Prices of Anarchy, Information, and Cooperation in Differential Games

TL;DR

This paper extends the concept of the price of anarchy to differential games, introduces the price of information and cooperation, and analyzes these indices for linear quadratic differential games under various information structures.

Contribution

It introduces the price of information and cooperation in differential games and characterizes these indices for scalar linear quadratic cases.

Findings

Derived explicit bounds for indices in large populations.

Characterized PoA and PoI for linear quadratic differential games.

Compared performance under open-loop and closed-loop information structures.

Abstract

The price of anarchy (PoA) has been widely used in static games to quantify the loss of efficiency due to noncooperation. Here, we extend this concept to a general differential games framework. In addition, we introduce the price of information (PoI) to characterize comparative game performances under different information structures, as well as the price of cooperation to capture the extent of benefit or loss a player accrues as a result of altruistic behavior. We further characterize PoA and PoI for a class of scalar linear quadratic differential games under open-loop and closed-loop feedback information structures. We also obtain some explicit bounds on these indices in a large population regime.