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The properties of cooperative driving strategies for planning and controlling Connected and Automated Vehicles (CAVs) at intersections range from some that achieve highly efficient coordination performance to others whose implementation is computationally fast. This paper comprehensively compares the performance of four representative strategies in terms of travel time, energy consumption, computation time, and fairness under different conditions, including the geometric configuration of intersections, asymmetry in traffic arrival rates, and the relative magnitude of these rates. Our simulation-based study has led to the following conclusions: 1) the Monte Carlo Tree Search (MCTS)-based strategy achieves the best traffic efficiency, whereas the Dynamic Resequencing (DR)-based strategy is energy-optimal; both strategies perform well in all metrics of interest. If the computation budget is adequate, the MCTS strategy is recommended; otherwise, the DR strategy is preferable; 2) An asymmetric intersection has a noticeable impact on the strategies, whereas the influence of the arrival rates can be neglected. When the geometric shape is asymmetrical, the modified First-In-First-Out (FIFO) strategy significantly outperforms the FIFO strategy and works well when the traffic demand is moderate, but their performances are similar in other situations; and 3) Improving traffic efficiency sometimes comes at the cost of fairness, but the DR and MCTS strategies can be adjusted to realize a better trade-off between various performance metrics by appropriately designing their objective functions.