Title: Repetitive Dilemma Games in Distribution Information Using Interplay of Droop Quota: Meek's Method in Impact of Maximum Compensation and Minimum Cost Routes in Information Role of Marginal Contribution in Two-Sided Matching Markets

Abstract: This paper is a preliminary report of the research plan and a digest of the results and discussions. On research note explores the complex dynamics of fake news dissemination and fact-checking costs within the framework of information markets and analyzes the equilibrium between supply and demand using the concepts of droop quotas, Meek's method, and marginal contributions. By adopting a two-sided matching market perspective, we delve into scenarios in which markets are stable under the influence of fake news perceived as truth and those in which credibility prevails. Through the application of iterated dilemma game theory, we investigate the strategic choices of news providers affected by the costs associated with spreading fake news and fact-checking efforts. We further examine the maximum reward problem and strategies to minimize the cost path for spreading fake news, and consider a nuanced understanding of market segmentation into "cheap" and "premium" segments based on the nature of the information being spread. Our analysis uses mathematical models and computational processes to identify stable equilibrium points that ensure market stability in the face of deceptive information practices and provide insight into effective strategies to enhance the informational health of the market. Through this comprehensive approach, this paper aims for a more truthful and reliable perspective from which to observe information markets.