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We study a toy two-player game for periodic double auction markets togenerate liquidity. The game has imperfect information, which allows us to linkmarket spreads with signal strength. We characterize Nash equilibria in caseswith or without incentives from the exchange. This enables us to derive newinsights about price formation and incentives design. We show in particularthat without any incentives, the market is inefficient and does not lead to anytrade between market participants. We however prove that quadratic fees indexedon each players half spread leads to a transaction and we propose aquantitative value for the optimal fees that the exchange has to propose inthis model to generate liquidity.

Equilibria and incentives for illiquid auction markets