The replicator dynamics and reaction network model of an unblocked pyramid game

• Main Author: Nocum, Karen P.
• Format: text
• Language: English
• Published: Animo Repository 2020
• Subjects: Equilibrium; Games; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_doctoral/1396; https://animorepository.dlsu.edu.ph/context/etd_doctoral/article/2433/viewcontent/Nocum_Karen_11699574_The_replicator_dynamics_and_reaction_network_model_of_an_unblocked_pyramid_game_Partial.pdf
• Institution: De La Salle University

We introduce a sequential game called 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 af- ter another. The analysis of the unblocked game shows the existence of Nash equilibria. Treated as a population game, we use the notion of replicator dynamics of evolution- ary game theory (EGT) to observe the evolutionary dynamics of the game. We further expanded this analysis of the pyramid game by constructing its reaction network (RN) model in order to identify the best moves for all players given some conditions per- taining to the population composition, reaction rate constants, and rewards and costs parameters. 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. The RN analysis reveals that nonnegative profits for any type of player suggest that the HR decision is a ben- eficial move, but nonpositive profits force players to take the LR decision as a better move. Results also suggest that in a pyramid game, an individual’s successful strategy is imitated by other players in the population. Keywords: sequential games, pyramid game, unblocked game, reaction network, replicator dynamics, asymptotically stable Nash equilibrium