Games and teams with shared constraints

Energy systems of the future are envisaged to encompass multiple interacting autonomous entities. The theory of games provides the foundations for the design and analysis of such systems. This paper reviews models and results that would be of use for such analysis. Classically, games have involved players whose strategies are coupled only through the dependence of utility functions on strategies of other players. However, in many practical settings in the energy domain, system-level limitations bind the choices players can make. In 1965, Rosen (Econometrica 33, 520-534 (doi: 10.2307/1911749)) pioneered the study of a class of games where there is a common constraint, called a shared constraint, that couples the strategies available to the players. We discuss how this seemingly benign extension has important ramifications, ranging from the very definition of an equilibrium concept, to other key issues such as existence, uniqueness and efficiency of equilibria. We show how the presence of a shared constraint naturally leads to notions of a price and forms the motivations for more recent models. Although most of the paper has the character of a survey, occasionally we also prove new results. This article is part of the themed issue 'Energy management: flexibility, risk and optimization'