More Games, in Theory

I've finally figured out what it is that annoys me about game theory. It's the -- usually unspoken -- assumptions made when determining what the rational strategy should be.

I started down this road in my AI-Class G-T post here, but I think I can put it in better terms now. Given the Prisoner's Dilemma payouts in that post the presumption is that one should always play Defect because:

• A. You risk doing serious time if the other player Defects and you don't;
• B. You could get a reward if you catch the other player Cooperating.

This makes some sense in a one-shot game where you expect to never see the other player again. But if you are playing more than one round -- unless your opponent is Christ-on-the-Cross (and probably even for that first round as well) -- everyone is going to play Defect. This makes the total payout for both players worse than if they had always Cooperated.

Sure. Sure. Maybe you "won" the first round and are ahead by a big six points after the hundredth round at -98 to -104. Big Whoop...Pride goeth before the Fall...

So, why is Defect-Defect assumed to be the rational strategy? It's because each player is afraid that the other player is just as greedy as they believe themselves to be. Afraid and Greedy are strong terms for risk-adverse and advantage-seeking, but there they are in plain daylight. Fear and Greed doth also lead to falling.

I think one can make the same argument for other canonical games:

• Chicken: Really just P-D with worse outcomes;
• Stag-Hare: The Hare player is afraid of being abandoned and selects the option which guarantees some self-advantage.

In all cases Cooperation leads to a better outcome for both players over time. In fact Christ-on-the-Cross might really be the best option all around.

So, why do we not Cooperate? My claim is that Fear and Greed are natural responses to evolving in an adverse environment with limited resources. Even single-celled organisms recoil from harmful substances and pursue the useful ones. Scale this up and over-amp it with competition and you get Defection as the rational response. If we had developed in a benign and plentiful environment we might have little need for risk-aversion and advantage-seeking. Perhaps then we would believe that the rational strategy is one which best benefits all the players.

I'm going to carry this even further and posit that all animal life on earth have developed four natural, one might even say knee-jerk, responses in order to survive:

1. Fear -- Risk aversion;
2. Greed -- Advantage maximization;
3. Disgust -- Recoil, e.g., from excrement or dead bodies (probably better represented by its opposite, Desire, but I like to keep things negative whenever possible);
4. Anger -- Blanking out fear and disgust in order to persevere.

These are what we commonly call emotions. Therefore the so-called rational game strategies are actually emotionally driven.

If only we lived in a world of bunnies and unicorns, eh?