danjcalderone

The following is an exposition of some of the results in the following manuscript.
Calderone, D.J. , Chasnov, B.J., Burden, S.A. and Ratliff, L.J., 2023 Consistent Conjectural Variations Equilibria: Characterization & Stability for a Class of Continuous Games. IEEE Control Systems Letters. pdf (arxiv)

Problem Setup

In this setup, we consider a problem setup where we have multiple agents transversing an environment in the presence of congestion and the targets for each agent have to be assigned as well as the paths for each agent. The motivating example for this formulation is to model interactions of robots on large sorting floors such as at Amazon distribution centers.

Problem Setup

As machine learning and complex prediction techniques become more ubiquitous, game theory must adapt to include models that accurately model how agents predict their opponents behavior. Nash equilibria in their traditional form do not capture this prediction behavior. Stackleberg equilibria, where a leader player predicts a follower player's optimization problem and uses this to their advantage. Consistent conjectural variations equilibria (CCVE) extend Stackleberge equilibria to the case where two players both attempt to predict their opponent's actions and optimize accordingly. The existence of computation of CCVE for two player games center around solving coupled Riccati equations as presented in INSERT LINK.

(Left) Illustration of Nash equilibria condition. (Right) Illustration of Stackelberg equilibria condtion.
(Left) Converged CCVE condition. (Right) Animation of back and forth evolution of conjectures.
(Left) Unstable CCVE. (Right) Evolution of unstable CCVE towards stable CCVE.
(Left) Stable CCVE as the limit point of evolution from unstable CCVE. (Right) Animation of evolution from unstable to stable CCVE.

As machine learning and complex prediction techniques become more ubiquitous, game theory must adapt to include models that accurately model how agents predict their opponents behavior. Nash equilibria in their traditional form do not capture this prediction behavior. Stackleberg equilibria, where a leader player predicts a follower player's optimization problem and uses this to their advantage. Consistent conjectural variations equilibria (CCVE) extend Stackleberge equilibria to the case where two players both attempt to predict their opponent's actions and optimize accordingly. The existence of computation of CCVE for two player games center around solving coupled Riccati equations as presented in INSERT LINK.