An Analysis of Top Trading Cycles in Two-Sided Matching Markets
We study top trading cycles in a two-sided matching environment (Abdulkadiroglu and Sonmez (2003)) under the assumption that individuals’ preferences and objects’ priorities are drawn iid uniformly. The distributions of agents’ preferences and objects’ priorities remaining after a given round of TTC depend nontrivially on the exact history of the algorithm up to that round (and so need not be uniform iid ). Despite the nontrivial history-dependence of evolving economies, we show that the number of individuals/objects assigned at each round follows a simple Markov chain and we explicitly derive the transition probabilities
Che, Yeon-Koo and Tercieux, Olivier, "An Analysis of Top Trading Cycles in Two-Sided Matching Markets" (2015). Cowles Foundation Discussion Papers. 2451.