Efficient parking allocation as online bipartite matching with posted prices

We study online bipartite matching settings inspired by parking allocation problems, where rational agents arrive sequentially and select their most preferred parking slot. In contrast to standard online matching setting where edges incident to each arriving vertex are revealed upon its arrival, agents in our setting have private preferences over available slots. Our focus is on natural and simple pricing mechanisms, in the form of posted prices. On the one hand, the restriction to posted prices imposes new challenges relative to standard online matching. On the other hand, we employ specific structures on agents' preferences that are natural in many scenarios including parking. We construct optimal and approximate pricing mechanisms under various informational and structural assumptions, and provide approximation upper bounds under the same assumptions. In particular, one of our mechanisms guarantees a better approximation bound than the classical result of Karp et al. [10] for unweighted online matching, under a natural structural restriction.