Co-Opetitive Linear-Quadratic Mean-Field-Type Games

Area of Science:

• Game Theory
• Mathematical Economics
• Computational Social Science

Background:

• Traditional game theory often models purely competitive or cooperative interactions.
• Real-world decision-making involves complex dynamics of simultaneous cooperation and competition.
• Understanding emergent behaviors in multi-agent systems requires flexible modeling frameworks.

Purpose of the Study:

• To introduce a novel co-opetitive mean-field-type game (MFTG) framework.
• To model decision-makers with evolving preferences for cooperation and competition.
• To design incentives promoting co-opetition over selfish behavior.

Main Methods:

• Development of a co-opetitive MFTG model incorporating partial cooperation and competition.
• Integration of evolutionary dynamics to describe the evolution of co-opetitive parameters.
• Design of incentive mechanisms to foster co-opetitive strategies.

Main Results:

• The proposed MFTG framework successfully models simultaneous cooperation and competition.
• Decision-makers' preferences dynamically adjust based on contributions to their utility.
• Incentives were shown to effectively promote co-opetitive behavior over purely selfish strategies.

Conclusions:

• Co-opetitive MFTGs offer a powerful approach to model complex strategic interactions.
• Evolving preferences and co-opetitive capacity are key factors in strategic dynamics.
• The framework provides a foundation for designing systems that encourage beneficial mixed strategies.