Exponential Weight Functions for Quasi-Proportional Auctions

TL;DR

This paper analyzes how exponential weight functions in quasi-proportional auctions influence bidder strategies, establishing the existence of a pure-strategy Nash equilibrium and comparing it to power weight functions.

Contribution

It introduces exponential weight functions into quasi-proportional auctions and characterizes their equilibrium behavior, a novel analysis in auction theory.

Findings

Exponential weight functions admit a pure-strategy Nash equilibrium.

Equilibrium bids are characterized explicitly.

Comparison shows differences with power weight function equilibria.

Abstract

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.