Replicator Analysis of Unblocked Pyramid Game
K. Nocum, and E. Nocon (120-142)
Abstract
We introduce a sequential game called a pyramid game, which models a known business scheme that lets players choose between low-risk (LR) and high-risk (HR) investment in order to reach their highest possible payoffs where decisions are made by one player after another. The analysis of the unblocked game shows the existence of Nash equilibria. Treating it as a population game, we use the notion of replicator dynamics of evolutionary game theory (EGT) to observe the evolutionary dynamics of the game. Using the EGT approach, it was found out that an asymptotic stable Nash equilibrium occurs when the stopping point 𝑇 is even in which all players choose an HR move. This value refers to the number of periods or instances when players make investment decisions, which also signifies the end of the game. Results also suggest that in a pyramid game, an individual’s successful strategy is imitated by other players in the population.