Do road users play Nash Equilibrium? A comparison between Nash and Logistic stochastic Equilibriums for multiagent modeling of road user interactions in shared spaces

Analyzing and modeling multiagent transportation systems such as cyclist-pedestrian interactions and their evasive-action mechanisms in shared spaces are important for operation and safety evaluations. However, there are limited studies that (1) modeled the multiagent nature of road user interactions and their concurrent sequential decision processes, and (2) investigated the ability of different equilibrium behavioral theories in predicting road user operational-level decisions and evasive-action mechanisms. This study proposes two novel multiagent approaches based on different equilibrium theories for modeling road user interactions: (1) the Multiagent Generative Adversarial Imitation Learning (MAGAIL), which utilizes Nash-Equilibrium (NE) theory that assumes fully rational and optimal mad user behavior, and (2) the Multiagent Adversarial Inverse Reinforcement Learning (MAAIRL), which utilizes Logistic-Stochastic-Best-Response-Equilibrium (LSBRE) theory that handles bounded rationality (sub-optimal) behavior. Unlike many of the traditional game-theoretic modeling approaches, which consider single time-step payoff modeling, the proposed approaches depend on Markov-Game that accounts for the stochastic nature of road user interactions and their sequential decision processes. The models recover road user multiagent reward functions and estimate their strategies using Multiagent Deep Reinforcement Learning. Using trajectories from three shared spaces in the USA and Canada, the study compared the proposed approaches' results and determined a behavior-based consistent paradigm to model equilibrium in multiagent transportation systems. The results show that LSBRE-based model predicted road user trajectories and their evasive action mechanisms with higher accuracy compared to the NE-based model.