The following codes are implementation of the boundary-value method for computing the equilibrium bids of asymmetric first-price auctions I have presented, together with Gadi Fibich in a recent GEB paper [1]. We have demonstrated the robustness and stability of this method for auctions with any number of players, and for players with mixed types of distributions, including distributions with more than one crossing. Accuracy of the results is controlled by numerical parameters and can be set to be as low as computer accuracy, see remarks within the codes. Similarly, see remarks within the codes to modify the default player distributions.
When using the codes directly or when using other implementations of the fixed-point iterations method, below please cite the following article:
[1] G. Fibich and N. Gavish, Numerical simulations of asymmetric first-price auctions, GEB, 73, 479-495, 2011 (pdf)Supplementary material of [1] – sample Matlab codes for computing the equilibrium bids with two players:
Boundary-value method with the fixed-point iterations:
fixedPointIterationsCode.m
Boundary-value method with Newton’s iterations:
Newtons_iterations.m
Code for three players:
computeEquilibrium_threePlayers.m
Enhanced code for two players:
The following code is an enhanced version for computing the equilibrium bids in asymmetric first-price auctions with two players. In particular, it has better accuracy and also computes the revenue.
computeEquilibrium_twoPlayers_Enhanced