This work delves into the transformative effects of algorithms and game theory on modern market definitions, particularly within the context of the internet and e-commerce. It explores how companies like Google, Amazon, and eBay have redefined market operations through vast computational capabilities. Key topics include the Adwords Problem, online advertising strategies, revenue maximization, and the theoretical foundations of market efficiency and stability. The shifts caused by digital platforms underscore the importance of robust models and algorithms in shaping competitive markets.
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Revolutionizing Market Models: Algorithms and Game Theory in Internet Economics
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Revolution in definition of markets • Massive computational power available for running these markets in a centralized or distributed manner
Revolution in definition of markets • Massive computational power available for running these markets in a centralized or distributed manner • Important to find good models and algorithms for these markets
Theory of Algorithms • Powerful tools and techniques developed over last 4 decades.
Theory of Algorithms • Powerful tools and techniques developed over last 4 decades. • Recent study of markets has contributed handsomely to this theory as well!
Adwords Market • Created by search engine companies • Google • Yahoo! • MSN • Multi-billion dollar market • Totally revolutionized advertising, especially by small companies.
The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine
The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine queries (online)
The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine Select one Ad Advertiser pays his bid queries (online)
The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine Select one Ad Advertiser pays his bid queries (online) Maximize total revenue Online competitive analysis - compare with best offline allocation
The Adwords Problem: N advertisers; • Daily Budgets B1, B2, …, BN • Each advertiser provides bids for keywords he is interested in. Search Engine Select one Ad Advertiser pays his bid queries (online) Maximize total revenue Example – Assign to highest bidder: only ½ the offline revenue
Algorithm Greedy Bidder 1 Bidder 2 Example: Bidder1 Bidder 2 Book Queries: 100 Books then 100 CDs CD B1 = B2 = $100 LOST Revenue 100$
Optimal Allocation Bidder 1 Bidder 2 Example: Bidder1 Bidder 2 Book Queries: 100 Books then 100 CDs CD B1 = B2 = $100 Revenue 199$
wine bread cheese Fisher’s Model, 1891 $ $$$$$$$$$ ¢ $$$$ milk • People want to maximize happiness – assume linear utilities. Find prices s.t. market clears
Fisher’s Model • n buyers, with specified money, m(i) for buyer i • k goods (unit amount of each good) • Linear utilities: is utility derived by i on obtaining one unit of j • Total utility of i,
Fisher’s Model • n buyers, with specified money, m(i) • k goods (each unit amount, w.l.o.g.) • Linear utilities: is utility derived by i on obtaining one unit of j • Total utility of i, • Find prices s.t. market clears, i.e., all goods sold, all money spent.
Arrow-Debreu Theorem, 1954 • Celebrated theorem in Mathematical Economics • Established existence of market equilibrium under very general conditions using a deep theorem from topology - Kakutani fixed point theorem.
