Perturbation Analysis for Studying the Bidding Strategy in Asymmetric First Price Auctions

Bidders\´ asymmetries are widespread in auction markets. In such cases the mathematical model is given by a system of coupled nonlinear ordinary differential equations that cannot be solved explicitly for the equilibrium strategies, except for very simple models. As a result, analysis of asymmetric auctions is considerably more complex than for symmetric ones, and relatively little is known at present on asymmetric auctions. In situations like this, where it is difficult or even impossible to obtain exact solutions, much insight can be gained by employing perturbation analysis, whereby one calculates an explicit approximation to the solution. In this paper we adopt this approach and use perturbation analysis to calculate the equilibrium bid strategies in first price auctions. As we see, these explicit approximations are quite insightful, making the sacrifice of "exactness" worthwhile