  We present a new type of game, the Liquidity Game. We draw inspiration from
the UK government bond market and apply game theoretic approaches to its
analysis. In Liquidity Games, market participants (agents) use non-cooperative
games where the players' utility is directly defined by the liquidity of the
game itself, offering a paradigm shift in our understanding of market dynamics.
Each player's utility is intricately linked to the liquidity generated within
the game, making the utility endogenous and dynamic. Players are not just
passive recipients of utility based on external factors but active participants
whose strategies and actions collectively shape and are shaped by the liquidity
of the market. This reflexivity introduces a level of complexity and realism
previously unattainable in conventional models.
  We apply Liquidity Game theoretic approaches to a simple UK bond market
interaction and present results for market design and strategic behavior of
participants. We tackle one of the largest issues within this mechanism, namely
what strategy should market makers utilize when uncertain about the type of
market maker they are interacting with, and what structure might regulators
wish to see.
