Highlights • Develop a Nash game for two CAVs independently passing an unsignalised intersection. • Explore the two-CAV cooperative control mechanism for an unsignalised intersection. • Extend the game-theoretical analysis to a n-player case where n$>$3. • Tailor an efficient branch & bound algorithm to solve the developed game models. • Reveal some generalized insights from different control mechanisms.

Abstract We in this paper investigate navigation strategies of two cross-moving connected and autonomous vehicles (CAVs) at an unsignalised intersection. As highly intelligent and automated entities, CAVs could make decisions independently or behave in a cooperative manner. A Nash game with discrete decision strategy is formulated to characterize the non-cooperative behaviour and a cooperative game is formulated to model the cooperative control mechanism. Results show that (i) pure-strategy Nash equilibria (NEs) for the non-cooperative game always exist and NEs hold if and only if at least one CAV takes its dominant strategy; (ii) more than two pure-strategy NE solutions may exist, but at most two different payoffs could arrive for each player at pure-strategy NEs; (iii) the optimal solution to the cooperative game must be in the NE solution set. These interesting findings provide useful managerial insights to CAV operators and transport authorities, and also enable us to tailor a branch & bound (B&B) algorithm to efficiently solve the models. We also extend the proposed methodology to the n-player case ($n\ge 3$) and give some more generalized insights. Numerical experiments are demonstrated in the end to test the computational accuracy and efficiency of the B&B method and show that our models and algorithm can be readily incorporated into future real-time CAV decision system to help navigate through unsignalised intersections.