Application Of Game Theory In Biology

Game theory is the revolutionary achievement of the development of microeconomics. In 1994, the Nobel economic prize was gave to the three mathematicians and economists, J. F. Nash, J. C. Harsanyi and R.Selten who made outstanding contributes. As a science devoting to research "mutual behavior rational man", game theory is nearly applied to economics and each fields of other social sciences. Aumann gave incisive introductions to development results before middle period of 1980s and to history of the subject in 《Game theory》 of authoritative 《Webster dictionary》 .After magnum opus, 《Theory of Games and Economic Behavior》 of Von Neumann who founded game theory and O.Morgenstern who was a mathematician. Some monographs of textbook ,such as Fudenberg' & Tirole' book , adding encyclopedical 《Game theory and applied enchiridion》 edited by Aumann & Hart, make comprehensive systemic even said coverall disposal.Evolutionary game theory , just as its name implies, is a new branch field, which was formed for biology with respect to the idea of evolution intersected game theory. It first appeared biology. The most main conception in evolutionary game theory is evolutionary stable strategy (ESS), which is often called evolutive stable strategy in economics. In 1973, it was introduced by J.M.Smith and G. R. Price , and then was more developed by J.M.Smith in his work 《Evolution and the Theory of Games》. The expert R. Dawkins in the field of evolution thought "Evolutionary stability was one of the most important progresses since Darwin". In this paper, the age is introduced. Consider when the ages of animals differ, evolution how influence the behavior of an animal. The entire paper is divided into three primary parts.The first part is foreword. We mainly illustrate the development of evolutionary game theory, the research survey in home and abroad and the leading contents of research in the text.The second part is preliminary knowledge. We present some central examples and conceptions of game theory and evolutionary game theory.In the third part, we analyze a model of Hawk-Dove game in which an animal only knows its own age but not the others' ages. In this model, we conclude that at evolutionary stability there are two critical points of age x₁ and x₂(x₁2). The animal whose ages between x₁ and x₂ plays hawk;while the one aged below x₁ or above x₂ plays dove.Moreover, on the basis of animals only knowing its own age but not others', there will have lower probability of fighting than that of the animals don't know their ages.