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arXiv · 2306.07663

Nash equilibria of the pay-as-bid auction with K-Lipschitz supply functions

Martina Vanelli·Giacomo Como·Fabio Fagnani
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Abstract

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.

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Martina Vanelli, Giacomo Como, Fabio Fagnani. 2023-06-13. Nash equilibria of the pay-as-bid auction with K-Lipschitz supply functions. https://arxiv.org/abs/2306.07663

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