Market Making with Decreasing Utility for Information

TL;DR

This paper introduces adaptive cost functions for combinatorial prediction markets where the market maker's utility for information decreases over time, ensuring information preservation, fair reward adjustment, and loss control.

Contribution

It proposes novel adaptive cost functions for decreasing utility scenarios in prediction markets, using mixed Bregman divergence to balance information retention and market maker's loss.

Findings

Designed cost functions that preserve prior information

Eliminated rewards for publicly revealed information

Maintained worst-case loss for market maker

Abstract

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.