Thursday, January 8, 2009

Economics- Game theory applied to Evolutionary theory

I studied H3 Economics as an additional academic course at SMU during my JC2 year. The course focused on a specific topic known as game theory which was popularized by the film “A Beautiful Mind” that featured Russell Crowe as the eminent Nobel Laureate John Nash.

One interesting concept that I learnt from the course is the Nash Equilibrium. The Nash Equilibrium is defined as the stable state in which the players of the game have no tendency to change their strategies given their knowledge of the strategies of their opponents. This concept can be illustrated by the notable game model known as the Prisoner’s Dilemma which is usually used to explain concepts such as deterrence in political science.

Now, what I found interesting in game theory is its application to the theory of evolution. The variations of genetics of a given species can be likened to the different strategies of the players. In the case of the evolution game model, the players are the genes possessed by individual species. These genes play against one another in a given environment with the better gene, or to put it in game theoretical term as the better strategy, winning the war of attrition and is therefore deemed fitter to survive and hence propagate that better gene. The process of evolution involves the various genes of the species finding that Nash Equilibrium whereby the better gene is retained as it dominates over inferior genes.

However in game theory, it is not necessary that only one Nash Equilibrium exists (eg: Hawk-Dove game model). It is possible for players to use more than one strategy as there is no sole dominant strategy. My idea regarding this concept is that it explains why supposedly ‘inferior’ genes are allowed to be expressed in reality. This is because these ‘inferior’ genes might be fitter in a given environmental condition. This environmental condition may also be dependent on the demographics of the different strategies present in the population as shown in the Macho-wimp game model.

Take for example the genetic characteristic known as introversion that is deemed to be inferior to the characteristic of extraversion in society. The demographics of introverts to extroverts is 1 is to 3. Obviously, nature has a way of telling us that introversion is less adaptable to the human environment and hence its minority. But why do introverts continue to exist? I postulate 2 possible reasons

1. This is a transitional evolutionary stage and the ultimate evolutionary stable state (ESS) is one where introverts are eliminated and the extraversion gene dominates.

2. A complete extrovert population is not an evolutionary stable state. Instead, the evolutionary stable state is one where there is a mixture of introverts and extroverts

The second line of argument is deemed plausible in game theory by the Macho-Wimp game model. Let me illustrate how this is so using a game model. First of all, let’s assume that extroverts dominate over introverts all the time. This is quite an observable social reality whereby extroverts are usually placed in leadership positions over introverts and are better able to attain power and influence through their more dominating personality. So in my Extrovert-Introvert game model, let’s assign a value of 5 to the player that uses the extrovert and a value of 3 to the player who uses the introvert. In the game theory model, payoffs are used to denote the ‘utility’ that each player gets from using that particular strategy. Of course, a rational player seeks to maximize his utility.

As seen in the table above, when player 1 is an introvert and player 2 is an extrovert, the payoff of 3 goes to player 1 and the payoff of 5 goes to player 2, vice versa. The payoff on the left of the comma is to player 1 and the payoff on the right of the comma is to player 2.

However, when an extrovert meets an extrovert, neither of them does as well than if they should individually meet an introvert. Put this assumption into the context of reality, a pure extrovert meeting a pure extrovert rarely get any work done and are unproductive. Or perhaps the power-struggle between two extroverts is destructive to both of them. So we shall assign a value of 2 to each player when extrovert meets an extrovert

On the other hand, when an introvert meets an introvert, both of them proceed with their task individually and produce their own work. Both do fairly well on their own without encountering an extrovert. For that matter, let’s assign a value of 4 to each player when an introvert meets an introvert.

Now, let me introduce the concept of Nash Equilibria which I had learnt. A player should choose the best response given his knowledge of the other player’s strategy. For example, if you are player 1 and you know player 2 is an extrovert, what strategy should you play then to maximize your payoff? The answer is to play the introvert strategy which would give you a payoff of 3 as compared to 2 should you have used an extrovert strategy. And if you know that your opponent is an introvert, then in order to maximize your payoff, you should choose an extrovert strategy which would get you a 5 as compared to a 4 if you choose introvert. In an evolutionary game model, individuals do not have control over whether they choose to be an extrovert or an introvert. Such characteristics are all determined by genetics and it is the genetics which play the game.

By using the best-response method which I had listed above, we can derive the 2 Nash Equilibriums which I have shaded in orange. The Nash Equilibriums denote the Evolutionary Stable States(ESS). The model shows that the Evolutionary stable states are when both players are unlike; when one player is an ‘introvert’ and the other an ‘extrovert’.

Why are the shaded cells the evolutionary stable states? First of all, the process of evolution is a dynamic procedure over a period of time. In an evolutionary game model, a population exists consisting of extroverts and introverts. The players of the population pair up randomly and the game is repeated between 2 random pairs. If there are too many extroverts, an introvert can successfully invade the population as it would get the payoff of 3 compared to many other extroverts who are getting a payoff of 2 from the extrovert-extrovert game. Over time, the introvert population would increase due to it being a better strategy and hence propagating itself. Similarly, an extrovert can successfully invade a population of introvert as the extrovert is able to exploit the pure introvert population and get a payoff of 5 most of the time which is higher than the 4 that an introvert gets from an introvert-introvert game. The population would tend towards the Nash Equilibrium, also known as the evolutionary stable state, where there is no tendency for either the extrovert population or introvert population to grow.


This is a simple game model which explains why 2 or more strategies may exist in a game. By applying this concept to the evolutionary model, I have a better understanding of what the theory of evolution is about; that the model of ‘superior’ genes and mere ‘war of attrition’ is too simplistic a postulation about the game of evolution. I have come to appreciate diversity more through my understanding of game theory; that everyone has a place in this reality. I have also come to accept certain characteristics of my own

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