Manuel Mueller-Frank

Yi-Chun Chen, Manuel Mueller-Frank, Mallesh M Pai

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.

Manuel Mueller-Frank, Minghao Pan, Omer Tamuz

The value of proof-of-work cryptocurrencies critically depends on miners having incentives to follow the protocol. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is well known not to constitute an equilibrium: Eyal and Sirer (2018) construct a profitable deviation called ``selfish mining'' which relies on strategically delaying disclosure of newly mined blocks rather than publishing them immediately. We propose inertial mining, a novel mining protocol. When miners follow inertial mining, they produce the outcome intended by Nakamoto, i.e., a single longest chain. But unlike the Bitcoin mining protocol, inertial mining constitutes an equilibrium (assuming no miner controls more than half of the mining power). Indeed, neither selfish mining nor any other deviation is profitable. Furthermore, inertial mining only changes miners' behavior in the event of off-path forks, and can be implemented in Bitcoin without any changes to its consensus mechanism or blockchain architecture.

Itai Arieli, Yakov Babichenko, Manuel Mueller-Frank

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.