  In this paper, we study the problem of multiple stochastic agents interacting
in a dynamic game scenario with continuous state and action spaces. We define a
new notion of stochastic Nash equilibrium for boundedly rational agents, which
we call the Entropic Cost Equilibrium (ECE). We show that ECE is a natural
extension to multiple agents of Maximum Entropy optimality for single agents.
We solve both the "forward" and "inverse" problems for the multi-agent ECE
game. For the forward problem, we provide a Riccati algorithm to compute
closed-form ECE feedback policies for the agents, which are exact in the
Linear-Quadratic-Gaussian case. We give an iterative variant to find locally
ECE feedback policies for the nonlinear case. For the inverse problem, we
present an algorithm to infer the cost functions of the multiple interacting
agents given noisy, boundedly rational input and state trajectory examples from
agents acting in an ECE. The effectiveness of our algorithms is demonstrated in
a simulated multi-agent collision avoidance scenario, and with data from the
INTERACTION traffic dataset. In both cases, we show that, by taking into
account the agents' game theoretic interactions using our algorithm, a more
accurate model of agents' costs can be learned, compared with standard inverse
optimal control methods.
