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On convergence of forecasts in prediction markets

Nina Badulina, Dmitry Shatilovich, Mikhail Zhitlukhin

Abstract

We propose a dynamic model of a prediction market in which agents predict the values of a sequence of random vectors. The main result shows that if there are agents who make correct (or asymptotically correct) next-period forecasts, then the aggregated market forecasts converge to the next-period conditional expectations of the random vectors.

On convergence of forecasts in prediction markets

Abstract

We propose a dynamic model of a prediction market in which agents predict the values of a sequence of random vectors. The main result shows that if there are agents who make correct (or asymptotically correct) next-period forecasts, then the aggregated market forecasts converge to the next-period conditional expectations of the random vectors.
Paper Structure (6 sections, 4 theorems, 36 equations)

This paper contains 6 sections, 4 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. The model
  3. Main results
  4. The general case
  5. The stationary case
  6. Extension: a model with continuous-time forecasts

Key Result

Proposition 1

Suppose that some agent (say, agent $m$) uses a strategy $\sigma^m=(\nu^m,\lambda^m)$ such that $\nu_t^m>0$ and $\lambda_t^{mn}>0$ for all $t\ge0$ and $n=1,\dots,N$. Then $W_t^m > 0$ and $\sum_{k=1}^M \nu_t^k \lambda_t^{kn}W_t^k>0$ for all $t\ge 0$.

Theorems & Definitions (11)

  • Proposition 1
  • Definition 1
  • Definition 2
  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 1 more