Sznajd Model And It's Applications In Product Market

In this article,we investigate the possibility of introducing the notion of tempreture to the one dimension Sznajd model.Firstly,we propose an extension of original model,and then,characterize different kinds of equilibriums into the extended system.It is shown that there exist a Hamiltonian compatible with the dynamics and its form resembles the one dimension ANNNI model.Also,we propose a definition of temperature-like quantity that measures the fluctuations in the system at equilibrium.The dynamic rules of two-dimension Sznajd model are briefly introduced.In order to consider temperature in the two-dimension model,we introduce a notion called the disagreement function.This function controls the dynamics—minimizing it locally which decide spin flipping.Minimization of disagreement function leads to four completely different final steady states.Then,we include a social temperature effect in the two-dimension Sznajd model,and give the analytical results by the mean-field approach.Moreover,we report on Monte Carlo simulations to test the mean-field results.Finally,we study the applications of Sznajd model in product market,mainly for two aspects of the applications:First,the advertising effect in duopoly markets;second,the price factor in the competition of two different products.We introduce extra field to Sznajd model and propose a modification in this model on the square lattice for the above applications.In model 1,a customer is selected randomly and then together with his three neighbors forms a panel which can influence eight nearest neighbors.If a panel consists of four customers sharing the same opinion then all eight neighbors will turn in the same direction.An advertising parameter is introduced,represents by h,h?[0,1].If product A is being advertised,a customer is not convinced by its neighbors he will be more responsive to advertising and with probability h will choose product A.So we can conclude that the stronger the advertising,i.e.the higher level h,the larger is the probability that product A will conquer the market.In model 2,we consider the reputation mechanism limiting the agents' persuasive power.We consider two different situations:case 1,the agents' reputation increase for each persuaded neighbor and case 2,the agents' reputation increase for each persuasion and decrease when a neighbor keeps his opinion.We use those two cases simulating and comparing with the actual data,and find that the results are in good agreement.