“Games Theory” is one of those terms designed to tempt and then frustrate the unwary. Games Theory! Doesn’t it just sound as if it ought to be a light-hearted and playful subject? It certainly sounds non-mathematical and anything but rigorous. Sadly, it is both, involving nasty things like probabilities and matrices. I’m going to skip that part of it.
Instead, let’s talk about a Games Theory term that is now part of common speech: The Zero Sum Game. Technically, the Zero Sum Game is defined as one in a closed system where nothing is added, subtracted, nor made in the system.
Take, for instance, a game of marbles. There are only a certain number of marbles in the game. If I take a marble, you lose that marble. If I take two marbles, you lose two marbles. Every gain is balanced by a loss. Net total of wins and loses: zero. No matter how many players, the sum of exchanges is always zero.
For some reason, this simple, harmless idea seems to have an irresistible appeal to the macho types as a metaphor for life. To the tough-guy, competitive types (of both sexes), “life is a Zero Sum Game.” If you want to win, someone else has to lose. Or the corporate CEO turned pundit brags about how he succeeded because he always knew that “economics is a Zero Sum Game.” You win and the competition loses. Of late, we have even been told that “international relations is a Zero Sum Game.” It’s a dog-eat-dog world out there, and we had better realize it.
Setting aside the simple truth that none is a closed system, there are other flaws to these glib metaphors. For example, let’s take a look at one of the most common of these misapplied metaphors: evolution. Evolution, we are told, is a Zero Sum Game. Darwin proved that all evolution is simply a matter of the survival of the fittest. Eat or be eaten. If you are to survive, the rabbit must die. You eat the rabbit. You win, he loses. Simple.
Equally simple is the inheritance of genes. You become the biggest and strongest. You get to mate. Your genes are passed along to shape your species. The other, the smaller, weaker, slower ones, pass nothing along. They are the mules of evolution. You win, they lose. Simple.
The problem with that analysis is that the end result of such competition would be that the most selfish would always be the begetter and archetype of every species. That would mean, genetics being what it is, that wherever you looked, you would see nothing but species completely populated by selfish individuals.
But that is not what you see. Members of most species either work together or at least have some mechanism to restrain pure selfishness. Such a model could never explain the existence of pack animals. Dogs hunt in packs, sharing their food and allowing their weaker members to survive right along with the expert killers. No dog, however strong, is allowed to monopolize the food.
As you look across the evolutionary spectrum, what you find is species after species that survive by some level of cooperation. Cold logic seems to dictate that the weakest members should simply be abandoned and left to die. But there are hundreds of examples of animals that will slow down and nurse the sick or injured until they can keep up.
Since these characteristics have managed to survive through the millennia, there must be some evolutionary benefit in cooperation or even in altruism. However popular it is with the bloody minded, the Zero Sum Game just does not explain the world as we actually find it. Life, apparently, is not a Zero Sum Game
There are folks modeling evolution as a Non-Zero Sum Game using a mechanism they call Reciprocal Altruism. To test this, they have come up with a nice, primitive, model entity called Tit-For-Tat. They have tested Tit-For-Tat using computer simulations and the results are interesting.
Essentially, Tit-For-Tat is an optimist. Each time it meets someone, it assumes that new entity will be willing to share marbles rather than taking marbles. If entity A meets an entity B with fewer marbles than it has, it will be willing to give that one a marble. But suppose that entity B is a selfish entity that, instead, steals a marble? Here is the cute part. Tit-For-Tats remember how they are treated. If entity B acts nicely, so will entity A the next time they meet. But, if entity B acts selfishly, so will entity A the next time.
So what happens? Over time do all of the generous entities get screwed and turn selfish? Do a few selfish guys end up with all the marbles? In short, aren’t all those altruists really losers who end up losing the whole game?
Not at all.
Over time, in simulation after simulation, the generous entities come to dominate the population in terms of both numbers of entities and the number of marbles they have. To rephrase that, in time the selfish ones end up getting screwed by just about everybody while the generous ones happily go about sharing their wealth.
Obviously, this is a pretty simplistic model, resembling real animals only marginally. But the interesting thing is that more complex models have pretty much the same results, but with more complex behaviors. In fact, more complex entities based on the same ideas evolve societies that match real species in ways that can be really spooky.
So what, as the macho types love to ask, is the bottom line?
Simply this: In the long run, it might be in our self-interest to be altruistic. It really isn’t a dog-eat-dog world out there. It isn’t true for dogs and it needn’t be true for us, either.