We study competitive equilibria in the classic Shapley-Shubik assignment
model with indivisible goods and unit-demand buyers, with budget constraints:
buyers can specify a maximum price they are willing to pay for each item,
beyond which they cannot afford the item. This single discontinuity introduced
by the budget constraint fundamentally changes the properties of equilibria: in
the assignment model without budget constraints, a competitive equilibrium
always exists, and corresponds exactly to a stable matching. With budgets, a
competitive equilibrium need not always exist.
We study the design of truthful mechanisms that do not use payments for the
generalized assignment problem (GAP) and its variants. An instance of the GAP
consists of a bipartite graph with jobs on one side and machines on the other.
Machines have capacities and edges have values and sizes; the goal is to
construct a welfare maximizing feasible assignment. In our model of private
valuations, motivated by impossibility results, the value and sizes on all
job-machine pairs are public information; however, whether an edge exists or
not in the bipartite graph is a job's private information.
Display advertising has traditionally been sold via guaranteed contracts -- a
guaranteed contract is a deal between a publisher and an advertiser to allocate
a certain number of impressions over a certain period, for a pre-specified
price per impression. However, as spot markets for display ads, such as the
RightMedia Exchange, have grown in prominence, the selection of advertisements
to show on a given page is increasingly being chosen based on price, using an
auction. As the number of participants in the exchange grows, the price of an
impressions becomes a signal of its value.