  We model a system of n asymmetric firms selling a homogeneous good in a
common market through a pay-as-bid auction. Every producer chooses as its
strategy a supply function returning the quantity S(p) that it is willing to
sell at a minimum unit price p. The market clears at the price at which the
aggregate demand intersects the total supply and firms are paid the bid prices.
We study a game theoretic model of competition among such firms and focus on
its equilibria (Supply function equilibrium). The game we consider is a
generalization of both models where firms can either set a fixed quantity
(Cournot model) or set a fixed price (Bertrand model). Our main result is to
prove existence and provide a characterization of (pure strategy) Nash
equilibria in the space of K-Lipschitz supply functions.

Systems and Control;Multiagent Systems;Social and Information Networks;Systems and Control;Optimization and Control