Precision game engineering through reshaping strategic payoffs

Area of Science:

• Game theory
• Computational economics
• Mathematical biology

Background:

• Nash equilibrium is a core concept in game theory, crucial for understanding strategic interactions.
• Existing Nash equilibria may not always lead to optimal system-wide outcomes.
• A need exists for methods to engineer games toward specific, desirable equilibria.

Purpose of the Study:

• Introduce a novel game engineering framework to achieve pre-defined Nash equilibria.
• Develop a method to modify strategic payoffs to shift games from undesired to desired equilibrium states.
• Demonstrate the framework's effectiveness and scalability across various game complexities.

Main Methods:

• Utilize mixed-integer linear programming (MILP) to identify optimal payoff perturbations.
• Analyze intricate combinations of players and strategies for payoff adjustments.
• Apply the framework to prototype games (e.g., Prisoner's Dilemma, Snowdrift) and complex configurations.

Main Results:

• The framework successfully identifies payoff modifications to achieve desired Nash equilibria.
• Demonstrated scalability on games with up to $$ payoff matrix entries.
• Effectively precludes undesired equilibrium states by reshaping strategic payoffs.

Conclusions:

• The game engineering framework provides a versatile toolkit for precision strategic decision-making.
• Enables the deliberate steering of game outcomes toward favorable Nash equilibria.
• Offers significant implications for economics, political science, and biology through controlled strategic interactions.