A mathematical framework of interactions in the metaverse
Yinkai Liu · Cambridge journal for junior scientists. · 2025
Virtual worlds such as META play important social and economic roles.With the development of virtual reality technology, future societies could have foresee transactions, have a separate identity, or even become employed in the simulated world.This paper does not concern individual behavior on the metaverse, but rather interactions between civilizations, including those with extraterrestrial properties, spanning a multitude of dimensions and technological capabilities.We adopt the lens of game theory, a common tool in strategic decision making, and exponential equation modeling, to simulate realistic communication scenarios between civilizations.We will use exponential modeling to determine the equations of cost and benefit of different types of interaction.We will also outline a more complex framework including the radius of detection and use Markov chains to model the probabilistic and casual transitions between events.Finally, we will use MATLAB simulations and numeric methods to analyze hypothetical situations with respect to trade and interactions in multiple dimensions.