or hungry. This is why a force--grace, salvation--is needed to lift us out of the Malthusian trap.

In sum, we can think of sin and salvation as two forces, each pulling us in different directions:



Sin is the product of Malthusian forces pulling us into zero sum war with each other. Conversely, grace is trying to push us into non-zero sum convergence.

Next Post: Part 6