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A Game-Theoretic Approach to Two-Person Negotiation Under Multiple Criteria

Author

Listed:
  • Natalia M. Novikova

    (FRC “Computer Science and Control” of Russian Academy of Sciences)

  • Irina I. Pospelova

    (Lomonosov Moscow State University)

Abstract

The most difficult decision problems arise when several parties with several criteria must reach a consensus. This problem can be modelled as a game with vector-valued payoffs. If the players are allowed to use mixed strategies, there can be many Nash equilibria, and therefore many outcomes. The role of negotiation is to choose a specific outcome, or to restrict the set of outcomes to a small subset. One promising approach to negotiation support is scalarization of the vector payoff function. Here we apply Germeier scalarizing function, also known as the Rawlsian function, to mixed-strategy multicriteria games. After developing the mathematical background, we extend to these games the principle of Best Guaranteed Value, the value that a player may count on regardless of the other players’ actions. We suggest that a good outcome for negotiation in a multicriteria game is a Nash equilibrium outcome that provides each player with the payoffs that are better than its Best Guaranteed Value. We describe all such outcomes, thereby defining a new negotiation support mechanism.

Suggested Citation

  • Natalia M. Novikova & Irina I. Pospelova, 2024. "A Game-Theoretic Approach to Two-Person Negotiation Under Multiple Criteria," Group Decision and Negotiation, Springer, vol. 33(1), pages 195-216, February.
    • Handle: RePEc:spr:grdene:v:33:y:2024:i:1:d:10.1007_s10726-023-09859-5
    DOI: 10.1007/s10726-023-09859-5
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