Equilibrium Liquidity and Risk Offsetting in Decentralised Markets

TL;DR

This paper models the strategic interactions in decentralised exchanges, highlighting how liquidity provision is influenced by risk management, private information, and replication costs, with implications for market stability and profitability.

Contribution

It introduces a structural game-theoretic framework for DEX liquidity provision, analyzing equilibrium existence and the effects of risk aversion and private information on liquidity.

Findings

Higher risk aversion reduces liquidity and profitability.

Private information has a non-monotonic impact on liquidity.

Liquidity depth is crucial for risk management in DEXs.

Abstract

We study the economic viability of liquidity provision in decentralised exchanges (DEXs) within a structural framework in which market outcomes are endogenous. We formulate strategic interactions as a sequential game: a risk-averse liquidity provider (LP) sets the supply of liquidity in the DEX and a costly dynamic replication strategy in a centralised exchange (CEX), price-sensitive traders determine trading volumes, and arbitrageurs align prices. We establish existence of equilibrium under general trading functions. We show that DEX liquidity depth is a central instrument for risk management, because the LP adjusts liquidity ex ante to manage exposure. In addition to the classical trade-off between liquidity demand and adverse selection, we identify two further determinants of the viability of liquidity provision: the ratio of risk aversion to replication costs and private information. The ratio governs the aggressiveness of replication: greater relative risk aversion reduces risk but also lowers equilibrium liquidity and its mean profitability. Private information has a non-monotonic effect. For moderate price movements, speculative benefits increase liquidity. For large price movements, anticipated adverse selection and replication costs lead to thinner markets.