## Composition of Markets with Conflicting Incentives

Citations: | 6 - 0 self |

### BibTeX

@MISC{Dimitrov_compositionof,

author = {Stanko Dimitrov and Rahul Sami},

title = {Composition of Markets with Conflicting Incentives},

year = {}

}

### OpenURL

### Abstract

We study information revelation in scoring rule and prediction market mechanisms in settings in which traders have conflicting incentives due to opportunities to profit from the market operator’s subsequent actions. In our canonical model, an agent Alice is offered an incentive-compatible scoring rule to reveal her beliefs about a future event, but can also profit from misleading another trader Bob about her information and then making money off Bob’s error in a subsequent market. We show that, in any weak Perfect Bayesian Equilibrium of this sequence of two markets, Alice and Bob earn payoffs that are consistent with a minimax strategy of a related game. We can then characterize the equilibria in terms of an information channel: the outcome of the first scoring rule is as if Alice had only observed a noisy version of her initial signal, with the degree of noise indicating the adverse effect of the second market on the first. We provide a partial constructive characterization of when this channel will be noiseless. We show that our results on the canonical model yield insights into other settings of information extraction with conflicting incentives.

### Citations

3923 |
Convex Optimization
- Boyd, Vandenberghe
- 2004
(Show Context)
Citation Context ...ver, for a fixed µ value, πA(σ, µ) is linear in σ. This means, for a fixed µ, πA(σ, µ) is concave ∀σ ∈ Σ. It remains to be shown that for a fixed σ, πA(σ, µ) is convex ∀µ ∈ M. We recall the following =-=[3]-=-: The sum of convex/concave functions is convex/concave, the composition functions f(x) = h(l(x)) is concave if h(x) is concave and non-decreasing and l(x) is concave. We note that for a fixed σ: X X ... |

1393 |
Microeconomic Theory
- Mas-Colell, Whinston, et al.
- 1995
(Show Context)
Citation Context ...e probability, the beliefs µ are consistent with Alice’s strategy σ, and σ is the optimal strategy given the beliefs µ. For a technical definition we refer the reader to the book by Mas-Colell et al. =-=[13]-=-. 4. STRATEGIC ANALYSIS OF MODEL In this section, we show that the wPBE of the 3-stage conflict of interest game can be characterized in terms of the minimax value of a related game. The main results,... |

279 |
Verification of forecasts expressed in terms of probability
- Brier
- 1950
(Show Context)
Citation Context ... subsidies in general, and it may be difficult to implement if the external incentives are not precisely known. Market scoring rule markets are based on proper scoring rules first introduced by Brier =-=[4]-=-, who introduced the quadratic proper scoring rule to measure the accuracy of weather forecasters. The logarithmic scoring rule, the basis of the logarithmic market scoring rule, was later introduced ... |

111 |
On general minimax theorems
- Sion
- 1957
(Show Context)
Citation Context ...tart by observing πA(·, ·) is continuous. We now show that for a fixed µ, πA(σ, µ) is a concave function of σ, and, for a fixed σ, πA(σ, µ) is a convex function of µ. Then using Sion’s minmax theorem =-=[15]-=-, we can say maxσ ′ minµ ′ πA(σ′ , µ ′ ) = minµ ′ maxσ ′ πA(σ′ , µ ′ ), showing the desired result. We start by writing down πA(σ, µ): πA(σ, µ) = EffU(σ) + EffV − πB(σ, µ) = X X σx(r)λU [πU(fx, f0 → r... |

110 | Combinatoral information market design
- Hanson
- 2003
(Show Context)
Citation Context ...s and extensions of our result, and we conclude and discuss directions for future work in Section 7. 2. RELATED WORK In this paper we considered market scoring rule (MSR) markets introduced by Hanson =-=[10]-=-. Hanson proved that risk-neutral traders that do not consider future payoffs have an equilibrium strategy of reporting their true beliefs. A recent strand of literature [5, 6, 8] examines what happen... |

36 | 2006. Information aggregation and manipulation in an experimental market
- Hanson, Oprea, et al.
(Show Context)
Citation Context ...z [18] for further pointers to this literature. In summary, Wolfers and Zitzewitz find that manipulation does not have any noticeable effect on price, except for a short period of time. Hanson et al. =-=[9]-=- consider the effect of external incentives on manipulation in prediction markets. The authors show that even with these external incentives, “manipulation has no significant effect on the accuracy of... |

29 |
and Eric Zitzewitz. Prediction markets
- Wolfers
- 2004
(Show Context)
Citation Context .... Due to their attractive incentive properties, prediction markets are promoted as a fast and accurate method of forecasting future events. Empirical research has confirmed their accuracy in practice =-=[18]-=-. This in turn has lead to proposals of prediction market to be used widely as a decision tool, for subjects ranging from national policy [11] to corporate governance [1]. However, there is one import... |

27 | Gaming prediction markets: Equilibrium strategies with a market maker
- Chen, Dimitrov, et al.
(Show Context)
Citation Context ...ysis of strategies within a single market: In this case, a security V is identical to the security U, but represents a future round of trading. As such, our model generalizes the model in Chen et al. =-=[5]-=-. Our model also applies to the analysis of settings in which the conflict of interest is not a market at all, but rather, some unspecified consequence of Bob’s decision. These applications are descri... |

27 |
Scoring rules and the evaluation of probability assessors
- WINKLER
- 1969
(Show Context)
Citation Context ...r scoring rule to measure the accuracy of weather forecasters. The logarithmic scoring rule, the basis of the logarithmic market scoring rule, was later introduced again to assess weather forecasters =-=[16, 17]-=-. Lambert et al. [12] show that a larger class of functions may be used to elicit different properties of a distribution, rather than just a point estimate of the mean. As observed by Agrawal et al. [... |

22 | Eliciting properties of probability distributions
- Lambert, Pennock, et al.
- 2008
(Show Context)
Citation Context ... the accuracy of weather forecasters. The logarithmic scoring rule, the basis of the logarithmic market scoring rule, was later introduced again to assess weather forecasters [16, 17]. Lambert et al. =-=[12]-=- show that a larger class of functions may be used to elicit different properties of a distribution, rather than just a point estimate of the mean. As observed by Agrawal et al. [2], a prediction mark... |

15 | Prediction mechanisms that do not incentivize undesirable actions
- Shi, Conitzer, et al.
- 2009
(Show Context)
Citation Context ...e for traders to mislead them. In principle, if the external incentive structure is known, one can correct the scoring rule for this effect, for example by using the techniques proposed by Shi et al. =-=[14]-=-; another seemingly attractive alternative is to provide additional markets that extract all relevant information. In practice, we never have complete markets, and incentive methods are deployed by di... |

13 | A Unified Framework for Dynamic Pari-Mutuel Information Market Design - Agrawal, Delage, et al. - 2009 |

12 | Bluffing and strategic reticence in prediction markets
- Chen, Reeves, et al.
- 2007
(Show Context)
Citation Context ...kets introduced by Hanson [10]. Hanson proved that risk-neutral traders that do not consider future payoffs have an equilibrium strategy of reporting their true beliefs. A recent strand of literature =-=[5, 6, 8]-=- examines what happens when traders trade multiple times in an MSR market and do consider future payoffs. The authors show that there is a class of information distributions in which the honest strate... |

11 | Non-myopic strategies in prediction markets
- Dimitrov, Sami
- 2008
(Show Context)
Citation Context ...kets introduced by Hanson [10]. Hanson proved that risk-neutral traders that do not consider future payoffs have an equilibrium strategy of reporting their true beliefs. A recent strand of literature =-=[5, 6, 8]-=- examines what happens when traders trade multiple times in an MSR market and do consider future payoffs. The authors show that there is a class of information distributions in which the honest strate... |

9 |
The quantification of judgment: Some methodological suggestions
- Winkler
- 1967
(Show Context)
Citation Context ...r scoring rule to measure the accuracy of weather forecasters. The logarithmic scoring rule, the basis of the logarithmic market scoring rule, was later introduced again to assess weather forecasters =-=[16, 17]-=-. Lambert et al. [12] show that a larger class of functions may be used to elicit different properties of a distribution, rather than just a point estimate of the mean. As observed by Agrawal et al. [... |

7 |
The policy analysis market: A thwarted experiment in the use of prediction markest for public policy
- Hanson
- 2007
(Show Context)
Citation Context ...pirical research has confirmed their accuracy in practice [18]. This in turn has lead to proposals of prediction market to be used widely as a decision tool, for subjects ranging from national policy =-=[11]-=- to corporate governance [1]. However, there is one important challenge in making this leap: Theoretical analysis, and most empirical studies, of prediction market accuracy has been done in settings w... |

2 |
Prediction Markets for Corporate Governance
- Abramowicz, Henderson
- 2006
(Show Context)
Citation Context ...d their accuracy in practice [18]. This in turn has lead to proposals of prediction market to be used widely as a decision tool, for subjects ranging from national policy [11] to corporate governance =-=[1]-=-. However, there is one important challenge in making this leap: Theoretical analysis, and most empirical studies, of prediction market accuracy has been done in settings where prediction markets are ... |