Problem
Research questions and friction points this paper is trying to address.
Cooperative Integer Programming Games
Optimal Coalition Structures
Stable Coalition Structures
Core Stability
Cooperative Integer Programming Games: Core Stability and Optimal Coalition Structures
🤖 AI Summary
本文解决了合作整数规划游戏中最优和稳定联盟结构的识别问题，通过引入稳定性不等式、提升稳定性割平面及多种求解策略来实现。
📝 Abstract
We introduce cooperative integer programming games (CIPGs), in which agents pool budget constraints to accomplish indivisible tasks jointly and the characteristic function maps every coalition to the optimal value of a pooled integer program. Our goal is to identify an optimal coalition structure (OCS) and a stable one (OSCS). We derive a stability inequality that keeps each formed coalition in the Core with respect to itself, and present two mixed-integer OCS formulations, aggregated and disaggregated, proving that the disaggregated formulation is integer-equivalent yet yields a tighter LP relaxation. Building on the stability inequality we develop lifted stability cuts, several separation strategies inside a cutting-plane algorithm, an SCS-feasible primal heuristic that constructs warm starts with guaranteed stability, and a payoff-refinement step computing the Shapley value and the nucleolus of every formed coalition. On benchmark cooperative knapsack games, the method certifies optimality with up to 16 players and reaches MIP gaps below 1% at 30 players while evaluating 766 of the roughly $10^9$ coalition values.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Cooperative Integer Programming Games
Optimal Coalition Structures
Stability Inequality
Mixed-Integer Formulations
Lifted Stability Cuts
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