As a two-sided digital platform, ride-sourcing has disruptively penetrated the mobility market. Ride-sourcing companies provide door-to-door transport services by connecting passengers with independent service suppliers labelled as “driver-partners”. Once a passenger submits a ride request, the platform attempts to match the request with a nearby available driver. Drivers have the freedom to accept or decline ride requests. The consequences of this decision, which is made at the operation level, have remained largely unknown in the literature. Using agent-based simulation modelling on the realistic case study of the city of Amsterdam, the Netherlands, we study the impacts of drivers’ ride acceptance behaviour, estimated from unique empirical data, on the ride-sourcing system where the platform applies regular and surge pricing strategies, and riders may revoke their requests and reject the received offers. Furthermore, we delve into the implications of various supply–demand intensities, a centralised fleet (i.e., mandatory acceptance on each ride request) versus a decentralised fleet (i.e., ride acceptance decision by each driver), ride acceptance rates, and surge pricing settings. We find that the ride acceptance decision of ride-sourcing drivers has far-reaching consequences for system performance in terms of passengers’ waiting time, driver's revenue, operating costs, and profit, all of which are highly dependent on the ratio between demand and supply. As the system undergoes a transition from undersupplied (i.e., real-time demand locally exceeds available drivers) to balanced and then oversupplied state (i.e., more available drivers than real-time demand), ride acceptance decisions result in higher income inequality. A high acceptance rate among drivers may lead to more rides, but it does not necessarily increase their profit. Surge pricing is found to be asymmetrically in favour of all the parties despite adverse effects on the demand side due to higher trip fare. This study offers insights into both the aggregated and disaggregated levels of ride-sourcing system operations and outlines a series of transport policy and practice implications in cities that offer such ride-sourcing systems.