Redistribution in online mechanisms

Following previous work on payment redistribution in static mechanisms, we develop the theory of redistribution in online mechanisms (e.g., [2, 10, 8]). In static mechanisms, redistribution is important as it increases social welfare in scenarios with no residual claimant. Many online scenarios also do not have a natural residual claimant, and redistribution there is equally important. In this work, we adopt a fundamental online mechanism design model where a single expiring item is allocated in each of T periods. Agents with unit demand are present in the market between their arrival and departure periods, which are private information along with the value an agent attributes to the item. For this model, we derive a number of properties characterizing redistribution in online mechanisms (including revenue monotonicity properties, and quantifying the effect an agent can have on the total revenue). We then design two redistribution functions. The first one generalizes the static redistribution proposed by Cavallo [2] making redistribution after the departure of the last agent. For this redistribution function we provide theoretical worst-case guarantees. The second function is truly “online” making redistribution to each agent on her departure. The performance of both functions is evaluated using numerical simulations.