To exchange ideas of this project, we held several conferences and seminars, as well as hosting visiting scholars, during the project period (2012-2014):
4th World Congress on Social Simulation
We hosted the 4th World Congress on Social Simulation on September 4-7, 2012, providing 5 keynote speeches, 6 tutorials, 5 special sessions, 1 workshop, and 22 parallel sessions. This conference received 123 presented papers and 150 participants from 22 countries.
http://www.aiecon.org/conference/wcss2012/index.htm Herbert Simon Series
http://www.aiecon.org/herbertsimon/series%2024/Herbert%20Simon%2024 .htm
Prof. Richard J. Zeckhauser (1/20/2014-1/21/2014) Group and Individual Decision Making
http://www.aiecon.org/herbertsimon/series23/Herbert%20Simon23.htm Prof. Carl Chiarella (7/2/2012)
Time-Varying Beta: A Boundedly Rational Equilibrium Approach Prof. Tony Xuezhong He
Asset Pricing Under Keeping Up with the Joneses and Heterogeneous Beliefs
Prof. Carl Chiarella (7/4/2012)
A Homoclinic Route to Volatility: Dynamics of Asset Prices under Autoregressive Forecasting
Prof. Tony Xuezhong He
Heterogeneous Beliefs and Prediction Market Accuracy Workshop
Prof. Cheong Siew Ann
Asian Economic Observatory Networks: A Data Driven Approach to Economics
Date:1/15/2014
Prof. Bing-Hong Wang
Research on Human Dynamics and Social Complex Systems Date:12/4/2013
Visiting Scholars
Prof. Tong Zhang, Prof. Yu Wu, and Prof. Wei Huang Agent-Based Trust Game
Visiting period:1/14/2014-2/18/2014 Prof. Tong Zhang
Agent-Based Trust Game
Visiting period: 10/23/2012-12/25/2012 Prof. Hai-Zhen Yang
Factors of Market Volatility
Visiting period: 10/1/2012-10/31/2012
科技部補助專題研究計畫出席國際學術會議心得報告
日期：103 年 10 月 15 日
一、 參加會議經過
此會議由 the Society for Computational Economics (SCE)所主辦，本人與該學會多位歷 任主席皆有深厚之學術交誼，故若有經費，其年會本人皆會積極參與，和與會者及學界老友互相切 磋琢磨。此次本人共報告兩篇論文，第一篇” The Donor-Recipient Games: Agent-Based vs.
Equation-Based Modeling 乃與政大馬文忠、曾嘉瑤合作，第二篇論文“The formation of Risk-Sharing Group” 則是與西南財經大學張彤、吳昱兩位教授的合作報告。除參與各場次聽取演講及參與討論之 外，本人此次並代表 CEF 2015 之主辦單位向 SCE 主席及理事報告 CEF2015 在台舉辦各重要事項 之進度及辦理方向，並於大會中為 CEF2015 宣傳，鼓勵今年與會者明年亦繼續共襄盛舉。
除此之外，本人同時與 CEF 經常合作之會議公司 Simple Meetings 代表 Mary McCain 商談 有關繼續聘用他們協助 CEF2015 之契約問題，此事將等該公司提出具體的合約書後決定。
二、 與會心得
此次會議，本人將重點放在目前 agent-based macroeconomics 的發展上。誠如其中一位講者，引 述 Jean-Claude Trichet 在擔任歐洲中央銀行主席時的一次演講所說：「當金融危機發生後，現行的
計畫編號 MOST－101－2410－H－004－010 – MY2 計畫名稱
以 代 理 人 基 模 擬 及 真 人 實 驗 探 究 良 善 社 會 複 雜 性 之 五 元 素 出國人員
姓名 陳樹衡 服務機構
及職稱 國立政治大學經濟系教授 會議時間
2014 年 6 月 22 日 至
2013 年 6 月 24 日
會議地點
Oslo, Norway
會議名稱
(中文)
(英文) )The 20th International Conference of Computing in Economics and Finance (CEF 2014)
發表題目
(中文) (英文)
The Donor-Recipient Games: Agent-Based vs. Equation-Based Modeling The formation of Risk-Sharing Group
1
經濟及財務模型所具有的嚴重缺陷就暴露無遺、、、既無法預測危機的來臨，也無法說明危機的 產生、、、在面對危機時，令人感到我們被傳統的分析工具所遺棄、、、我們所學到的最重要的 一堂課是：只靠單一的工具、方法、或典範是危險的、、、那些在現有模型下假設均質化、效用 極大化的個人，無法捕捉到危機下的行為。而代理人基模型(agent-based modeling)，模型，就允許 個體間較複雜的互動。各種統體模型，必須更能整合金融系統所扮演的關鍵角色、、、而我也非 常歡迎其他學門的投入：物理學、工程學、心理學、生物學。讓這些學門的專家和經濟學家以及 銀行家一起合作，將是非常有價值的事。」
本人這期的研究計畫，是在研究影響良善社會形成的五個元素：社會偏好、社會信任、社會網 路、社會智慧、以及社會規範。此次的研究，將做為下期預定的代理人基總體模型的基礎之一，
代理人基模型，本身就具有跨領域的特性，因為它是一種由下而上（bottom-up）建構模型的概念，
利用電腦程式先建構異質性的個體及其所存在的空間，賦予個體不同的特質和行為法則，再經由 個體間的互動，由模擬產生動態的總體行為，總體行為是否會達到均衡，或是不斷的變動，則不 一定是模擬的觀察重點。在建構模型的過程中，自然就必須融入不同學門的研究：計算機科學、
心理、物理、社會學、甚至是地質學等。本人長期從事 agent-based modeling 的研究及推廣，從 90 年代只有極少數人的參與，到現在相當多的學門皆已建構出 agent-based models，並得到越來越多 政策決策者的注意，更激勵本人從事此方法的研究。
本次會議中有關代理人基總體模型的論文，偏重政策模擬，大部分利用 Eurace@Unibi 這個代理 人基總體模型加以調整來進行。它是 Herbert Dawid (德國 Bielefeld 大學)等人，改進 Eurace 代 理人基總體模型而成。Eurace 為歐盟 FP6 的計畫之一，結合歐洲多位代理人基重量級學者（除 Herbert Dawid 外，尚包括Domenico Delli Gatti, Mauro Gallegati 等人共同合作而成。
Eurace@Unibi 是一個封閉式的、有空間概念的經濟體，此模型中，含有勞動部門、投資及消費部 門、以及金融和信貸市場。其目的即是做為政策分析和總體經濟議題研究的平台，尤其是關係到 科技發展及傳播方面的政策模擬，譬如 Herbert Dawid 的團隊近年來，所從事的關於產業升值的 政策，包括提升勞動力的補助、協助企業投資技術方面的政策、針對特定區域性的政策、無針對 性的政策等，以及各種政策對所得分配的影響。
由本人所帶領的人工智慧經濟學研究中心，其在代理人基模擬的技術上，在全球亦屬知名，但 礙於人力和財力之不足，無法建構如 Eurace 或 Eurace@Unibi 之類仿歐盟經濟體之大型模型。直 至今年，始獲科技部補助經費，始可開始建構屬於台灣的代理人基總體模型。然而經費仍舊有限，
不能像歐盟般，每年提供數什名博士後研究之經費，始能完成 Eurace 及其新的版本。但本人仍將 竭盡所能，善用所有資源，來建構屬於台灣的代理人基總體模型，為台灣的經濟政策，提供多一 種模擬及分析的工具。
三、 發表論文全文或摘要 請見附檔
四、 建議 無
五、攜回資料名稱及內容
此次會議資料袋中，僅有議程、Norwegian Business School 簡介及 Oslo 簡介。會議議程請 見：http://comp-econ.org/CEF_2014/Schedule.htm
2
六、其他 無
3
Agent-Based Modeling of the Donor-Recipient Games
Wen-Jong Ma
Graduate Institute of Applied Physics National Chengchi University
Taipei, Taiwan 116 E-mail: [email protected] Chia-Yao Tseng
Graduate Institute of Applied Physics National Chengchi University
Taipei, Taiwan 116
E-mail: [email protected]
Shu-Heng Chen AI-ECON Research Center Department of Economics National Chengchi University
Taipei, Taiwan 116 E-mail: [email protected]
Abstract
In this paper, we study the donor-recipient game using agent-based modeling.
The donor-recipient game is a theoretical environment frequently used to study the influence of social norms on the emergent pro-social behavior, in particular, the preva-lence of the altruistic punishment or indirect reciprocity. The conventional approach to this problem is replicate dynamics, which is an equation-based approach. Agent-based modeling, as an alternative to the equation-Agent-based approach, provides us a great flexibility to incorporate various considerations of social behavior, information dissemination, learning, and location specificity.
Keyword: The Donor-Recipient Game, Agent-Based Models, Social Norm, Altruistic Punishment, Social Learning, Word of Mouth, Basin of Attraction
1 Motivation and Introduction
In this paper, we compare the system behavior driven by group interactions (replicator dynamics) with that driven by individual interactions (agent-based model). In a broader context, this study is a continuation of the recent interest in the comparison between the mean-filed model and agent-based model or the individual-based model (Vinkovic and Kirman, 2006; Aoki and Yoshikawa, 2012; Van Dyke Parunak, 2012; Burger, Haskovec, and Wolfram, 2013). We recast this comparison work into the familiar donor-recipient game (benevolence game) for the following two reasons.
First, the donor-recipient game has been used as a benchmark to understand the sig-nificance of social norms to pro-social behavior, such as cooperation and costly punish-ment (altruistic punishpunish-ment) (Ohtsuki and Iwasa, 2007; Ohtsuki, Iwasa, and Nowak, 2009; Yu, Chen and Li, 2011). However, the conclusions are mostly derived from the use of standard replicator dynamics. It is, therefore, interesting to examine its robustness
1
by explicitly addressing the limitations of the analytical tools employed. This comes to our second point of interest. The fundamental process behind the downward causation of norms to individual behaviors involves a highly complex process of individual inter-actions. The norm is not equivalent to the law; generally speaking, there is no formal central authority or legal institution to enforce its validity. Hence, the consequences of each doing of each individuals can be highly heterogeneous and stochastic, depending on their personal encounters in time and in space.
Naturally, one wonders how well the replicate dynamics can harness this underlying complex process. To do so, we extend the replicate-dynamics model of benevolence as studied by Yu, Chen and Li (2011) into its agent-based counterpart. This extension al-lows us to examine the sensitivity of a few simplifications made by the former model.
The specific important one concerning us in this paper is time. The replicator dynamics as a model of group dynamics puts a quite strong regularity on the processes in time, as if all agents share a same time table; the schedule of a sequence of events is homogenously applied to all individuals. In spirit, it is another tatonnement process, i.e., no bilateral or trilateral or multilateral transactions can be allowed without having market-clearing con-dition being satisfied first (Fisher, 1983). Alternatively, no transactions can be allowed un-der the disequilibrium status. The similar restriction happens in the replicator dynamic model of benevolence: no one can review and revise their strategies unless the reputation associated with the use of each strategy has come to its stationary state.
In reality, people go ahead doing what they prefer to do, feeling no obliged to waiting for others, begin the presence of equilibrium or the presence of stationary distribution.
This heterogeneous-in-time among agents can introduce a great amount of disturbances to the replicator dynamics, but that does not mean the inapplicability of the replicator dynamics with the presence of this additional complication. As we may know, the agent-based modeling of Walrasian process actually converges to the original Walrasian equi-librium, and hence becomes another route for the tatonnement process (Gintis, 2007).
Nevertheless, only after proper simulations are done, we will not know whether this generality can hold for the case of the benevolence game as well.
Given this motivation, the agent-based used in this paper has several features. First of all, we allow agents to learn and adapt with their own schedule; in other worlds, learning in this agent-based mode is asynchronous. Basically, what we do is to define an event and use the hitting time of this event to control agents learning schedule; in this way, the adaptation schedule is not only asynchronous but also stochastic. Second, through the introduced events, we can then also control the frequency of the adaptation of agents, from short, medium to long. Third, in addition to time and frequencies, we also manipulate the information received by agents at two different forms of the word of mouths. At a coarser level, agents are able to see the fitness of each strategy by observing how it contributes to accumulation of wealth of the “users”, but not the intensity of users’
experience with the strategy.1 At a finer level, agents are also able to observe the intensity and can weight the raw fitness by this intensity.
1These two forms of the word of mouths can be motivated by our daily experiences with the question-naires in the social medium. Some simply ask the interviewees their evaluations of service without getting additional background information, but some would. Reading the result from the first case, one can only get a rough feeling of how good the service is, but not about its reliability or general applicability.
2
Table 1: Payoff Matrix of the Donor-Recipient Game
Donor
Cooperate (C) Defect (D) Punishment (P) Recipient (b, -c) (0,0) (-β, -α)
2 The Agent-Based Model
2.1 Donor-Recipient Game
In our agent-based model, agents are randomly matched in pair and in time. Each point in time (step) two agents are randomly chosen out of the whole population as a pair to play the donor-recipient game. One of them plays the role of the donor, and the other one plays the role of recipient. These roles are also randomly determined. The donor could do of the following three possible actions: cooperation (C), defection (D), and punishment (P). The recipient can do nothing reciprocally. If the donor decide to “cooperate”, he will make a contribution to the recipient at his own cost of c, but it in turn will increase the wealth of the recipient by b. If the donor decides to “defect”, he will give nothing to the recipient, and recipient also gains nothing from his action. The donor can also make a punishment to the recipient again at his own cost α and that will cause a damage of β to the recipient’s wealth. Normally, we assume that b is greater than c, and β is greater than α. The consequence of each choice made by the donor can then be summarized by a payoff matrix shown in Table 1. The payoffs that agents receive in each run of the game will be constantly cumulatively attributed to agents’ wealth. Denote the wealth of agent i in time t by Wi(t).
In addition to the payoff, there is an additional consequence imposed on the donor, i.e., his social status as recognized by the society. In a simple setting, there are only two statuses available in the society, namely, a good man (G) or a bad man (B). As to which status being assigned, it is determined by the ruling social norm. Basically, the social norm will decide the donor’s status or reputation based what he did and to whom: did he do good thing for good man or bad thing for bad man, etc. In other words, the social norm is a mapping:
N : A×R→R, (1)
whereN denotes the ruling social norm, A is the action space for the donor,
whereN denotes the ruling social norm, A is the action space for the donor,