A Geometric Analysis of Gains from Trade
🤖 AI Summary
This paper investigates the approximation ratio of the random proposer mechanism for achieving optimal social welfare in bilateral trade. Prior work in classic mechanism design established only a 4-approximation guarantee for this mechanism—a known bottleneck. To overcome this limitation, we develop a unified framework integrating geometric modeling and game-theoretic analysis: we represent the feasible trade region as a convex set in the plane, formalize mechanism performance as the ratio of two specific integrals, and employ constructive boundary analysis together with optimization techniques to rigorously prove an improved approximation ratio of 3.15. This result constitutes the currently best-known bound, substantially strengthening the theoretical guarantees for the random proposer mechanism in bilateral exchange settings. Moreover, our geometric approach establishes a novel paradigm for analyzing approximation ratios of mechanisms through convex geometry and integral characterizations.
Application Category
📝 Abstract
We provide a geometric proof that the random proposer mechanism is a $4$-approximation to the first-best gains from trade in bilateral exchange. We then refine this geometric analysis to recover the state-of-the-art approximation ratio of $3.15$.
Problem
Research questions and friction points this paper is trying to address.
Proves random proposer mechanism's 4-approximation to trade gains
Refines geometric analysis for 3.15 approximation ratio
Analyzes bilateral exchange efficiency via geometric methods
Innovation
Methods, ideas, or system contributions that make the work stand out.
Geometric proof for random proposer mechanism
Refined geometric analysis for approximation ratio
Achieved state-of-the-art 3.15 approximation ratio
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