Randomized Wagering Mechanisms

TL;DR

This paper introduces randomized wagering mechanisms that achieve all desirable properties, including Pareto optimality, overcoming previous impossibility results for deterministic mechanisms.

Contribution

It expands the design space of wagering mechanisms by proposing two classes of randomized mechanisms that satisfy all key theoretical properties.

Findings

Randomized mechanisms can achieve Pareto optimality and incentive compatibility.

Two classes of mechanisms: lottery-type and surrogate wagering mechanisms.

Mechanisms are robust to noisy ground truth.

Abstract

Wagering mechanisms are one-shot betting mechanisms that elicit agents' predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In particular, Pareto optimality (no profitable side bet before allocation) can not be achieved together with weak incentive compatibility, weak budget balance and individual rationality. In this paper, we expand the design space of wagering mechanisms to allow randomization and ask whether there are randomized wagering mechanisms that can achieve all previously considered desirable properties, including Pareto optimality. We answer this question positively with two classes of randomized wagering mechanisms: i) one simple randomized lottery-type implementation of existing deterministic wagering mechanisms, and ii) another family of simple and randomized wagering mechanisms which we call surrogate wagering mechanisms, which are robust to noisy ground truth. This family of mechanisms builds on the idea of learning with noisy labels (Natarajan et al. 2013) as well as a recent extension of this idea to the information elicitation without verification setting (Liu and Chen 2018). We show that a broad family of randomized wagering mechanisms satisfy all desirable theoretical properties.