引入前景理论的股权拍卖异质投标者竞价策略演化均衡研究

Prospect Theory Embedded Evolutionary Stability Analysis on Bidding Strategies of Heterogeneous Bidders in Equity Auction

为了研究风险投资退出股权拍卖的价格形成机理,运用演化博弈分析投标者竞价策略的演化路径与均衡。考虑到心理因素对有限理性投标者的影响,将行为经济学的前景理论引入到演化博弈中。利用前景价值函数构建收益感知矩阵以取代由支付函数构成的收益矩阵,将参照依赖、认知差异、损失规避等心理因素融入到竞价策略的动态演化分析中,以刻画出更加贴近现实的有限理性投标者的认知与决策。针对不同市场供需情况分类探讨了异质投标者竞价策略演化均衡的一般规律。研究发现,竞价系统最终均衡与市场供需关系、系统初始状态以及投标者的相对支付有关。最后为政府及拍卖规则设计者提供了相关参考建议。

The auction, as an effective method to reveal value in asymmetric information environment, can be applied to the venture capital（VC） exit market to help venture capitalists disclose asymmetric information, and reveal the true value of withdrawing equity, thereby enhancing the efficiency of resources allocation. So how to study the price formation mechanism in the VC exit equity auction？ The evolutionary game theory provides us with a feasible and practical method. The bidding behavior of bidders in the VC exit equity auction market who submit their tenders in a space of bounded rationality and uncertainty influence each other in a direct or indirect way, and can be portrayed as a repeated game.Therefore, the evolutionary game can be used to explore and analyze the formation and evolution of bidding strategies in multi-round auction.Compared with the traditional game theory, the evolutionary game seems more realistic because it considers the limited rationality of participants. However, the payoff matrix in the evolutionary game is still built by objective revenue based on the traditional expected utility theory. Moreover, participants of limited rationality are easily to be affected by psychological factors during the decision-making process. After considering the impact of psychological factors on the limited rational participants in their decision-making process, we introduce the prospect theory into the game analysis which can be used to describe and portray the cognition and decision-making of limited rational participants. The original payoff matrix composed by payment function is replaced by the revenue perception matrix built by the prospect value function. In addition, the psychological factors, such as reference dependence, overestimation of low probability events, underestimation of high probability event, loss aversion, etc., are introduced into the evolutionary analysis, which can make the study closer to the decision-making behavior in reality. In order to find out the evolution rules of heterogeneous bidders＇ bidding strategies in the VC exit equity auction, the evolutionary path and equilibrium of heterogeneous bidders＇ strategies under three different cases are analyzed. They are as follows： first, the demand of each enterprise is less than supply; second, the demand of the big enterprise is greater than the supply, while the small one is not; third, the demand of each enterprise is greater than the supply. It is found that the ultimately equilibrium of the equity auction system is impacted by market supply and demand, the initial state of system, as well as the bidders＇ relative revenue perception. In order to lead the bidders to adopt the high-priced strategy in the auction, then improve the transaction efficiency of the market, the following suggestions are proposed for mechanism designers.（1） Adjust the auction rules,and set the reserve price as the minimum bid. The settings of reserve price can directly affect the expected revenue perception of bidders when they choose different bidding strategies, encourage bidders to select the high-priced strategy and avoid the low-priced strategy. Therefore, it is important to promote the VC exit market to achieve the evolutionary stable equilibrium where both sides of bidders report the high-priced strategy.（2） Hide the VC exit equity supply. It is found that compared with the condition that the demand of bidder is less than the supply, the bidder is more likely to report the high-priced strategy when his demand is greater than the supply. This phenomenon in financial markets can be explained by some psychological factors. When the bidder shows strong interest on equity and has relatively strong demand, he will have more interest in the auction, and then bid more and more positively and aggressively.（3） Formulate relevant policies or rules, which can encourage bidders to select the high-priced strategy, and give several dominant or recessive punitive measures to those reporting low-priced strategy. This will undoubtedly promote the bidders to effectively choose high-priced strategy. This study can provide relevant references for the government as well as auction rules designers.