喆学（190）：精读期刊论文《优化付费订阅的免费多人游戏》引言

摘要：This post will introduce the introduction of the intensive reading journal article "Optimizing Free Multiplayer Games with Paid Su

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“喆学（190）：精读期刊论文

《优化付费订阅的免费多人游戏》

引言”

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"Zhexue (190): Intensive reading of journal articles

“Optimizing free-to-play multiplayer games with premium subscription”

Introduction"

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本期推文将从思维导图、精读内容、知识补充三个方面介绍精读期刊论文《优化付费订阅的免费多人游戏》引言。

This post will introduce the introduction of the intensive reading journal article "Optimizing Free Multiplayer Games with Paid Subscriptions" from three aspects: mind map, intensive reading content, and knowledge supplement.

一、思维导图（Mind Maps）

二、精读内容（Intensive reading content）

(1)研究背景(Research Background)

近年来，全球电子游戏产业迅猛发展，2020年总收入高达1593亿美元，超越电影与音乐产业总和。其中，多人在线游戏如《英雄联盟》《堡垒之夜》等成为主要推动力。例如，《堡垒之夜》截至2019年注册账户达2.5亿，月活跃玩家最高达7830万；《英雄联盟》自2009年上线以来，月均游戏时长超10亿小时，成为史上最受欢迎的多人在线游戏之一。

In recent years, the global video game industry has developed rapidly, with total revenue reaching US$159.3 billion in 2020, surpassing the combined revenue of the film and music industries. Among them, massively multiplayer online games such as League of Legends and Fortnite have become the main driving force. For example, as of 2019, Fortnite had 250 million registered accounts and a peak of 78.3 million monthly active players; League of Legends, since its launch in 2009, has accumulated more than 1 billion hours of playtime per month, becoming one of the most popular massively multiplayer online games in history.

电子游戏商业模式不断演进，早期以零售制为主，玩家一次性付费购买完整游戏。随着开发成本上升和互联网普及，自2010年起，“游戏即服务”（GaaS）模式兴起，开发者通过持续更新内容实现长期盈利。随后发展为免费游玩（F2P）模式，核心游戏免费，靠广告或售卖虚拟物品盈利。多人在线游戏广泛采用F2P，并通过“赛季通行证”创新收费方式，玩家付费订阅即可获取限定内容。以《堡垒之夜》为例，其“战斗通行证”2019年创收18亿美元，成为行业新标杆。

The business model of video games has evolved continuously. Early models were primarily retail-based, with players paying a one-time fee to purchase the complete game. With rising development costs and widespread internet access, the "Game as a Service" (GaaS) model emerged starting in 2010, allowing developers to generate long-term profits through continuous content updates. This later evolved into the free-to-play (F2P) model, where the core game is free, and revenue is generated through advertising or the sale of virtual items. Multiplayer online games (MMORPGs) widely adopt F2P and have innovated their monetization methods with "season passes," where players pay to subscribe and access limited content. Fortnite's Battle Pass, for example, generated $1.8 billion in revenue in 2019, becoming a new industry benchmark.

尽管F2P游戏核心内容免费，玩家仍愿为虚拟物品付费。部分游戏售卖带微优势的道具，但《堡垒之夜》《英雄联盟》等主流作品只卖“皮肤”等纯外观道具，以保持公平。付费物品能直接提升表现或形象，更关键的是游戏内社交比较：拥有稀有外观者在互动中获得额外满足，非拥有者则因被比下去而失落；同理，性能道具也引发上下比较。这种“社会比较”机制被心理学广泛验证，并成为驱动玩家消费的核心力量。

Despite the core content of F2P games being free, players are still willing to pay for virtual items. Some games sell items that confer subtle advantages, but mainstream titles like Fortnite and League of Legends only sell purely cosmetic items like "skins" to maintain fairness. Paid items can directly enhance performance or image, but more importantly, they rely on in-game social comparison: those who possess rare cosmetic items gain additional satisfaction from interactions, while those who don't possess them feel lost due to being compared to others. Similarly, performance items also trigger comparisons between players. This "social comparison" mechanism has been widely validated in psychology and has become a core force driving player spending.

(2)研究内容(Research Content)

本文研究含付费订阅的免费多人游戏如何制定最优运营策略，以最大化全生命周期利润。游戏向所有玩家开放核心内容，仅对订阅用户定期发放虚拟物品；开发商通过调整订阅价格和物品更新节奏获利。为刻画玩家人数动态，作者将Bass扩散模型与演化博弈的复制者方程结合，让“向上比较”与“向下比较”效应同价格一起决定免费与付费玩家的均衡比例。该比例、全体玩家平均效用及开发商广告投入共同决定游戏是吸引新玩家还是流失老玩家，从而反作用于收益。

This paper studies how a free-to-play multiplayer game with a paid subscription model can formulate an optimal operational strategy to maximize profits throughout its entire lifecycle. The game opens its core content to all players, while periodically distributing virtual items only to subscribers; the developer profits by adjusting subscription prices and the pace of item updates. To characterize the dynamics of player numbers, the authors combine the Bass diffusion model with the replicator equation of evolutionary game theory, allowing the "upward comparison" and "downward comparison" effects, along with price, to determine the equilibrium ratio of free and paid players. This ratio, the average utility of all players, and the developer's advertising investment collectively determine whether the game attracts new players or loses existing ones, thus in turn affecting revenue.

研究发现，开发商在“增长”与“变现”间存在根本权衡：过早收费抑制扩散，只拉新又难盈利。借助最优控制理论，作者针对“向下比较”强于或弱于“向上比较”的两种场景，分别给出动态定价与广告策略。共同结论：初期应不惜亏损，猛投广告冲用户规模，暂缓付费订阅；待基数足够后再上线会员。若向下比较占主导，订阅价需随时间递减，以减轻免费玩家落差、留住人流；反之则维持恒价。这与“游戏越火越涨价”的直觉相反——早期高价反而应被用来制造稀缺，把变现节奏拖后，换取更快成长。

Research reveals a fundamental trade-off between "growth" and "monetization": charging too early inhibits expansion, while simply attracting new users makes profitability difficult. Using optimal control theory, the authors provide dynamic pricing and advertising strategies for two scenarios where "downward comparison" is stronger or weaker than "upward comparison." The common conclusion is: initially, developers should invest heavily in advertising to scale up the user base, even at a loss, while delaying paid subscriptions; a membership should be introduced only after a sufficient user base is established. If downward comparison dominates, the subscription price should decrease over time to mitigate the gap for free players and retain users; conversely, a constant price should be maintained. This contradicts the intuition that "the more popular the game, the higher the price"—early high prices should be used to create scarcity, delaying monetization for faster growth.

研究表明，开发商应主动强化社交比较效应以提升全生命周期盈利，但需同时推迟会员上线，承受更久、更大的前期亏损。具体操作上，可先采用随机匹配聚集玩家，待规模成型后再切换为“付费优先”匹配，把社交落差转化为付费动力；即便允许单买道具或部分订阅，主要结论依然稳健。此外，文章还讨论了开发商现金流紧张和玩家预算有限对策略的制约。上述发现为采用会员制的手游、端游提供了可操作的盈利路径：先养池子、再收网，社交杠杆是核心，时间换空间是关键。

Research indicates that developers should proactively enhance the social comparison effect to improve profitability throughout the entire product lifecycle, but this requires delaying the launch of memberships and enduring longer and larger upfront losses. In practice, random matching can be used to gather players initially, and then switched to "pay-first" matching once a certain scale is achieved, converting the social gap into a motivating force for spending. Even if individual item purchases or partial subscriptions are allowed, the main conclusions remain robust. Furthermore, the article discusses the constraints on the strategy imposed by developers' tight cash flow and players' limited budgets. These findings provide a workable profit path for mobile and PC games adopting a membership system: first cultivate the player base, then reap the rewards; social leverage is the core, and trading time for space is crucial.

三、知识补充（Knowledge supplement）

社交比较机制是指个体在缺乏客观标准或希望进行自我评价时，通过与他人进行比较来获得自我信息、确定自我价值和指导行为的心理过程。该概念最早由社会心理学家Festinger（1954）在其“社会比较理论（Social Comparison Theory）”中提出。他认为，人们具有一种基本动机，即评估自我意见和能力的准确性，而当缺乏客观参照时，个体会通过与他人比较来实现这一目标。

The social comparison mechanism refers to the psychological process by which individuals, when lacking objective standards or seeking self-evaluation, compare themselves with others to gain self-information, determine their self-worth, and guide their behavior. This concept was first proposed by social psychologist Festinger (1954) in his Social Comparison Theory. He posited that people have a fundamental motivation to assess the accuracy of their own opinions and abilities, and when lacking objective benchmarks, individuals achieve this goal by comparing themselves with others.

社交比较机制并非单一行为，而是一个包括动机、对象选择、比较过程和心理结果在内的动态系统。其主要构成包括：

The social comparison mechanism is not a single behavior, but rather a dynamic system encompassing motivation, object selection, comparison process, and psychological outcomes. Its main components include:

1.比较动机（Comparison Motives）

自我评价动机：通过比较来判断自身的能力、地位或表现。

Self-evaluation Motives: Judging one's own abilities, status, or performance through comparison.

自我提升动机：通过与比自己差的人比较（向下比较），获得积极情绪与自我肯定。

Self-improvement Motives: Comparing oneself with those who are less qualified (downward comparison) to achieve positive emotions and self-affirmation.

自我改进动机：通过与比自己优秀的人比较（向上比较），激发学习、模仿与进步行为。

Self-improvement Motives: Comparing oneself with those who are more qualified (upward comparison) to stimulate learning, imitation, and improvement.

2.比较对象（Comparison Targets）

个体通常选择相似性高的人作为比较对象（如同龄人、同行、同事），因为相似对象的比较结果被认为更具参考价值。

Individuals typically choose those with whom they are highly similar (e.g., peers, colleagues, and colleagues) as comparisons between similar individuals are considered more valuable.

3.比较方向（Comparison Direction）

向上比较：与能力或地位更高者比较，可能带来激励或挫败。

Upward comparison: Comparing with those with higher abilities or status can be motivating or discouraging.

向下比较：与不如自己的人比较，常用于维护自尊或缓解压力。

Downward comparison: Comparing with those who are less capable than oneself is often used to maintain self-esteem or relieve stress.

水平比较：与相似者比较，以维持自我概念的稳定性。

Horizontal comparison: Comparing with similar individuals helps maintain self-concept stability.

4.心理与行为结果（Outcomes）

社交比较可能引发一系列认知与情绪反应，如自尊变化、嫉妒、模仿、合作或竞争行为等。这些反应通过反馈调节个体的态度与行为决策

Social comparison can trigger a range of cognitive and emotional responses, such as changes in self-esteem, envy, imitation, and cooperative or competitive behavior. These responses, through feedback, regulate individuals' attitudes and behavioral decisions.

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翻译：谷歌翻译

参考资料：谷歌、Chat GPT

参考文献：Yunke Mai, Bin Hu. Optimizing free-to-play multiplayer games with premium subscription [J]. Management Science ,2023, 69(6): 3437-3456.