Working paper

Title: Probabilistic Mechanisms for Public Good Provision and Its Undominatedness. 

Author: Hocheol SHIN (Seoul National University)

Abstract:
This paper explores the design of strategy-proof mechanisms in the context of public good provision and extends the analysis to probabilistic settings. Traditional deterministic mechanisms make binary yes/no decisions regarding the provision of public goods. In contrast, probabilistic mechanisms assign probabilities to the provision of the public good, offering a more flexible framework for decision-making. Building on prior research that characterized necessary and sufficient conditions for undominatedness in deterministic mechanisms, this study extends the results for probabilistic mechanisms. We first consider a class of deterministic strategy-proof mechanisms that satisfy Anonymity and No Positive Transfers to Winners. We show that these mechanisms are undominated by all probabilistic strategy-proof mechanisms if and only if they satisfy Existence of Budget-Balance Point and Strong Unanimity of Non-Edge Agents. We then examine a class of probabilistic strategy-proof mechanisms that satisfy No Transfers to Nulls, Non-Degeneracy, Determinacy with One Null, and Countable Boundary Points, demonstrating that they are undominated by all probabilistic strategy-proof mechanisms if and only if they satisfy Strong Unanimity.