The Incomplete Strategy Minority Game Model Analysis And Simulations

Minority Game model is one of the most popular and simple models for the multiagents complex system.In this paper the Incomplete Minority Game(IMG) model is well defined and carefully studied as a new adaption of minority game model,with considerations of various failsafe action modes,and we try to give a analytical approach on the effect on system efficiency brought by incomplete strategy.In an IMG game agents know the location of incomplete/untrustful bits and switch to the other strategy or start failsafe action:random action(R0),action of random strategy(R 1),action of the original best strategy(R4).After large numbers of simulations,we find that limited incompleteness can improve the system efficiency distinctly.Using the failsafe mode of "Back-to-Best" will bring the biggest improvement to system efficiency. Along with the change of efficiency,the critical value of game systemα_c also decrease monotonously to zero.We also introduce the Irrational Agents Minority Game (IAMG) model,in which agents can't tell the exact untrustful bits in strategy but tend to abandon the predictions of strategy with a probability p_I.Compared with the IMG model,the IAMG model has similar but smaller effect,but the improvement of system efficiency is limited,and the critical value of p_I is smaller.Basing on the IMG model,in this paper we suggest the Incomplete Minority Mix-Game (IMMG) model,which is a mixed-game system contains agents using incomplete strategies and agents using standard strategies.There is a critical value of average incompleteness(?)_c,at which value the distribution of incompleteness has no effect on system efficiency.When average incompleteness is little than this value,the more even the distribution is,the higher the system efficiency is.When average incompleteness grows high than the critical value,concentration of incompleteness is helpful.In the same way,the Irrational Agent Mixed Minority Game IAMMG model is suggested, which is based on IAMG model.Similar results with IMMG model are found,and the junction point are of smaller values.The "Wealthy-Resign" payoff function is introduced into IMMG system to evaluate the effect of incompleteness by comparing the average profits of two groups of agents.After a series of simulations,it can be found that IMG agents can averagely earn higher profits than the average level if incompleteness rate is little.And the increase of incompleteness can decrease the difference of profit between IMG agents.Compar- ing between the failsafe modes,"back-to-best" has the best performance.When P_I is close to 1,or IMG group is not the minority group in game,IMG group will lost the campaign with SMG agents.At last,some prospects on the further development of incomplete minority game are purposed.More simulations should be done to understand the effect of randomness in minority game and complex system.