Testing Evolutionary Theories

Evolutionary game theory deals with interactions between populations of players of different types. Each type plays a particular strategy, which is not consciously chosen, but in fact inherited or assigned by mutation. For example, an agent of type A plays strategy A and only A, while an agent of type B plays strategy B and only B. The type with the more successful strategy survives while the other(s) die out. Eventually, the majority of the players (or even the entire population) consists of types playing the more successful strategy.

Let u(a,b) be the payoff to an agent from playing strategy a when the other player plays strategy b. An evolutionary stable strategy (ESS) of a symmetric game is some strategy, or action, b* B, the set of all possible actions, such that:

1. (b*,b*) is a Nash equilibrium of the game, and
2. u(b,b) < u(b*,b) for every best response b B to b* with b b*.
   
   Evolutionary models are useful for thinking about competition and relative survival rates among different strategies, and modelling inherited forms of behavior. The development of social norms is a key aspect of this, since from the early hunter-gatherer stages of human society, the ability to solve collective-action problems was crucial for survival. Small bands of hunter-gatherers were not only focused on seeking individual returns, but were also dependent on each other for mutual protectionm sharing food, and child-rearing. Those who tackled these issues most successfully, and learned to recognize who was deceitful and who was a trustworthy reciprocator, had an advantage over the rest. Even today, while most forms of logical reasoning need to be taught, people seem to instinctively grasp "deontic" relationships -- about what is forbidden, obligated, or permitted. Modern humans have inherited a propensity to learn social norms, a trait that has been detected in children as young as three years old.

An Indirect Evolutionary Approach -- Adaptation through Experience

In an indirect evolutionary model, players receive objective payoffs, but make decisions based on the transformation of these payoffs into intrinsic preferences. One who values reciprocity, fairness, and trust adds a subjective change parameter to their own or others' actions, depending on whether or not they are consistent with one's norms.

The sequential prisoners' dilemma is especially useful to discuss and test this approach. A "rational egoist" will choose not to trust and co-operate, since she expects that the other player will not trust or co-operate either. This leads to lower payoffs for both players, if both are rational egoists. It leads to higher payoffs for the rational egoist of the other chooses to co-operate. However, most contractual relationships have an element of trust involved. An indirect evolutionary approach explains how a mixture of norm-users and rational egoists emerges, when theory only assumes the existence of rational egoists.

Conditional cooperators playing a trustworthy strategy, on the other hand, will frequently receive a higher payoff, implying that in an evolutionary process with complete information, only they will survive. Where a player's type is common knowledge, rational egoists will not survive, since other players will not trust them. Full information, of course, is a strong assumption and probably not always true in the real world.

Next: A laboratory experiment testing indirect evolutionary theory