Evolutionary game theory

http://en.wikipedia.org/wiki/Evolutionary_game_theory

Evolutionary game theory (EGT) in layman's terms. Evolutionary game theory is the application of game theory to "interaction dependent strategy evolution in populations." EGT differs from classical game theory by focusing on how entities interact and change rather than how they interact to achieve equilibrium. Despite the fact that EGT is mathematically based, it has peaked the interest of the disciplines within the social sciences.

The originators of EGT, Smith and Price, forged a computer model called "The logic of animal conflict" as a way to present a theory for why animals have not adapted a "total war" strategy in their interactions with one another. The focus was how male animals maximize their ability to compete for resources in order to compete for dominance over territories and mates. Game theory was used to "test" different "evolutionary strategies" to see which one emerged with the highest payoff for the animal which explained why animals have only a "limited war" strategy which minimizes risk of serious injury.

Important in game theory is that the sets of models be tested over and over again. Only by repeated testing and replication can any insights be drawn. The models are useful in economics because they provides insight into how adjustments are made between two "equilibria." Game theory is also helpful to biologists because it helps to understand organisms in terms of evolution and strategy applications. Game theory is also used to detect "evolutionary stable" characteristics of animals which may mean that the strategies are heavily influenced by genetics, meaning that these strategies are biologically driven.

Successful applications of evolutionary game theory have given way to insights into human behavior because it has predicted behaviors in animals where "strong assumptions of rationality can not be made." In other words, because humans have autonomy in distinct thought and action, it is difficult to predict what a person will do. In spite of this, EGT has still shown some measure of predictability.

Replicator equations are the common methodology or formula used to study "evolutionary dynamics." Continuous replicator equations assume infinite populations and continuous time.

Helbing, Dirk & Johansson, Anders. "Evolutionary dynamics of populations with conflicting interactions: Classification and analytical treatment considering asymmetry and power." November, 2, 2009

Electronic address: http://arxiv.org/abs/0911.0359

Game theory is a theory of how principle entities interact with each other. Game theory is a mathematical system that encompasses mathematical analysis and methods of statistical physics coupled with applications that range from biology to economics. Game theory stems from physics and physicist have become increasingly interested it evolutionary game theory which takes into account the interaction between large numbers of entities that could range from bacteria to animals to human beings. Evolutionary game theory is the study of conditions in which coordination and cooperation of interacting entities occur.

This article is statistical and mathematical interpretation of the researchers study of such conditions and discusses these conditions as a way of understanding a) how cooperation breaks down, b) how subcultures coexist, c) how commonly shared behaviors evolve and d) the occurrence of conflict or polarization. The study conducted used "multi-population replicator equations" as a way of describing populations with "conflicting interactions and different powers." Though it is largely math based, the researchers claim that this article has social, economic, and biological relevance.

There are four different kinds of "games": The harmony game, the prisoner's dilemma, the stag-hunt game, and the snow drift game. If you apply the last three games to "social systems," they will describe social dilemma situations.

http://en.wikipedia.org/wiki/Stag_hunt

The stag hunt is a type of "game" in game theory. The game describes the conflict between safety cooperation and social cooperation. Rousseau described a situation where two individual go out to hunt. Each one has the choice of hunting either a stag or a rabbit. Each must choose what they will hunt without knowing what the other will choose. If the individual is going to hunt the stag, he will need help from the other. It is possible for him to hunt the rabbit by himself but the rabbit is worth less than the stag. This is deemed as an analogy of social cooperation. There exists a complex mathematical equation to illustrate the stag hunt, that is the "test" or "game" in game theory.

http://en.wikipedia.org/wiki/Prisoners_dilemma

The prisoner dilemma is another "game" in game theory. The scenario was developed in 1950 for RAND by Merrill Flood and Melvin Dresher. The "classic" form is as follows: Two suspects are apprehended by police. The police have insufficient evidence to convict either suspect. They separate the prisoners and offer them the same deal. If one testifies (defects) and the other remains silent (cooperates with their co-defendant) the "betrayer" goes free and the loyal co-defendant receives the full brunt of the consequence (10 year sentence). If both remain silent, cooperating with each other, they each receive the lighter sentence of 6 months. If each co-defendant defects (telling on the other) they each receive a 5 year sentence. Each has the choice to betray or remain silent and neither knows what the other will do. How will they act?

In the EGT formula it may be assumed that each only cares about minimizing their own time in jail. It may be assumed therefore, that the only concern of each individual in the game is to maximize individual payoff. In this case, the choice that each makes would be to defect even though, if they both remained silent, more reward for the individual would be gained by cooperation. The game is repeated over and over again giving each player the opportunity to punish the other for betrayal. It is only when the game is played for a random number of times that the equilibrium of cooperation can be achieved.

In this game, no matter what, the individual always receives a higher payoff if he betrays, which makes the betrayal a "dominance strategy." If they both act like one another and betray then the payoff is lower, the highest payoff being that they both stay silent.

In the game, the best "deterministic" strategy is "tit for tat." In other words, tit for tat shows up the most when the game is played a number of times consecutively and each person finds out what the other person did in the previous steps, whether there was betrayal or cooperation.

http://www.physorg.com/news111145481.html

Kummerli, Rolf, Colliard, Caroline, Fiechter, Nicolas, Ptipierre, Blaise, Flavien, and Keller, Laurent. "Human cooperation in social dilemmas:comparing the snowdrift game with the prisoner's dilemma." Proc. R. Soc. B, doi:10.1098/rspb.2007.0793.

The snowdrift game is a game played in game theory that, like the prisoner dilemma game, seeks to explain why human beings cooperate to the extent that they do. Other surrounding inquiry of this game includes questions such as "why does natural selection favor cooperation?"

Situationally, the snowdrift game involves 2 drivers who are trapped on opposite sides of a snowdrift. Each has the option to either stay in their respective cars or to shovel snow and clear a path. The maximum payoff for the individual is to let the other person do all of the shoveling work to clear the path. There is payoff in being exploited by doing all the shoveling while the other sits in the car because shoveling helps you out even if the other person sits. This is the likened to the prisoner dilemma (only opposite) where one prisoner betrays while he is simultaneously defended. The snowdrift game is also similar to the prisoner game in that if both betray (neither shovels) the payoff is not good for either.

In this game, as in the prisoner game, the tit-for-tat strategy emerged. Here however, there were better payoffs for participants who used the strategy than for those that did not. This study found that females were more likely to use this strategy which resulted in more cooperation among females than among males with higher payoffs for individual females. The take away message from this game: Humans adapt the degree of cooperation according to the social context and the behavior or gender of their partner in the games.

The snowdrift game may offer potential explanations for the high level of cooperation among humans and may have more "real life" implications than the prisoner game.