  PinFi is a class of novel protocols for decentralized pricing of dissipative
assets, whose value naturally declines over time. Central to the protocol's
functionality and its market efficiency is the role of liquidity providers
(LPs). This study addresses critical stability and sustainability challenges
within the protocol, namely: the propensity of LPs to prefer selling in
external markets over participation in the protocol; a similar inclination
towards selling within the PinFi system rather than contributing as LPs; and a
scenario where LPs are disinclined to sell within the protocol. Employing a
game-theoretic approach, we explore PinFi's mechanisms and its broader
ramifications. Our findings reveal that, under a variety of common conditions
and with an assumption of participant integrity, PinFi is capable of fostering
a dynamic equilibrium among LPs, sellers, and buyers. This balance is
maintained through a carefully calibrated range of block rewards for LPs,
ensuring the protocol's long-term stability and utility.
