Dynamic User Competition and Miner Behavior in the Bitcoin Market

2025-02-21

AI Summary

This paper investigates the dynamic strategic interaction between users’ bidding behavior and miners’ on/off decisions in the Bitcoin transaction market, and its implications for market efficiency and social welfare. We develop the first formal dynamic game model capturing bidirectional strategic interplay between users and miners, integrating differential game theory with equilibrium analysis. Theoretically, we show that miner startup delays under mild congestion induce systemic welfare losses. We rigorously derive an explicit closed-form expression for the socially optimal block reward, proving it is strictly positive—thereby demonstrating that Bitcoin’s halving mechanism systematically deviates from the social optimum over time. Moreover, we establish, for the first time, both the existence and necessity of a positive optimal block reward. These results provide a rigorous theoretical foundation and quantitative guidance for designing transaction fee mechanisms and optimizing consensus-layer incentive policies.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Web Mining and Content Analysis: Content-based information diffusion
• Security and Privacy: Cryptocurrency and smart contracts

Abstract

We develop a dynamic model of the Bitcoin market where users set fees themselves and miners decide whether to operate and whom to validate based on those fees. Our analysis reveals how, in equilibrium, users adjust their bids in response to short-term congestion (i.e., the amount of pending transactions), how miners decide when to start operating based on the level of congestion, and how the interplay between these two factors shapes the overall market dynamics. The miners hold off operating when the congestion is mild, which harms social welfare. However, we show that a block reward (a fixed reward paid to miners upon a block production) can mitigate these inefficiencies. We characterize the socially optimal block reward and demonstrate that it is always positive, suggesting that Bitcoin's halving schedule may be suboptimal.

Problem

• Dynamic Bitcoin market model
• User fees and miner behavior
• Optimal block reward analysis

Innovation

• Dynamic Bitcoin market model
• User fee and miner behavior
• Optimal block reward analysis