Game Theory reflects human nature

19:55, Nov 11 2012

Sadly, humans are incapable of keeping their promises and all agreements are subject to treachery. Here's why.

John Maynard Smith and George R Price in 1973 used a branch of science called Game Theory to explain the behaviour of living organisms. This was subsequently popularised by Richard Dawkins in his book The Selfish Gene.

The strategy of any organism is to survive and spread its genes into the gene pool. To deal with the competition for mating, a strategy might be "attack opponent; if he retaliates run away". Game theory treats the participants as robotic gene survival machines whose behaviour can be programmed into a computer. An example of how Game Theory can shed light on the behaviour of real organisms is that of the Hawk- Dove game.

The strategy of the Hawk is to fight hard and only retreat if injured. The strategy of the Dove is to threaten but never hurt anyone. If a Hawk fights a Dove, the Dove runs away and doesn't get hurt. If a Hawk fights a Hawk, they fight until one is seriously injured or killed. If a Dove meets a Dove they waste time by posturing until one decides to back down. In advance an individual cannot tell whether his opponent is a Hawk or a Dove and the participants retain no memory of previous encounters.

In Dawkins' account of the game, +50 points are assigned for a win, 0 points for a loss, -100 points for injury or death and -10 points for time wasting. The outcome of various interactions can be assessed. For example, in a population comprising only Doves, on average any individual Dove can expect to win half the encounters and lose half; Doves never get injured or die as a result of contests, but because they threaten and posture they waste time. The winning score for a Dove is +50-10=+40 and the losing score is 0-10= -10 giving an average of (40-10)/2= +15.

If a rogue Hawk invades the Dove population, it always wins, so it has an average score of +50. We can regard the points as equivalent to genes, in that a winner is a survivor, and gets to pass on his genes. A sole Hawk in a Dove population is a highly successful strategy.


If a Hawk meets a Hawk, the average score is a rather poor (+50-100)/2 = -50/2 = -25.

If a single Dove finds itself in a population of Hawks the score is 0, because he always loses.

A single Hawk in a population of Doves and vice versa are the extremes. Given a community of Doves and Hawks, there is a stable ratio of Dove to Hawk numbers. This occurs when the average score for Doves is exactly the same as for Hawks. Running the programme shows this ratio to be 5/12 Doves and 7/12 Hawks and the average score for any individual in this stable community is +6.

The point is that this score is much lower than if everyone would just agree at the outset to adopt the Dove strategy (+15 versus +6). Alas organisms (including humans) aren't clever enough to see this; what actually happens is that agreements are subject to abuse. An individual Dove starts to think that by becoming a Hawk he can increase his average score considerably. Why be content with only +15 when potentially +50 is on offer? Sounds good, but if other Doves become Hawks it won't be long before the entire community is Hawks and the average score is back to -25.

If at the start, all the participants agree to be Doves, the agreement (or conspiracy) is open to corruption because an individual can potentially gain more through treachery.

Colonies of organisms eventually form what is called an Evolutionary Stable System, which by definition is the ratio (for example the number of Doves to Hawks) that is the most resistant to treachery from within.

All agreements are subject to treachery and this is why, for example, getting the world's 196 nations to agree to limit greenhouse gas emissions as part of combating global warming is so difficult. In the long term a clean environment is in everyone's interest, the pay-off score is high. However, the temptation to break the agreement and avoid the cost of expensive pollution control equipment, may just be too great for some nations (the equivalent of turning from Dove to Hawk).

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