arXiv subjects

Manuel Mueller-Frank

Publications and source records attributed to Manuel Mueller-Frank.

4 recordsLinked to original sources

arXiv2026

The Wisdom of the Crowd and Higher-Order Beliefs

We propose a new simple procedure called Population-Mean-Based Aggregation (PMBA) that enables a principal to "aggregate" information about an unknown state of the world from agents without understanding the information structure among them. PMBA only requires agents to communicate their beliefs about the state, and some agents to communicate their expectations of the population average belief. In a large population, for any finite number of possible states, and under weak assumptions on the information structure, allowing individual agents' beliefs to be misspecified, we show that PMBA infers the true state (in probability or almost surely under the stated conditions). We show how PMBA can be reinterpreted as a linear regression procedure, and how it can be used to aggregate information from a finite number of agents, allowing us to reuse existing results on inference in linear models. We conduct a novel experiment to show that the real-world performance of our procedure exceeds that of existing methods.

econ.TH↗

arXiv2026

Decentralized Equilibrium for Bitcoin Mining

Cryptocurrencies such as Bitcoin are defined by protocols that specify how participants record transactions and create new currency units. These protocols are not enforced by law or any central entity and instead are intended to be incentive compatible. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is known not to constitute an equilibrium (Eyal and Sirer, 2018). This leaves open the question of whether the decentralized outcome intended by Nakamoto can be sustained in equilibrium in the Bitcoin mining game. We propose inertial mining, a novel mining protocol that induces that outcome, i.e., a single longest chain in which each miner's asymptotic share of blocks equals its share of computational power. Our main result establishes that inertial mining constitutes an equilibrium, assuming no miner controls one half or more of the computational power. Inertial mining coincides with Nakamoto's protocol on the equilibrium path, and can be implemented in Bitcoin without any changes to its consensus mechanism or blockchain architecture. When a single miner controls more than half of the computational power, we show that no decentralized equilibrium exists.

cs.CR↗

arXiv2021

Sequential Naive Learning

We analyze boundedly rational updating from aggregate statistics in a model with binary actions and binary states. Agents each take an irreversible action in sequence after observing the unordered set of previous actions. Each agent first forms her prior based on the aggregate statistic, then incorporates her signal with the prior based on Bayes rule, and finally applies a decision rule that assigns a (mixed) action to each belief. If priors are formed according to a discretized DeGroot rule, then actions converge to the state (in probability), i.e., \emph{asymptotic learning}, in any informative information structure if and only if the decision rule satisfies probability matching. This result generalizes to unspecified information settings where information structures differ across agents and agents know only the information structure generating their own signal. Also, the main result extends to the case of $n$ states and $n$ actions.

cs.LG↗

arXiv2019

Social learning equilibria

We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce Social Learning Equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.

math.ST↗