Market Making with Decreasing Utility for Information
This work solves a specific problem in combinatorial prediction markets for market makers needing to adapt to decreasing information utility, though it appears incremental as it builds on known cost-function-based frameworks.
The paper tackles the problem of designing prediction markets where the market maker's utility for information decreases over time, addressing sudden revelation and gradual decrease settings. It proposes adaptive cost functions using mixed Bregman divergence to preserve gathered information, eliminate rewards for revealed information, and maintain worst-case loss.
We study information elicitation in cost-function-based combinatorial prediction markets when the market maker's utility for information decreases over time. In the sudden revelation setting, it is known that some piece of information will be revealed to traders, and the market maker wishes to prevent guaranteed profits for trading on the sure information. In the gradual decrease setting, the market maker's utility for (partial) information decreases continuously over time. We design adaptive cost functions for both settings which: (1) preserve the information previously gathered in the market; (2) eliminate (or diminish) rewards to traders for the publicly revealed information; (3) leave the reward structure unaffected for other information; and (4) maintain the market maker's worst-case loss. Our constructions utilize mixed Bregman divergence, which matches our notion of utility for information.