近年來，電玩遊戲從個人電腦轉往智能手機發展，遊戲生命週期顯著縮短。主要是因為遊戲開發門檻降低，許多新進競爭者進入，改變了手遊市場的特性。另一方面是因為智能手機與個人電腦的使用環境不同，玩家的遊戲習慣也不同。面對激烈的競爭，一些遊戲廠商為提升產品獲利能力，透過一連串的機制設計，使玩家陷入互相爭奪競爭優勢的迭代性多人囚徒困境。

囚徒困境往往被定義為兩個理性自利的參與者之間的賽局理論，但現實生活中的行為研究則需考量多人賽局的架構，以便瞭解真實社會的問題。過去有許多關於雙人囚徒困境賽局的研究論文發表，即使多數研究報告宣稱，多人賽局情境的模擬通常奠基於參與者間的二元互動，然而一個由Macy開發的隨機學習模型卻指出，在臨界狀態下，門檻效應可能導致參與者由背叛轉往合作模式。

本研究試圖透過代理人基模型（Agent-based model, ABM）來模擬由使用者定義的各種參數（收益曲線、參與者個性、鄰人範圍、迭代次數）對迭代性多人囚徒困境賽局的影響。呈現不限數量且具有不同個性的參與者在迭代性多人囚徒困境賽局中的多重互動行為，試圖找出使參與者由奈許均衡（Nash equilibrium）轉往合作的臨界點。該臨界點代表了遊戲內合作者人數與整體人數之最終比例，即合作者與背叛者之最終比例，同時也代表了遊戲的終局，因此達到臨界點所需的迭代次數可視為產品生命週期。

研究結果顯示，當背叛者收益曲線與合作者收益曲線之間的相差值越大時，臨界點越低並且產品生命週期越短；鄰人範圍越小，產品生命週期越長；參與者個性與初始分佈狀況對產品生命週期有明確的影響，並且會影響參與者的最終分布狀況。遊戲的產品生命週期與上述各項參數的設計有明確的關聯性，可透過上述參數的調整來達到延長產品生命週期的目的。此外，本研究可能讓我們進一步了解社會體系中刺激或抑制合作的因素，而這幾乎涵蓋所有社交行為的本質。

In recent years, the development of computer games have moved toward mobile devices, but the life cycle of a game is significantly decreasesing. Because of lowering the threshold for game development, many new entrants would join the competition and change the market with less cost. On the other hand, because of the different environment and characteristics of smartphone and personal computer, the player's gaming habits has also been changed. Faced with such fierce competition, some game designers try to adopt a series of mechanisms to improve product profitability, enable these players to compete with each other, and guide the players to an iterative multiplayer prisoner's dilemma.

The Prisoners’ Dilemma is usually viewed as a Game Theory and emphasize on the ratioanl interaction among players. However, investigations require a multi-person model of the game to understand what the problem that people have had. Much has writton about the two-agent iterated Prisoners’ Dilemma game. Some studies claim the simulation of multi-agent games are based on mutualinteractions among the agents. A stochastic learning model that Macy created has asserted that threshold effects would shift the relation ships of agents from a defective equilibrium to cooperation.

This study attempts to use Agent-based model to examine the effect of various user-based parameters (payoff curve, participant personality, neighbor rang, iteration numbers) in an iterative multiplayer prisoner's dilemma game. This tool is suitable for an unlimited number of participants with various personalities, and can be used to try to figure out the critical point of the participants' strategy transferred from Nash equilibrium to cooperation. The critical point represents the final ratio of cooperators in the game, and also represents the end of the product life, so the iteration number required to reach the critical point can be considered as the product life cycle.

When the gap between the traitor’s payoff curve and the cooperator’s payoff curve is greater, the critical point is lower, and the product life is shorter. In addition, when the neighbor range is smaller, the product life is longer; the participant personality and the initial distribution have significant effect on the product life, and it will significantly affect the final distribution of participants. The product life of a game has a clear relevance with the design of these parameters. A game designer would extend the product life by adjusting these parameters. In addition, this study asserts that social behaviors are the catalsts to the social system cooperation.

論文審定書…………………………………………………………………………... i
誌謝…………………………………………………………………………………... ii
摘要………………………………………………………………………………….... iii
Abstract……………………………………………………………………………..... v
目錄………………………………………………………………………………….... vii
表次………………………………………………………………………………….... viii
圖次………………………………………………………………………………….... viii
第一章 緒論………………………………………………………………………. 01
第一節 研究背景與動機……………………………………………………........ 01
第二節 研究目的與問題……………………………………………………........ 01
第三節 研究流程與論文結構………………………………………………........ 03
第二章 文獻探討…………………………………………………………………. 04
第一節 囚徒困境……………………………………………………………........ 04
第二節 奈許均衡……………………………………………………………........ 06
第三節 帕雷托最適…………………………………………………………........ 07
第四節 線上遊戲的社群結構………………………………………………........ 09
第五節 線上遊戲的參與者個性……………………………………………........ 15
第六節 代理人基模型………………………………………………………........ 20
第三章 研究設計…………………………………………………………………. 22
第一節 研究結構……………………………………………………………........ 22
第二節 研究模式……………………………………………………………........ 22
第三節 研究方法……………………………………………………………........ 24
第四章 實證分析…………………………………………………………………. 28
第一節 　收益函式…………………………………………………………….... 28
第二節 　鄰人範圍…………………………………………………………….... 33
第三節 　參與者個性………………………………………………………….... 33
第五章 結論與建議………………………………………………………………. 41
第一節 收益函式對遊戲產品生命週期之影響……………………………........ 41
第二節 鄰人範圍對遊戲產品生命週期之影響……………………………........ 42
第三節 參與者個性對遊戲產品生命週期之影響…………………………........ 42
第四節 後續研究建議………………………………………………………........ 43
參考文獻…………………………………………………………………………….... 44

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