A healthy dose of reality for game-theoretic approaches to residential demand response

This paper addresses the assumptions underpinning many control schemes for residential demand response (RDR), with particular focus on those that adopt the framework of non - cooperative games. We propose four principal assumptions that we believe are necessary to give a realistic grounding to research on RDR, so that they might be more readily applied to the real problems faced by aggregators and households in a future energy network. These are that: (i) The energy use levels of households do not take continuous values, they take discrete and hybrid values; (ii) In addition to the system state variables, each household has a private state, representing the states of the goals it addresses in consuming electricity; (iii) Households have private preferences that are state-based, and therefore non-convex and combinatorial, and moreover, the monetary costs imposed by the system operator represents only part of their preferences for electrical energy use; and (iv) Household behaviour is strategic, both at the level of equilibrium analysis and algorithmic design. For each assumption we argue why it is necessary that a RDR scheme satisfy it, and illustrate the effects of violating our proposed assumption, with reference the existing literature on RDR schemes. We also provide several examples of techniques that satisfy each assumption, and illustrate our assumptions by developing a model that satisfies all four.