社交网络中的竞争扩散：质量还是播种？
Competitive Diffusion in Social Networks: Quality or Seeding?
AI总结：
本文研究了社交网络中营销和产品消费的战略模型，分析了企业在有限预算下如何通过产品质量或初始播种优化产品扩散，并探讨了预算和网络结构对最优分配的影响。
摘要：
本文研究了社交网络中营销和产品消费的战略模型。我们考虑两个企业竞争以最大化其产品的消费量。企业有有限的预算，可用于投资产品质量或用于网络中的初始播种以促进产品扩散。在企业决策后，代理根据我的最佳反应动态选择消费，导致局部线性更新。我们表征了企业之间的博弈纳什均衡，并研究了预算和网络结构对最优分配的影响。我们证明，在均衡时，当企业预算接近时，企业会将更多预算投入质量，但随着预算差距增大，质量竞争效果减弱，企业会将更多预算用于播种。此外，我们证明，当企业预算相等时，如果平衡图中播种预算非零，则对于其他图也非零；如果星形图中播种预算为零，则对于其他图也为零。作为实际扩展，我们考虑产品有预设质量，只能轻微提升的情况。在某些时间点，企业学习到网络结构后，决定利用有限预算通过提升质量或播种新代理来扩大市场份额。我们证明在这种情况下，最优预算分配简化为阈值策略。有趣的是，我们推导出与原始问题相似的结果，其中预设质量模拟了原始设置中预算的作用。
英文摘要：
In this paper, we study a strategic model of marketing and product consumption in social networks. We consider two firms in a market competing to maximize the consumption of their products. Firms have a limited budget which can be either invested on the quality of the product or spent on initial seeding in the network in order to better facilitate spread of the product. After the decision of firms, agents choose their consumptions following a myopic best response dynamics which results in a local, linear update for their consumption decision. We characterize the unique Nash equilibrium of the game between firms and study the effect of the budgets as well as the network structure on the optimal allocation. We show that at the equilibrium, firms invest more budget on quality when their budgets are close to each other. However, as the gap between budgets widens, competition in qualities becomes less effective and firms spend more of their budget on seeding. We also show that given equal budget of firms, if seeding budget is nonzero for a balanced graph, it will also be nonzero for any other graph, and if seeding budget is zero for a star graph it will be zero for any other graph as well. As a practical extension, we then consider a case where products have some preset qualities that can be only improved marginally. At some point in time, firms learn about the network structure and decide to utilize a limited budget to mount their market share by either improving the quality or new seeding some agents to incline consumers towards their products. We show that the optimal budget allocation in this case simplifies to a threshold strategy. Interestingly, we derive similar results to that of the original problem, in which preset qualities simulate the role that budgets had in the original setup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
