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.

翻译：本文建立了一个由n个非对称企业组成的系统模型，这些企业在共同市场通过支付竞标拍卖销售同质产品。每个生产商选择供给函数作为其策略，该函数给出其愿意以最低单价p出售的数量S(p)。市场在总需求与总供给的交点处出清，企业按投标价格获得支付。我们研究了此类企业间竞争的博弈论模型，并聚焦于其均衡（供给函数均衡）。我们考虑的博弈是对两种经典模型的推广：企业既可设定固定产量（古诺模型），也可设定固定价格（伯特兰模型）。主要成果是证明了在K-Lipschitz供给函数空间中（纯策略）纳什均衡的存在性，并给出了其刻画。