A Network Analysis of Skill Game Dynamics
Casino games can be classified in two main categories, i.e. skill games and gambling. Notably, the former refers to games whose outcome is affected by the strategies of players, the latter to those games whose outcome is completely random. For instance, lotteries are easily recognized as pure gambling, while some variants of Poker (e.g. Texas Hold'em) are usually considered as skill games. In both cases, the theory of probability constitutes the mathematical framework for studying their dynamics, despite their classification. Here, it is worth to consider that when games entail the competition between many players, the structure of interactions can acquire a relevant role. For instance, some games as Bingo are not characterized by this kind of interactions, while other games as Poker, show a network structure, i.e. players interact each other and have the opportunity to share or exchange information. In this paper, we analyze the dynamics of a population composed of two species, i.e. strong and weak agents. The former represents expert players, while the latter beginners, i.e. non expert ones. Here, pair wise interactions are based on a very simple game, whose outcome is affected by the nature of the involved agents. In doing so, expert agents have a higher probability to succeed when playing with weak agents, while the success probability is equal when two agents of the same kind face each other. Numerical simulations are performed considering a population arranged in different topologies like regular graphs and in scale free networks. This choice allows to model dynamics that we might observe on online game platforms. Further aspects as the adaptability of agents are taken into account, e.g. the possibility to improve (i.e. to becomean expert) Results show that complex topologies represent a strong opportunity for experts and a risk for both kinds of agents.