  In this paper, we introduce and study a class of games called price-coupling
games that arise in many scenarios, especially in the electricity industry. In
a price-coupling game, there is a part of the objective function of a player
which has an identical form for all players and there is coupling in the cost
functions of players through a price which is determined uniformly for all
players by an independent entity called the \textit{price-determining player}
(e.g. independent system operator (ISO) in an electricity market). This price
appears in the objective function only in the part which is identical for all
players. We study the existence of equilibria in such games under two broad
categories, namely \textit{price-anticipative} and \textit{price-taking}
formulations. In the price-anticipative formulation, the players anticipate the
price and make their decisions while in the price-taking formulation, the
players make their decisions considering the price as a given parameter. We
model the price-anticipative case as a leader-follower formulation where the
players (leaders) conjecture the price (follower's decision) and make their
decision. The price-taking formulation is modelled as an $N+1$ player game with
the additional player as the price-determining player. The existence of an
equilibrium in such games are not easy mainly because of the coupled-constraint
structure of the game and the non-convexity of the action set. We give
conditions for the existence of equilibria in both formulations. We apply our
results to analyze the existence of an equilibrium in the generation expansion
planning problem using the above results.
