Multiplayer Game Model To Study The Phenomenon,

The phenomenon of Competition and Cooperation in the real world is important. And why and how the emergence of cooperation in groups formed by selfish individuals caused great interest among researchers. Game Theory is a useful tool for investigation in the problem. In this paper, we focused on some original game models, a modified version of classical Snowdrift Game. We studied the enhancement of cooperation in these models, their behavior on different networks and also the effect of"punishment".We studied two kinds of models, derived from the original snowdrift game and evolving under different evolutionary rules in detail. And cooperation behavior could be identified. We found that when agents make their decisions through"Imitation", all of them would become defectors in the end. But if they do this through"Self-questioning"schemes, then cooperation among agents would never be extinct. And we continued the research by putting the N-person Evolutionary Snowdrift Game(NESG) model on a dynamical Eguíluz-Zimmermann network, or on a static well-mixed network.We proposed a model named the Time-involved Multi-person Snowdrift Game (TMSG), in which agents would get additional rewards if more of them participated actively and hence finished with less time. Following replicator dynamics, we anylysed this new model and found descriptions of steady state and frequency of cooperation with a function of the parameters representing the cost-to-benefit ratio c /b , additional reward w /b , and size of sampling group N . Cooperation is enhanced in general for w≠0 and a stable state with all cooperative agents (AllC state) emerges for small groups N and small c /b . In contrast, such a harmonious AllC state does not exist in the original NESG(when w = 0 in this model). The condition for the existence of an AllC state is estimated to be ( N ? 1)c < w and good agreement is found when compared with data from computational simulation.We also studied the evolving behavior of this model on a dynamic network. And in this situation, the state of the system could be traced through both computater programs and analytic analysis without obvious difference in result.The role of punishment in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost ofαso as to punish a non-cooperative (D) opponent byβ. And in other situations a punisher acts the same like a cooperator in original Snowdrift Game. We used the technique of replicator dynamics to analyse the behavior of the model on a well-mixed network, on which agents following an"Imitation"way to evolve. And steady state and time-series of evolution of frequency of strategies were recorded and researched in detail. Depending on the initial fractions of the characters,α,β, and the cost-to-benefit ratio r in SG, the three-character system evolves either into a steady state consisting only of C and P characters or only of C and D characters in a well-mixed population. The former situation represents an enhancement in cooperation relative to SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the steady states and dynamics obtained by simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by tracking the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P-agents is greater than r /β.