Quadratic Games∗

We study general quadratic games with multi-dimensional 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 possibly 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 closed form. We illustrate our framework by studying information aggregation in large asymmetric Cournot markets and by considering the effects of stochastic payoff interactions in beauty contest games. 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. ∗We thank Kostas Bimpikis, Johannes Hörner, Matt Jackson, David Myatt, Alessandro Pavan, Andy Skrzypacz, Xavier Vives, Bob Wilson, Anthony Lee Zhang, and seminar participants at Stanford, UIUC, the 22nd Coalition Theory Network Workshop, and the 2017 Workshop on Markets with Information Asymmetries at Collegio Carlo Alberto for helpful comments and suggestions. Lambert is grateful to Microsoft Research New York and the Cowles Foundation at Yale University for their hospitality and financial support. †Stanford Graduate School of Business; [email protected]. ‡Stanford Graduate School of Business; [email protected]. §Stanford Graduate School of Business and NBER; [email protected].