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anonymous /Main.java
Created Jul 25, 2010

import java.util.*;
public class Main {
static TreeSet<Double> bidHistory;
public static void main(final String[] args) {
final EnumMap<Participant, Double> cuts = new EnumMap<Participant, Double>(Participant.class);
final double paidToBill = 1;
cuts.put(Participant.BILL, 0.0);
optimizeCut(paidToBill, cuts, Participant.ME);
for (int x = 0; x < 15; x++) {
System.out.println(toString(cuts) + "\t\t" + toString(netProf(paidToBill, cuts)) + "\t"
+ ttl(netProf(paidToBill, cuts)));
optimizeCut(paidToBill, cuts, Participant.BILL);
optimizeCut(paidToBill, cuts, Participant.ME);
}
metaOptimizeCut(paidToBill, cuts, Participant.ME, Participant.BILL);
System.out.println("Evil Me: " + toString(cuts) + "\t" + toString(netProf(paidToBill, cuts)) + "\t"
+ ttl(netProf(paidToBill, cuts)));
metaOptimizeCut(paidToBill, cuts, Participant.BILL, Participant.ME);
System.out.println("Evil Bill: " + toString(cuts) + "\t" + toString(netProf(paidToBill, cuts)) + "\t"
+ ttl(netProf(paidToBill, cuts)));
}
static double bidWinProb(final double bid) {
if (bidHistory == null) {
final int sampleWins = 100000, bidders = 10;
final Random r = new Random();
bidHistory = new TreeSet<Double>();
for (int x = 0; x < sampleWins; x++) {
double maxBid = 0;
for (int y = 0; y < bidders; y++) {
final double b = 0.5 + r.nextGaussian() * 0.1;
if (b > maxBid) {
maxBid = b;
}
}
// System.out.println(maxBid);
bidHistory.add(maxBid);
}
}
return ((double) bidHistory.headSet(bid).size()) / bidHistory.size();
}
static void metaOptimizeCut(final double paidToBill, final EnumMap<Participant, Double> cuts,
final Participant participant, final Participant other) {
double bestNetCut = 0, bestNetProf = 0;
for (double x = 0; x < 1; x += 0.01) {
cuts.put(participant, x);
optimizeCut(paidToBill, cuts, other);
final double netProf = netProf(paidToBill, cuts).get(participant);
// System.out.println(x + "\t" + netProf);
if (netProf > bestNetProf) {
bestNetProf = netProf;
bestNetCut = x;
}
}
cuts.put(participant, bestNetCut);
optimizeCut(paidToBill, cuts, other);
}
static EnumMap<Participant, Double> netProf(final double paidToBill, final EnumMap<Participant, Double> cuts) {
final double adCut = cuts.get(Participant.BILL);
final double netCut = cuts.get(Participant.ME);
final double bid = paidToBill * (1 - adCut) * (1 - netCut);
final double winProb = bidWinProb(bid);
final EnumMap<Participant, Double> ret = new EnumMap<Participant, Double>(Participant.class);
ret.put(Participant.BILL, paidToBill * adCut * winProb);
ret.put(Participant.ME, paidToBill * (1 - adCut) * netCut * winProb);
return ret;
}
static void optimizeCut(final double paidToBill, final EnumMap<Participant, Double> cuts, final Participant participant) {
double bestCut = 0;
double bestProf = 0;
for (double x = 0.0; x < 1.0; x += 0.01) {
cuts.put(participant, x);
final double prof = netProf(paidToBill, cuts).get(participant);
// System.out.println(x + "\t" + prof);
if (prof > bestProf) {
bestProf = prof;
bestCut = x;
}
}
cuts.put(participant, bestCut);
}
static String toString(final EnumMap<Participant, Double> cuts) {
return String.format("Bill: %.3f\tMe: %.3f", cuts.get(Participant.BILL),
cuts.get(Participant.ME));
}
static String ttl(final EnumMap<Participant, Double> cuts) {
final double ttl = cuts.get(Participant.BILL) +
cuts.get(Participant.ME);
return String.format("Ttl: %.3f, each: %.3f", ttl, ttl / 2);
}
}
enum Participant {
BILL, ME;
}
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