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Multivariate Multi-Objective Allocation in Stratified Random Sampling: A Game Theoretic Approach.

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This study introduces a game theoretic approach for multivariate multi-objective allocation problems with limited stratum variance information. The findings demonstrate its effectiveness in optimizing sample size allocation.

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Area of Science:

  • Statistics
  • Operations Research
  • Game Theory

Background:

  • Multivariate allocation problems often lack sufficient stratum variance data.
  • Traditional methods struggle with limited information scenarios.

Purpose of the Study:

  • To propose a game theoretic framework for multivariate multi-objective allocation.
  • To address sample size allocation challenges with minimal variance information.

Main Methods:

  • Utilized a game theoretic approach based on weighted goal programming.
  • Employed simulation techniques to establish the payoff matrix.
  • Solved the allocation problem using a minimax game strategy.

Main Results:

  • The game theoretic approach effectively handles multivariate multi-objective allocation.
  • Weighted goal programming provides a viable solution for limited variance data.
  • Simulation-based payoff matrix determination is feasible.

Conclusions:

  • Game theory offers a robust solution for complex allocation problems.
  • The proposed method enhances sample size allocation efficiency under data scarcity.
  • Weighted goal programming is a practical tool for statistical allocation.