[论文解读] Implementing Optimal Outcomes in Social Computing: A Game-Theoretic Approach

Arpita Ghosh, Patrick Hummel|arXiv (Cornell University)|Feb 15, 2012

Experimental Behavioral Economics Studies被引用 6

一句话总结

本文提出一种博弈论框架，用于评估‘最佳贡献’机制（即仅最高质量的回答可获得高额奖励）能否在社交计算系统中实现最优结果。研究发现，当贡献质量仅取决于专业知识时，可通过对称均衡实现最优结果；但当努力程度为内生选择时，必须引入不完美的排名机制，以激励努力并实现最优实施。

ABSTRACT

In many social computing applications such as online Q&A forums, the best contribution for each task receives some high reward, while all remaining contributions receive an identical, lower reward irrespective of their actual qualities. Suppose a mechanism designer (site owner) wishes to optimize an objective that is some function of the number and qualities of received contributions. When potential contributors are strategic agents, who decide whether to contribute or not to selfishly maximize their own utilities, is such a "best contribution" mechanism, M_B, adequate to implement an outcome that is optimal for the mechanism designer? We first show that in settings where a contribution's value is determined primarily by an agent's expertise, and agents only strategically choose whether to contribute or not, contests can implement optimal outcomes: for any reasonable objective, the rewards for the best and remaining contributions in M_B can always be chosen so that the outcome in the unique symmetric equilibrium of M_B maximizes the mechanism designer's utility. We also show how the mechanism designer can learn these optimal rewards when she does not know the parameters of the agents' utilities, as might be the case in practice. We next consider settings where a contribution's value depends on both the contributor's expertise as well as her effort, and agents endogenously choose how much effort to exert in addition to deciding whether to contribute. Here, we show that optimal outcomes can never be implemented by contests if the system can rank the qualities of contributions perfectly. However, if there is noise in the contributions' rankings, then the mechanism designer can again induce agents to follow strategies that maximize his utility. Thus imperfect rankings can actually help achieve implementability of optimal outcomes when effort is endogenous and influences quality.

研究动机与目标

• 确定在具有策略性参与者的社交计算系统中，最佳贡献机制（MB）能否实现最优结果。
• 分析贡献质量仅取决于贡献者专业知识的场景，与涉及内生努力决策的场景。
• 研究在不同奖励结构下，对称均衡与非对称均衡中是否可实现最优结果。
• 探讨机制设计者在未知效用参数时，如何学习最优奖励参数。
• 考察排名噪声在努力为内生选择时对实现最优结果的作用。

提出的方法

• 形式化一个博弈论模型，其中参与者根据其专业知识和效用函数决定是否参与贡献。
• 引入一种最佳贡献机制（MB），包含两个参数：pB（对最佳贡献的奖励）和pC（对其他所有贡献的奖励）。
• 使用阈值策略分析对称均衡，即参与者仅在其专业知识超过某一阈值时才参与。
• 推导出通过适当选择pB和pC可实现最优结果的条件。
• 引入噪声排名函数（si = qi + ǫi）以建模质量评估的不完美性，从而为努力提供边际激励。
• 通过比较静态分析与均衡分析表明，在噪声排名下有∂π/∂qi > 0，从而产生努力激励。

实验结果

研究问题

• RQ1 当贡献质量仅取决于专业知识时，最佳贡献机制MB是否能在均衡中实现最优结果？
• RQ2 当贡献者还需内生选择其努力程度时，最优结果能否实现？这又如何依赖于排名的精确度？
• RQ3 当努力为内生选择时，排名噪声在实现最优结果中起到何种作用？
• RQ4 当效用参数未知时，机制设计者如何学习最优奖励参数pB和pC？
• RQ5 是否存在导致次优结果的非对称均衡？这些情况能否避免？

主要发现

• 当贡献质量仅取决于专业知识时，通过适当选择pB和pC，可借助对称均衡实现最优结果。
• 即使不了解参与者的精确效用参数，机制设计者也可通过迭代调整学习最优奖励。
• 当努力为内生选择且排名完美时，任何竞赛机制均无法实现最优结果。
• 在噪声排名（si = qi + ǫi）下，若∂π/∂qi > 0，且努力的边际成本不过高，则可实现最优结果。
• 不完美排名可激励参与者投入更多努力，因为质量提升可增加获胜机会，即使排名不完美。
• 该结果与委托-代理理论中的发现类似：不完全监控可通过使努力在结果排名中更具影响，从而改善激励。