🏛️ 拍卖理论

# 二价拍卖模拟：为什么说真话是最优策略 import random class VickreyAuction: """Vickrey（二价密封）拍卖""" def __init__(self, bidders): self.bidders = bidders # {name: true_value} def run(self, bids): """执行拍卖，bids = {name: bid}""" sorted_bids = sorted(bids.items(), key=lambda x: x[1], reverse=True) winner = sorted_bids[0][0] price = sorted_bids[1][1] # 次高出价 return winner, price def analyze_strategy(self, name, true_value, bid): """分析不同出价策略的期望收益""" # 模拟其他竞拍者 others = {k: v for k, v in self.bidders.items() if k != name} other_values = list(others.values()) second_highest = sorted(other_values, reverse=True)[0] if other_values else 0 if bid > second_highest: # 赢了 payoff = true_value - second_highest else: # 输了 payoff = 0 return payoff # 实验：3个竞拍者，真实估值 [100, 80, 60] auction = VickreyAuction({'A': 100, 'B': 80, 'C': 60}) # 策略1：报真话 truthful = {'A': 100, 'B': 80, 'C': 60} winner, price = auction.run(truthful) print(f"真话策略: {winner}赢了，付{price}") # A赢了，付80。A的收益 = 100-80 = 20 # 策略2：A低报到70 lowball = {'A': 70, 'B': 80, 'C': 60} winner, price = auction.run(lowball) print(f"低报策略: {winner}赢了，付{price}") # B赢了！A失去了本可以赚20的机会 # 策略3：A高报到150 highball = {'A': 150, 'B': 80, 'C': 60} winner, price = auction.run(highball) print(f"高报策略: {winner}赢了，付{price}") # A赢了，付80。收益还是20——高报没有帮助！ # 结论：在Vickrey拍卖中，偏离真话不会带来额外收益 # 但可能带来损失（低报导致输掉有利的交易）