Ex-Post Equilibrium and VCG Mechanisms

TL;DR

This paper explores how restricting attention to certain subsets of alternatives can enable ex-post equilibrium in large, incomplete information social choice settings, making VCG mechanisms more feasible.

Contribution

It characterizes the subsets that induce ex-post equilibrium and links their existence to the presence of a type-independent optimal social alternative for each player.

Findings

Identifies conditions for subsets to induce ex-post equilibrium.

Shows welfare implications of restricting attention to subsets.

Extends previous work on combinatorial auctions to broader social choice settings.

Abstract

Consider an abstract social choice setting with incomplete information, where the number of alternatives is large. Albeit natural, implementing VCG mechanisms may not be feasible due to the prohibitive communication constraints. However, if players restrict attention to a subset of the alternatives, feasibility may be recovered. This paper characterizes the class of subsets which induce an ex-post equilibrium in the original game. It turns out that a crucial condition for such subsets to exist is the existence of a type-independent optimal social alternative, for each player. We further analyze the welfare implications of these restrictions. This work follows work by Holzman, Kfir-Dahav, Monderer and Tennenholtz (2004) and Holzman and Monderer (2004) where similar analysis is done for combinatorial auctions.