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Raul Garcia1, Seyedmohammadhossein Hosseinian2, Mallesh Pai3

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This summary is machine-generated.

This study introduces a new type of zero-sum game where players manage actions and budgets. A mixed-integer linear programming model was developed, showing heuristic methods are significantly less optimal.

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Area of Science:

  • Game Theory
  • Operations Research
  • Mathematical Optimization

Background:

  • Traditional two-player zero-sum games lack mechanisms for budget-constrained action selection.
  • Real-world scenarios in security and advertising involve strategic decision-making with resource limitations.

Purpose of the Study:

  • To extend two-player zero-sum games by incorporating a budget constraint for action selection.
  • To develop a mathematical formulation for this extended game.
  • To analyze the game's properties and explore its practical applications.

Main Methods:

  • Formulation of the problem as a mixed-integer linear programming (MILP) model.
  • Derivation of analytical results concerning the game's solution.
  • Computational experiments to compare MILP solutions with heuristic approaches.

Main Results:

  • A novel MILP formulation for budget-constrained zero-sum games was successfully developed.
  • Analytical insights into the game's solution characteristics were provided.
  • Heuristic methods demonstrated an average suboptimal performance with a relative gap of at least 20% compared to the MILP formulation.

Conclusions:

  • The proposed MILP formulation offers an effective method for solving budget-constrained zero-sum games.
  • The findings have significant implications for strategic decision-making in security and advertising.
  • The study highlights the limitations of heuristic approaches in this context, emphasizing the value of precise optimization.