Dynamics of religious group growth and survival
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We model and analyze the dynamics of religious group membership and size. A groups is distinguished by its strictness, which determines how much time group members are expected to spend contributing to the group. Individuals differ in their rate of return for time spent outside of their religious group. We construct a utility function that individuals attempt to maximize, then find a Nash Equilibrium for religious group participation with a heterogeneous population. We then model dynamics of group size by including birth, death, and switching of individuals between groups. Group switching depends on the strictness preferences of individuals and their probability of encountering members of other groups. We show that in the case of only two groups one with finite strictness and the other with zero there is a clear parameter combination that determines whether the non-zero strictness group can survive over time, which is more difficult at higher strictness levels. At the same time, we show that a higher than average birthrate can allow even the highest strictness groups to survive. We also study the dynamics of several groups, gaining insight into strategic choices of strictness values and displaying the rich behavior of the model. We then move to the simultaneous-move two-group game where groups can set up their strictnesses strategically to optimize the goals of the group. Affiliations are assumed to have three types and each type of group has its own group utility function. Analysis on the utility functions and Nash equilibria presents different behaviors of various types of groups. Finally, we numerically simulated the process of new groups entering the religious marketplace which can be viewed as a sequence of Stackelberg games. Simulation results show how the different types of religious groups distinguish themselves with regard to strictness.