There is a fierce competition between two-sided mobility platforms (e.g., Uber and Lyft) fueled by massive subsidies, yet the underlying dynamics and interactions between the competing plat-forms are largely unknown. These platforms rely on the cross-side network effects to grow, they need to attract agents from both sides to kick-off: travellers are needed for drivers and drivers are needed for travellers. We use our coevolutionary model featured by the S-shaped learning curves to simulate the day-to-day dynamics of the ride-sourcing market at the microscopic level. We run three scenarios to illustrate the possible equilibria in the market. Our results underline how the correlation inside the ride-sourcing nest of the agents choice set significantly affects the plat-forms' market shares. While late entry to the market decreases the chance of platform success and possibly results in "winner-takes-all", heavy subsidies can keep the new platform in competition giving rise to "market sharing" regime.

Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap in the literature by proposing a novel coevolutionary model, in which each individual selects an action from a binary set and has an opinion on which action they prefer. Actions and opinions coevolve on a two-layer network. For homogeneous parameters, undirected networks, and under reasonable assumptions on the asynchronous updating mechanics, we prove that the coevolutionary dynamics is an ordinal potential game, enabling analysis via potential game theory. Specifically, we establish global convergence to the Nash equilibria of the game, proving that actions converge in a finite number of time steps, while opinions converge asymptotically. Next, we provide sufficient conditions for the existence of, and convergence to, polarized equilibria, whereby the population splits into two communities, each selecting and supporting one of the actions. Finally, we use simulations to examine the social psychological phenomenon of pluralistic ignorance.

This paper explores the Coevolutionary Optional Prisoner's Dilemma (COPD) game, which is a simple model to coevolve game strategy and link weights of agents playing the Optional Prisoner's Dilemma game. We consider a population of agents placed in a lattice grid with boundary conditions. A number of Monte Carlo simulations are performed to investigate the impacts of the COPD game on the emergence of cooperation. Results show that the coevolutionary rules enable cooperators to survive and even dominate, with the presence of abstainers in the population playing a key role in the protection of cooperators against exploitation from defectors. We observe that in adverse conditions such as when the initial population of abstainers is too scarce/abundant, or when the temptation to defect is very high, cooperation has no chance of emerging. However, when the simple coevolutionary rules are applied, cooperators flourish.