On Applications of the Equilibrium Value Method

In 2010, Jain et al. [JJUW10] provided the first proof that QIP=PSPACE. Jain et al. used a constructive argument which applied the matrix multiplicative weight update method to a semidefinite programming problem formulation of a QMAM protocol to achieve this proof. The proof that QIP= PSPACE was alternately characterized by Xiaodi Wu [Wu10] that same year; Xiaodi Wu’s method, however, was simplified through the application of the equilibrium value method. In this survey, we evaluate the equilibrium value method and its flexibility as a proof technique. We consider Gutoski and Watrous’s proof that QRG=RG=EXP [GW07]. We look at Gutoski and Wu’s proof that QRG(2)=PSPACE [GW10, GW12], which uses the equilibrium value method. Finally, we reason about the feasibility of providing an alternate characterization that QRG=RG=EXP using the equilibrium value method.