  We analyze the efficiency of markets with friction, particularly power
markets. We model the market as a dynamic system with $(d_t;\,t\geq 0)$ the
demand process and $(s_t;\,t\geq 0)$ the supply process. Using stochastic
differential equations to model the dynamics with friction, we investigate the
efficiency of the market under an integrated expected undiscounted cost
function solving the optimal control problem. Then, we extend the setup to a
game theoretic model where multiple suppliers and consumers interact
continuously by setting prices in a dynamic market with friction. We
investigate the equilibrium, and analyze the efficiency of the market under an
integrated expected social cost function. We provide an intriguing
efficiency-volatility no-free-lunch trade-off theorem.

Systems and Control;Optimization and Control