  In quasi-proportional auctions, the allocation is shared among bidders in
proportion to their weighted bids. The auctioneer selects a bid weight
function, and bidders know the weight function when they bid. In this note, we
analyze how weight functions that are exponential in the bid affect bidder
behavior. We show that exponential weight functions have a pure-strategy Nash
equilibrium, we characterize bids at an equilibrium, and we compare it to an
equilibrium for power weight functions.
