I saw a really interesting use of game theory in last week’s New Scientist about the origin of leadership and I wanted to share it here.
Regular readers will know that I’ve written about game theory many times in the past: I find game theory to be a very elegant way of modelling human behaviour with many applications in economics and the social sciences.
This piece of game theory concerns the question of why hierarchy exists in society. Why do we have leaders? Imagine the following scenario. Let us imagine two people, Persons A and B, who both need to hunt in order to eat. They can choose from one of two forests to hunt in, but they must travel together for their protection.
Person A is familiar with Forest 1 as it is where he typically hunts. Person B is familiar with Forest 2: that is where he usually hunts.
Which forest will they choose to go to? Obviously each person will prefer to go to the forest that they are most familiar with and to hunt there: by doing this they maximise their own success (the “number of kills” and the amount of food they can bring back). The following diagram shows the payoffs:
photo: hans s
Person A knows all the ins and outs of Forest 1, so he’s an efficient operator. In Forest 1, Person A gets 3 “kills” but Person B gets 1 “kill” as he doesn’t know it at all.
If they both decided to travel to Forest 2, the opposite is true. Person B gets 3 “kills” as he knows the forest well, Person A only gets 1.
If Person A and Person B couldn’t agree on which forest to travel to, neither of them would bring back any food, let alone reach a forest, because they can’t travel unless they travel together for protection.
In the scenario, what would happen? Well, Person A would choose to travel to Forest 1, the forest he knows the most well. If he chooses Forest 1, he has possible payoffs of either 3 kills or no kills. If he chose to travel to Forest 2, he has the possibility of no kills or 1 kill. Conversely as the payoffs are opposite for Person B, he will choose to travel to Forest 2, his favoured forest.
The end result is that both people will attempt to travel to their own favoured forest and neither of them would have any food to eat.
photo: Hamed Saber
For society, the best solution is that both people work together to agree where they want to hunt (this way society as a whole gains food from 4 “kills”). However, for this to happen, one person must take a lead but someone else must agree to follow: somebody must accept a smaller payoff and a smaller amount of food than which he would have had if he was leader.
This illustrates the importance of hierarchy and leadership in society: without somebody taking the lead to make a decision and other people following, society would not function. Society needs a leader and a follower.
Natural selection might be expected to select the leaders. After all, they are more successful at hunting and perform better. But natural selection at the group level would favour groups which worked well together (as the game theory diagram shows, groups which have a leader and follower are more successful as a whole).