asymmetric_common_value_auctions

Code accompanying paper "Information Asymmetries in Common Value Auctions with Discrete Signals"

Description of files

Core functions

Core equilibrium computation and utility calculation

• equilibrium.m: the main algorithm for computing a representation of the equilibrium in an asymmetric common value auction, based on the recurrence relation and the two pass algorithm of the paper
• calculate_all_utilities.m: takes as input the representation of the equilibrium and calculates the expected utility of each of the two players conditional on any signal
  • calculate_utililty.m: calculates the expected utility of some player conditional on some signal
• expected_utilities.m: simply calls the equilibrium and the calculate utilities functions to return the expected utilities for some input signal and prior setting.
• single_general_instance.m: solves the equilibrium of a single instance and then plots the equilibrium CDFs of the two bidders
• plot_all_cdfs.m: plot the equilibrium cdfs associated with an equilibrium representation computed by the algorithm
  • plot_cdf.m: plot the cdf of some bidder conditional on some signal

Related to information acquisition

• utilities_of_all_outcomes.m: computes the equilibrium expected utilities for all possible outcomes of a selling process of an extra signal, i.e. of Y gets the signal, if Z gets the signal, if both get it and if none gets it.

Example calls of the core functions

Equilibrium calculation for single instances

• main.m: several examples of calling the core functions so as to plot the equilibrium bid strategies

Equilibrium utilities as a function of the prior

• binary_symmetric.m: both players have binary signals. Swipe over some parameter range and plot utilities as a function of the prior.
• binary_symmetric_single_instance.m: for the binary signal case for a single instance of the parameters plot the utilities as a function of the prior.
• many_value_signals.m: one player is completely informed, the other player gets an almost continuous signal

Information acquisition related examples

• compare_outcomes_for_all_priors.m: for fixed signals of the two bidders and for a fixed extra available signal, what are the equilibrium utilities of the players as a function of the prior probability of V=1?
• compare_outcomes.m: swipe over all possible signal qualities of two symmetric bidders, all signal qualities of an extra signal, and all priors of V=1, and check whether it is optimal to sell exclusively the signal exclusively to one bidder (i.e. selling exclusively generates higher sum of utilities than all other outcomes)