## Evolutionary game theory

Game theory, in addition to its application to simple games, can be applied to the complex concept of evolution as well. A simple approach to understanding evolutionary game theory is the use of the hawk dove game. It can be modeled by the following playoff matrix:

 Hawk Dove Hawk ½(V – C) V Dove 0 V/2

V represents the food that each player gets, and C represents the loss of fitness due to injury when two hawks collide.

The ideal strategy depicted here would be that the entire population is dove, in order to take out the C term. However, when combined with the concept of evolutionary stability, which states that an equilibrium is only stable when no individual with another strategy can invade and disturb it, then hawk-hawk is the dominant strategy, despite its losses. Now with the new information on evolutionary stability, we can extend game theory to evolutionary theory by playing multiple games over time, from generation to generation. Replicator Dynamics, which are a set of equations for modeling game theory over time, also shows that over time, Cooperation (Dove) is unstable and will move towards Defection (Hawk), which is a stable equilibrium. However, the most interesting addition to evolutionary game theory comes from the addition of local interactions to the game. People that are close to each other (ex. Neighbors, friends, acquaintances) are connected, and the payoff matrix changes accordingly. For example, making an enemy out of a neighbor may lead to much lower payoffs in the long run due to constantly interacting with them, thus the strategy would change depending upon how connected a person is to another (strong vs. weak). The introduction of interactions is interesting because depending upon which values for the playoff matrix are picked, the strategy goes from Defection being the dominant strategy to there being a mix. If the values are picked correctly, cooperation can be dominant if the population is predominantly defector, and vice versa. There can even be an oscillation between Cooperation and Defection over time, which would make for very interesting evolutionary theory! There can be many more options and considerations added to model evolution over time, and it can only become more complex, as things like language and communication, race, and such factors are added.

References:

http://plato.stanford.edu/entries/game-evolutionary/

http://ibmathsresources.com/2013/04/30/game-theory-and-the-prisoners-dilemma/