Networked Online Human Experiments in Econophysics 2011 年 10 月 黄吉平 复旦大学物理系

致谢：软物质与交叉课题研究组 梁源 (10’PHD) 邱桐 (10’PHD) 孟现文 (11’PHD) 王玮 (09’PHD) 魏建榕 (08’PHD) 王禹 (09’PHD) 宋坤钰 (09’MSC) 郑文智 (10’MSC) 杨光 (11’PHD) 李晓辉 (11’PHD) 安克难 (11’MSC) 张惠澍 (11’MSC) 聂国熹 (11’MSC) 沈翔瀛 (11’MSC) 朱晨歌 (11’MSC)

王玮 （本组 06 级硕士生 /09 级博士生） 陈昱（东京大学） 黄吉平 Ref. 1 Ref. 1 “Herd Behavior in a Complex Adaptive System”, PNAS 108, (2011) 赵瓅 （本组 07 级硕士生） H. Ohashi ( 东京大学 ) 杨光 （本组 07 级本科生 /11 级博士生） H. E. Stanley ( 波士顿大学 )

王玮（本组 06 级硕士生 /09 级博士生）陈昱（东京大学） 黄吉平 Ref. 2: Ref. 2: “Heterogeneous Preferences, Decision-Making Capacity and Phase Transitions in a Complex Adaptive System”, PNAS 106, (2009)

导 言 复杂系统的研究方向可粗略分为三类：结构、功能、以及联系结构与 功能的动力学机制 (1) 复杂系统的结构 —— 复杂网络 (2) 复杂系统的功能 —— 涌现现象 (of 复杂网络 ) (3) 复杂系统的动力学机制 —— 涌现机制 (in 复杂网络 ) 经济物理的研究对象（经济市场）属于复杂系统 经济物理的研究方向可粗略分为三类：结构、功能、以及联系结构与 功能的动力学机制 (1) 经济市场的结构 —— 复杂网络 (2) 经济市场的功能 —— 涌现现象 (of 复杂网络 ) (3) 经济市场的动力学机制 —— 涌现机制 (in 复杂网络 )

我们关注的是 (1) 经济市场的结构 —— 复杂网络 (2) 经济市场的功能 —— 涌现现象 (of 复杂网络 ) (3) 经济市场的动力学机制 —— 涌现机制 (in 复杂网络 ) 经济物理中网络化真人在线实验 (Networked online human experiments in econophysics; NOHE in econophysics) ：是指利用通信技术和计算机技 术，把不同计算机互联起来，按照一定的实验规则通信，以达到所有 用户可以共同参与并完成经济物理实验的目的。

网络化真人在线 实验部分现场 网络化真人在线 实验 — 部分现场

网络化真人在线实验（可控）的作用 理论 : 建模（解析或计算机模拟）  唯象理论 + 基础理论 实验 : 可控实验  规则 应用（政策建议） + 验证理论

网络化真人在线实验 ( 可控 ) 的分类 J. H. Kagel & A. E. Roth, The Handbook of Experimental Economics, Princeton University Press, “Speaking to theorists” （ experimenters vs theorists ） 2.“Searching for facts/meaning” （ experimenters vs theorists ） 3.“Whispering in the ears of princes” （ experimenters vs policymakers ）

缺陷 : 缺陷 : 实验结果的可重复性或普适性？ —— 特定时间 + 特 定地点 + 特定人群 一种解决方案： 一种解决方案： (1) 重复做 N 次实验（ N  100, 1000, …… ）：？？？（此法 并不彻底） (2) 基于行为人的计算机模拟 : 给定具体条件，重复实验结 果（超越了 “ 特定时间 ” 、 “ 特定地点 ” 和 “ 特定人 群 ” 的限制） AND/OR (3) 基于解析理论：给出具体条件下的动力学过程，并验 证实验结果（揭示了其中的动力学过程 …… ） ………………………… 网络化真人在线实验的缺陷及解决方案

例一：有益跟风 (Ref. 1)

In order to survive, self-serving agents in various kinds of complex adaptive systems (CASs) must compete against others for sharing limited resources with biased or unbiased distribution by conducting strategic behaviors. This competition can globally result in the balance of resource allocation (say, Ref. 2). As a result, most of the agents and species can survive well. I. Introduction

One of the strategic behaviors is herding. The formation of herd can be found in the collective behaviors of many species, including human beings: stock markets, the world of fashion, violent mobs, etc. People used to pay heed to what others are doing, and imitate successful persons, or those of higher status, and follow the current trend unconsciously. ( 微观上看，既有理性，亦有非理性。 —— 在此 ，经济学家已有大量的实证和理论研究！ )

Herd behavior & financial crisis （宏观上看 —— ） It is generally believed that the formation of a herd in the market (a resource-allocation complex adaptive system) could ruin both the stability and the efficiency, e.g. the subprime mortgage crisis.

II. Experiments (see Ref. 1 & Ref. 2) M1M1 M2M2 N2N2 N1N1 If M1/N1>M2/N2, Room 1 wins.

Human players: students from Fudan University NnNn Game control program (GCP) Imitators: played by a robotic agent generated by a computer program NmNm β=Nm/Nnβ=Nm/Nn The desktop of GCP used in the experiment. (a) the control panel for the organizer, (b) the panel for the subjects (students).

The performance of the whole system efficiency stability predictabilityW 1, the winning rate of Room1

III(1). Model (agent-based computer simulations; see Ref. 1 & Ref. 2) situationchoice …… P-11 P1 For each situation: P(0)=L/P P(1)=(P-L)/P L is randomly chosen from 0~P Normal agent S strategies For each round, the normal agent chooses the best performed strategy. Room 1 Room 2

Group k imitator Best local player

The market behavior for an open system III (2). Computer Simulation Results

Extension: The market behavior for a closed system (a) /, (b) e, (c) σ 2 /N, and (d) w 1 as a function of M 1 /M 2, for a closed market system. Parameters: N = 150, P = 16, S = 4, k=5, and β=0, 2.0, 4.0, and 9.0. Simulations are run for 200 times, each over 400 time steps (first half for equilibration, the remaining half for statistics).

Extension ： Follow the majority in an open system

Extension ： Follow the majority in a closed system Parameters: N=150, P=16, S=4, =5, and β = 0, 2.0, 4.0, and 9.0. Others are the same as those information in the previous figure.

IV. Theoretical Analysis of an Open System (See Ref. 1) At time T, the preference of the best strategy held by normal agent i is L i and the choice is x i (x i =0 or 1). Imitator j chooses to follow agent μ, and his/her choice is y j =x μ. His/her preference is L j =L μ. The number of players in Room 1 is the correlation between the imitators who followed the same normal agent the correlation between normal agents and the imitators who followed them

at time T, the winning rate of Room 1 is α(T) for the strategy with the preference L, the expectation of its point at this time is The expectation of the cumulative point from t=1 to t=T is the market will never reach the optimal state the market will fluctuate around the optimal state

= /N

V. 小结 It is a common belief that the formation of a herd in a CAS will cause excess volatility, which can ruin the balance of resource allocation in the CAS. Here this belief is challenged with the results obtained from a modeled economic system based on a resource-allocation system. Based on this system, we designed and conducted a series of computer- aided human experiments including herd behavior. We also performed agent-based simulations and theoretical analyses, in order to confirm the experimental observations and reveal the underlying mechanism. We report that, as long as the ratio of the two resources for allocation is biased enough, the formation of a typically sized herd can help the system to reach the balanced state. This resource ratio also serves as the critical point for a class of phase transition identified herein, which can be used to discover the role change of herd behavior, from a ruinous one to a helpful one. This work is also of potential value to some fields, ranging from management and social science, to ecology and evolution, and to physics.

例二： “ 看不见的手 ” (Ref. 2)

“ 看不见的手 ”—— 亚当 · 斯密《国富论》（其然） Free markets appearing chaotic and unrestrained, but essentially “ordered”  Adam Smith assume the existence of an “invisible hand”  Used the “invisible hand” to successfully explain many many phenomena and thus suggested: Government does not need to do anything  The great depression causes corrections to the “invisible hand”: Specific conditions must exist for the “invisible hand” to play a role, And thus economists suggested an inverse proposal to ensure the “conditions”: Government needs to macroscopically manipulate  The latest financial crisis offers again challenges to the existing macroscopic manipulation?? … … I 、导言

“ 看不见的手 ”—— 当代经济学家的看法（其然） 【复旦大学经济系陆教授】： “ 在经济学里，所谓 “ 看不见的手 ” ，是说，当 信息充分（价格已经直接或间接地反应了应有的信息，这里的价格并不一 定是真正的价格，而是市场信号），市场竞争（没有垄断，没有人能够控 制市场），没有外部性（人的行为对他人的影响都已经反映在其自己面对 的价格上）这些条件都满足时，每个人都追求自利的动机，市场的价格机 制可以自动实现资源最优配置，而这些条件其实在现实中很难满足，于是 就出现所谓 “ 市场失灵 ” ，在有些条件下，可用政府干预的方式来弥补市场 的缺陷。 ”

“ 看不见的手 ” 的微观机制？（其所以然）

市场导向资源分配博弈 基于 “ 市场导向资源分配博弈 ”(MDRAG) 的资源分配实验 不均匀分布 共享 少数派获胜 独立决策 换为人民币结算 (¥) 规则 M 1 /N 1 > M 2 /N 2 或 M 1 /M 2 >N 1 /N 2  房间 “1” 获胜 M 1 /N 1 < M 2 /N 2 或 M 1 /M 2 <N 1 /N 2  房间 “2” 获胜 人物、房屋 的卡通造型 源于网络 II 、实验

实验一 已知： M 1, M 2, M 3, N 1, N 2, N 3 TimesGroupRoundsM1M1 M2M2 M3M3 1A(N=12) A(N=12) B(N=12) C(N=24) D(N=10) D(N=10) “ 看不见的手 ” 出现了 !

TimesGroupRoundsM1M1 M2M2 1D(N=10) E(N=10) F(N=11)1~ F(N=11)11~ C(N=24)1~ C(N=24)16~ 弛豫时间 未知： M 1, M 2, N 1, N 2 “ 看不见的手 ” 出现了 ! 实验二

TimesGroupRoundsM1M1 M2M2 1G(N=10)1~ G(N=10)6~ G(N=10)11~ G(N=10)16~ G(N=10)21~ G(N=10)26~ G(N=10)31~ G(N=10)36~ G(N=10)41~ 与实验二类似，但中途改变 M 1 /M 2 “ 看不见的手 ” 出现了 ! 实验三

MDRAG 的模拟结果与实验一致 : / =M 1 /M 2

小结 - “ 看不见的手 ” 起作用的充分条件是：资源竞争的参与者所 持有的策略必须具备足够的多样性，对分布于各处的资源的 偏好能随环境演化而自动调整；市场参与者的决策能力必须 与环境的复杂程度相匹配。 - 在模拟结果中存在多个相变过程，而正是在这些相变的临 界点附近 “ 看不见的手 ” 的调节功效可以被发挥到极致，此时 的资源分配市场呈现出配置有效、波动稳定、波动方向不可 预测的状态。

总 结 介绍了经济物理中的网络化在 线真人实验 给出两个例子： 有益跟风、看不见的手