AI clarifies cooperation and competition in strategic planning games
Formalizing Cooperation and Competition: An AI-Assisted Mathematical Addendum to a 2018 Planning Thesis
Computer Science and Game TheoryArtificial Intelligence
Summary
This paper looks at how people decide whether to work together or compete in strategic planning situations involving resources and costs. Using AI, the authors carefully check and formalize previous ideas on how groups approve plans and ensure fairness. They provide computer-verified proofs and code that guarantee participants won’t be worse off and that negotiations end fairly. Their work also shows some limits of simple assumptions and compares different planning strategies on many example cases.
What this means in practice
- •For network schedulers: Use verified negotiation methods to allocate network resources fairly without worsening any participant's situation.
- •For supply chain planners: Model cooperation and competition among partners with precise mathematical checks to ensure stable and approved agreements.
Authors
Haitham Masaud Amar
Abstract
We present an AI-assisted mathematical addendum to Strategic Trip Planning: Striking a Balance Between Competition and Cooperation (Amar, 2018). We reconstruct selected relationships between strategic choice, cooperative stability, participant approval and enforcement. The thesis's Nash-to-core proposition is under-specified until outsider opportunities are stated. We verify two-person implications under fixed outsiders and explicit efficiency conditions. Under isolation, the original example has an empty TU core; its funded counterpart uses an explicit external subsidy. For a monotone resource model we characterize the exact financing gap. A finite negotiation procedure implemented in Lean is proved to terminate with participant approval, joint-cost non-worsening and local optimality against permitted approved moves. Supporting formalizations address bargaining geometry and regret-based efficiency. A resource-game counterinstance shows why monotonicity alone provides no uniform price-of-anarchy bound. Reproducible computations compare a documented heuristic reconstruction with the verified procedure on 44 source-based instances and 96 starting cases from four additional synthetic network families. Acceptance-matched heuristic and randomized pairwise-search controls contextualize the optimization results. The mathematical ingredients are established results; the contribution is a traceable reconstruction linking source statements, explicit assumptions, checked proofs, executable code and retained counterinstances. The study illustrates how AI-assisted investigation can turn engineering intuitions from legacy research into precise mathematical claims whose conditions and computational consequences can be inspected and reproduced.