Quadratic Games

41 Pages Posted: 22 Aug 2018 Last revised: 30 Jul 2021

See all articles by Nicolas S. Lambert

Nicolas S. Lambert

Stanford Graduate School of Business - Knight Management Center

Giorgio Martini

Stanford Graduate School of Business

Michael Ostrovsky

Stanford Graduate School of Business

Date Written: August 2018

Abstract

We study general quadratic games with multidimensional actions, stochastic payoff interactions, and rich information structures. We first consider games with arbitrary finite information structures. In such games, we show that there generically exists a unique equilibrium. We then extend the result to games with infinite information structures, under an additional assumption of linearity of certain conditional expectations. In that case, there generically exists a unique linear equilibrium. In both cases, the equilibria can be explicitly characterized in compact closed form. We illustrate our results by studying information aggregation in large asymmetric Cournot markets and the effects of stochastic payoff interactions in beauty contests. Our results apply to general games with linear best responses, and also allow us to characterize the effects of small perturbations in arbitrary Bayesian games with finite information structures and smooth payoffs.

Suggested Citation

Lambert, Nicolas S. and Martini, Giorgio and Ostrovsky, Michael, Quadratic Games (August 2018). Available at SSRN: https://ssrn.com/abstract=3236718

Nicolas S. Lambert (Contact Author)

Stanford Graduate School of Business - Knight Management Center ( email )

655 Knight Way
Stanford, CA 94305-7298
United States

Giorgio Martini

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Michael Ostrovsky

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305
United States
650-724-7280 (Phone)

HOME PAGE: http://faculty-gsb.stanford.edu/ostrovsky/

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