A game-theoretic price determination algorithm for utility companies serving a community in smart grid

Distributed power network is the major trend of future smart grid, which contains multiple non-cooperative utility companies who have incentives to maximize their own profits. The energy price competition forms an n-person game among utility companies where one's price strategy will affect the payoffs of others. More interestingly, the use of dynamic energy pricing schemes incentivizes homeowners to consume electricity more prudently in order to minimize their electric bill. In this paper, two models of price determination are introduced for utility companies under different assumptions. In the first model, a Nash equilibrium solution is presented and the uniqueness of Nash equilibrium point is proved. The second model accounts for more sophisticated factors such as the cost of energy generation and the homeowner's reaction to the change of energy usage as a factor of energy price. Although it is no longer possible to prove the uniqueness of Nash equilibrium for the second model, we present a practical solution in which no utility company can increase its expected profit by adjusting the price function. Experimental results show the effectiveness of our two models both in reliability of solution and in runtime.