Mechanisms that play a game, not toss a coin

TL;DR

This paper introduces a method to convert randomized mechanisms into deterministic ones by having agents play a game, maintaining desirable properties while improving verifiability across multiple domains.

Contribution

It proposes novel derandomization techniques for mechanisms, enabling deterministic, audit-friendly solutions with preserved normative properties in various decision-making domains.

Findings

Derandomized mechanisms retain good normative properties.

Agents' equilibrium strategies are mostly sincere.

Emergence of a new normative property in one domain.

Abstract

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so an agent's best action is to play randomly, and this play then injects ``randomness'' into the mechanism. This derandomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three related methods to derandomize randomized mechanism in six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel derandomized mechanisms for these six domains with good normative properties. Each mechanism has a mixed Nash equilibrium in which agents play a modular arithmetic game with an uniform mixed strategy. In all but one mixed Nash equilibrium, agents report their preferences over the original problem sincerely. The derandomized methods are thus ``quasi-strategy proof''. In one domain, we additionally show that a new and desirable normative property emerges as a result of derandomization.