No abstract

No abstract

We study market scoring rule (MSR) prediction markets in the presence of risk-averse or risk-seeking agents that have unknown yet bounded risk preferences. It is well known that if agents can be prescreened, then MSRs can be corrected to elicit agents’ beliefs. However, agents cannot always be screened, and instead, an online MSR mechanism is needed. We show that agents’ submitted reports always deviate from their beliefs, unless their beliefs are identical to the current market estimate. This means, in most cases it is impossible for a MSR prediction market to elicit an individual agent’s exact belief. To analyze this issue, we introduce a measure to calculate the deviation between an agent’s reported belief and personal belief. We further derive the necessary and sufficient conditions for a MSR to yield a lower deviation relative to another MSR. We find that the deviation of a MSR prediction market is related to the liquidity provided in the MSR’s corresponding cost-function prediction market. We use the relation between deviation and liquidity to present a systematic approach to help determine the amount of liquidity required for cost-function prediction markets, an activity that up to this point has been described as “art” in the literature.

This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.

No abstract