Some bidding games converging to their unique pure equilibrium

TL;DR

This paper studies Bayesian bidding games, proving the structure of pure Nash equilibria, providing conditions for their uniqueness, and proposing a dynamic process to find extremal equilibria, relevant for markets with inelastic demand.

Contribution

It introduces a class of Bayesian bidding games with a proven equilibrium structure, conditions for uniqueness, and a convergence dynamic to extremal equilibria.

Findings

Pure Nash equilibria form a non-empty sublattice.

A sufficient condition for equilibrium uniqueness is identified.

A dynamic process converges to the extremal equilibria.

Abstract

We introduce a class of Bayesian bidding games for which we prove that the set of pure Nash equilibria is a (non-empty) sublattice and we give a sufficient condition for uniqueness that is often verified in the context of markets with inelastic demand. We propose a dynamic that converges to the extrema of the equilibrium set and derive a scheme to compute the extreme Nash equilibria.