On Matching and Thickness in Heterogeneous Dynamic Markets

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Formal model with two arrival types (hard/easy), stochastic pool dynamics and myopic matching shows myopic matching is asymptotically optimal — waiting immediately gives the right scaling. Analysis (coupling, one‑dimensional reductions) and simulations on ten years of three exchange programs confirm this. Thickening by batching matches harms performance; increasing participation helps or hurts depending on composition because waiting time scales as 1/p_H or 1/p_H^2 in two regimes. Chains (altruistic donors) strongly reduce required extra arrivals to achieve the same wait.

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1. 0:00Start
2. 27:09Myopic policy: bilateral matching Theorem I (informal): Among all Markovian matching policies, myopic matching achieves order optimal waiting time.
3. 37:24Insight: merging programs Initiatives to merge programs
4. 41:35Myopic policy: chain matching Segment Formation: Local search; break ties in favor of H pairs and random among each type