A Game-Theoretic Foundation for Bitcoin's Price: A Security-Utility Equilibrium

TL;DR

This paper develops a game-theoretic model to value Bitcoin, linking its price, security, and hash rate within a rational expectations equilibrium, and provides testable predictions about market responses to protocol changes.

Contribution

It introduces a novel RESUNE framework that endogenously links Bitcoin's price, security, and hash rate, offering new insights into their interdependence and stability conditions.

Findings

The model predicts a halving event reduces both hash rate and price.

Existence and stability conditions for the equilibrium are established.

The framework decomposes Bitcoin's value into utility, security, and speculation.

Abstract

This paper introduces a structural game-theoretic model to value decentralized digital assets like Bitcoin. Instead of relying on speculative beliefs, it frames the asset's price within a Rational-Expectations Security-Utility Nash Equilibrium (RESUNE). This equilibrium is a fixed point where the market-clearing price dictates the hash rate through a free-entry mining model, which in turn endogenously sets the network's security. The security, defined as one minus the probability of a 51% attack, is determined via a global games model of attacker coordination, providing a unique and continuous security function. We prove the existence of a RESUNE and offer conditions for its uniqueness and stability. The model predicts that the stabilizing direct effect of price on demand must outweigh the potentially destabilizing feedback from price to security. The framework generates testable predictions, such as a protocol halving causing a contraction in both hash rate and price. A structural Vector Autoregression (VAR) model is proposed to test this mechanism. The model decomposes Bitcoin's value into transactional utility, security, and speculative components and explains the observed unidirectional causality from price to hash rate.