LMSR reduces bluffing and strategic reticence in prediction markets
We’ve heard over and over that prediction markets can outperform experts, polls, and group consensus. But there are several different kinds, which one works the best?
To evaluate this question, I have decided on a framework which aligns the incentives of the traders to reach the efficient market equilibrium (a.k.a. Perfect Bayesian Equilibrium, PBE). What that means is that I want each trader to want to reveal all the information he/she has available by adjusting the market price when they find new information. We achieve this by eliminating the potential incentives to either bluff or withhold information.
In order for the market to be efficient, it must fully and immediately reflect all the available information into the new market prices. When traders are strategically withholding information, in order to realize bigger gains in the future, then the markets are not reaching equilibrium.
Conditionally independent signals are essential to allowing any market to reach the Perfect Bayesian Equilibrium. However, conditionally dependent signals open the door to allow for traders to strategic mislead other traders by bluffing or withholding private information.
Previously on this blog, I’ve preached that decentralization and trader independence are key. One main reason may be seen here – conditionally independent signals are a result of a decentralized market.
As far as I know, the only mechanism for achieving the Perfect Bayesian Equilibrium in a theory-based prediction market is a proper scoring rule. Currently, the most effective market scoring rule is Hanson’s Logarithmic Market Scoring Rule (LMSR).
The two other most popular mechanisms for prediction markets are CDA (continuous dual auction), in which the traders place calls and interact with each other like a real stock market, and DPM (dynamic pari-mutuel), in which the simple pari-mutuel market is supplemented by a mechanism to incentivize early trading.
LMSR is superior to CDA and DPM for several reasons.
First, traders receiving conditionally independent signals will miss out on potential gains by either delaying trading (withholding) or bluffing. More specifically, truthful betting is a PBE for all traders in LMSR. Meaning, each trader is realizing his/her maximum payoff, given the current state of the world.
Second, traders in CDA are not incentivized to fully reveal their private information. Any offer made by one trader is a signal to all the other traders in the market. This offer may discourage a potential trade. For example, a trader with private information will not fully reveal his/her information right away. Instead, he/she will leak information to the market little by little to obtain a greater profit over time.
Third, in DPM, traders have incentives to partially withhold information from the market until just before the end of the market. Thus, the market will only reach equilibrium right before the market closes.
And lastly, in CDA and DPM, the market is a zero-sum game, thus risk-neutral participants will have to incentive to participate. LMSR, on the other hand, which is a proper scoring rule, is a positive-sum game, will incentivize even risk-neutral participants.
References:
“Bluffing and Strategic Reticence in Prediction Markets”
- Yiling Chen, Daniel M. Reeves, David M. Pennock,
Robin D. Hanson, Lance Fortnow, and Rica Gonen