Multi-exit neural networks represent a promising approach to enhancing model inference efficiency, yet like common neural networks, they suffer from significantly reduced robustness against adversarial attacks. While some defense methods have been raised to strengthen the adversarial robustness of multi-exit neural networks, we identify a long-neglected flaw in the evaluation of previous studies: simply using a fixed set of exits for attack may lead to an overestimation of their defense capacity. Based on this finding, our work explores the following three key aspects in the adversarial robustness of multi-exit neural networks: (1) we discover that a mismatch of the network exits used by the attacker and defender is responsible for the overestimated robustness of previous defense methods; (2) by finding the best strategy in a two-player zero-sum game, we propose AIMER as an improved evaluation scheme to measure the intrinsic robustness of multi-exit neural networks; (3) going further, we introduce NEED defense method under the evaluation of AIMER that can optimize the defender's strategy by finding a Nash equilibrium of the game. Experiments over 3 datasets, 7 architectures, 6 attacks and 4 baselines show that AIMER evaluates the robustness 13.52% lower than previous methods under AutoAttack, while the robust performance of NEED surpasses single-exit networks of the same backbones by 5.58% maximally.