### Stable matching on the complete graph

Probability Seminar

8th March 2024, 3:30 pm – 4:30 pm

Fry Building, 2.04

Consider a situation where a number of objects acting to maximize their

own satisfaction are to be matched. Each object ranks the other objects

and a matching is then said to be stable if there is no pair of objects

that would prefer to be matched to each other rather than their current

partners. We consider stable matching of the vertices in the complete

graph based on i.i.d. exponential edge costs. Our results concern the

total cost of the matching, the typical cost and rank of an edge in the

matching, and the sensitivity of the matching to small perturbations of

the underlying edge costs.

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