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This paper analytically examines the ride-pooling market equilibrium under a single or multiple ride-pooling service(s) considering different pooling sizes (number of riders sharing the same vehicle) and endogenous congestion effect of the ride-pooling fleet, and investigates the optimal operation decisions of the service operator(s) regarding the pricing, fleet size, and pooling size in different administrative and market regimes. We firstly examine the scenario with a single ride-pooling service platform given a specific vehicle type for either profit-maximization or social welfare-maximization (different administrative regimes), and then extend the model to the scenario with two differentiated ride-pooling services (given different vehicle types), where the platforms may either compete or cooperate (different market regimes). We have the following major findings. First, the pooling size should be optimized to accommodate the congestion effect and thus simultaneously increase operator's profit and social welfare. The optimal pooling size balances the marginal pickup time, crowding cost and waiting time cost, and the optimal value is different in different market regimes. Second, the ride-pooling service operator will internalize the congestion effect of providing more vehicles to serve customers, which yields a larger ratio of waiting customers to vacant vehicles (larger demand–supply ratio). Under two differentiated ride-pooling services, in addition to the direct congestion effect of providing more vehicles, its effect on the other operator's decision will also be internalized by the service operator in concern. Our results also suggest that the competition between platforms tends to reduce the waiting customers-vacant vehicles ratio (demand–supply ratio), while the cooperation between or integration of two operators might yield a large ratio. Third, when the endogenous congestion effect of fleet size is zero, the operator's profit at social optimum will always be negative when the matching function exhibits increasing return to scale and the marginal operation cost is less than the average operation cost, which means that the social welfare seeking operator has to be subsidized. When the endogenous congestion effect of the fleet size is positive, the ride-pooling service operator may earn a positive profit at social optimum under certain conditions. This study enhances the understanding in relation to users' reactions to differentiated ride-pooling services, how such services interact with congestion, and how such services can be optimized in different market regimes. • Ride-pooling market equilibrium with flexible pooling size in the presence of congestion effect. • Optimization of pooling size, fleet size, and fare of ride-pooling service. • Differentiated ride-pooling services under competition/cooperation/integration market regimes. • Complex interactions among customer traveling behaviors, service operation decisions and road traffic congestion. [ABSTRACT FROM AUTHOR]