The Price of Cooperation in Differential Games

Philipp Hungerländer^*

The idea of quantifying the gap between the social optimum and game equilibria led to several research results in the recent past. The price of anarchy quantifies the loss of efficiency due to non-cooperation. The price of information captures the different outcomes of games under different information structures and the price of cooperation measures the benefit or loss of a player due to altruistic behavior. In this talk we characterize the price of cooperation for a class of scalar linear quadratic differential games under open-loop information structures. We obtain several explicit (tight) bounds on this index, indicating the conditions under which cooperation does pay off. Finally we compute price of cooperation for several specific models from communication networks and economics.

Mathematics Subject Classification: 91A25

Keywords: Differential games; Linear-quadratic games; Nash equilibria; Efficiency; Cooperation

Minisymposion: Computational Optimization Methods in Statistics, Econometrics and Finance