The present paper tries to answer analytically how much the reference group influence can affect an actual market share of a particular brand or product. It is found that the increase of the size of a reference group and the probability of following the majority within the reference group may lead to the temporary modest prevalence of one brand. This result requires a relatively large size of a reference group and a high probability of following the majority within the reference group. If these conditions are not satisfied the effect on the market share is negligible.
We consider a system of heterogeneous agents playing the Minority Game on two markets. At each time step, each agent plays on one of the markets only. The agents can change the market according to some switching scheme. Various switching schemes are investigated: those that depend on the performance of the agents on each of the markets, and those that determine the actual market as a function of the number of games lost on the markets. We discuss the influence of the chosen switching scheme on the overall performance of the system of agents. In particular, we study both aggregate attendance (price returns) and volatilities for various schemes of the market choice.
We propose a dynamic three-strategy symmetric model of the Ultimatum Game with players using a sampling procedure. We allow an intermediate strategy, interpreted as a social norm, to evolve in time according to beliefs of players about an average offer. We show that a social norm converges to a self-consistent offer of about 15 % in the unique globally asymptotically stable equilibrium of our model.
We construct a symmetric version of the ultimatum mini game and analyze the stability of its equilibria in the replicator dynamics. We show that the mere symmetry does not lead to a unique social norm consistent with the observed experimental results. Moreover, the average offer in the population has to be lower than 50 % in order to have one of the equilibria consistent with the experimental data.
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