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IUT 77142 Degree Master of Science Title Coexistence of Different Strategies in Evolutionary Dynamics by Limited Resources on a Scale Free Graph Author Sara Sadat Veradi Esfahani Supervisor F Fazileh Assis Prof Department Physics Date September 11 2013 Language Persian Abstract Cooperation among creatures can guarantee their life and their survival According to this fact one can explain the formation of complex biological structures Gathering together the single cells can produce more complete and more resistant creatures Charles Darwin was among the first scientists who introduced a theory for evolution by means of natural selection His theory has three basic facts Number of off springs are always greater than the number of their parents the species population is constant and there are always small differences between inheritable characteristics of parents and children therefore it can be inferred that the surviving children are those who can better adapted to the environment This phenomenon is known as natural selection At this point understanding of cooperation formation among individuals of one particular species and then among different species will be very important as natural selection opposes it There are always differences advantages and weaknesses even among individuals of a same species so why stronger individuals help the weaker to survive Cooperation is still distinguished among species for years however accurate explanation for the process of cooperation needs more effort In 1972 Robert Trivers an evolutionary biologist and mathematician mentioned a simple model describing interaction of two independent entity which appeared to be helpful in understanding of this altruistic behavior Although it is beneficial for both entities to cooperate in the mentioned interaction both will eventually decide to defect at the end The mentioned interaction is actually a famous model in game theory introduced by two mathematician Merrill Flood and Melvin Dresher a basic model for studying interactions and cooperation in game theory After that a mathematician named Albert Tucker formulated it and gave it the name prisoner s dilemma All of the interactions of the same type are known as games There are a great variety of them all of them are studied in game theory Logic is the foundation of game theory however if game theory is used for describing evolution without considering logic we use the evolutionary game theory which is concluding the result of a game as a function of population of individuals entering the game as specific species There are a variety of methods for achieving cooperation in games One of these methods use a limited resource In this model a number will be given to each player interpreted as the player s resource This resource distributes among players as they interact or increases because of an environmental resource which benefits all of the players Whenever this resource reaches a specific threshold the owner of the resource add an offspring to the population and share the resource with the offspring Take into account this resource and death it has been verified that cooperation can survive A more complicated way of game is done on a graph that is having nodes of the graph as players In this case the only players who are connected through an edge can interact The theory studying this type of games is known as evolutionary graph theory In this research limited resource model is applied to a specific graph scale free graph in order to show the function of a graph in intensifying the final result of the game Keywords game theory prisoner s dilemma limited resource model scale free graph

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