# Price of Privacy in the Keynesian Beauty Contest

## TL;DR

This paper investigates how privacy concerns affect strategic guessing in the Keynesian Beauty Contest, revealing a trade-off between privacy and social welfare, with implications for information aggregation and coordination.

## Contribution

It introduces a model of privacy costs into the Keynesian Beauty Contest and quantifies the resulting social welfare loss, providing new insights into privacy's impact on strategic behavior.

## Key findings

- High privacy concerns lead to significant social welfare loss.
- Agents obscure information more when their signals are strong.
- Lower signal quality reduces the privacy-related costs.

## Abstract

The Keynesian Beauty Contest is a classical game in which strategic agents seek to both accurately guess the true state of the world as well as the average action of all agents. We study an augmentation of this game where agents are concerned about revealing their private information and additionally suffer a loss based on how well an observer can infer their private signals. We solve for an equilibrium of this augmented game and quantify the loss of social welfare as a result of agents acting to obscure their private information, which we call the 'price of privacy'. We analyze two versions of this this price: one from the perspective of the agents measuring their diminished ability to coordinate due to acting to obscure their information and another from the perspective of an aggregator whose statistical estimate of the true state of the world is of lower precision due to the agents adding random noise to their actions. We show that these quantities are high when agents care very strongly about protecting their personal information and low when the quality of the signals the agents receive is poor.