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

Natalia M. Novikova () and Irina I. Pospelova ()
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Natalia M. Novikova: FRC “Computer Science and Control” of Russian Academy of Sciences
Irina I. Pospelova: Lomonosov Moscow State University

Group Decision and Negotiation, 2024, vol. 33, issue 1, No 9, 195-216

Abstract: 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.

Keywords: Multicriteria zero-sum games; Germeier’s scalarization; Mixed strategies; Negotiated outcomes; 91A35; 91A40; 91B06 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10726-023-09859-5

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