A Cooperative Game-Theoretic Model for Multi-Agent Coordination in Humanitarian Logistics Systems Under Non-Sub Additive Conditions: A Framework for Indonesia
Keywords:
Cooperative Game Theory, Humanitarian Logistics, Multi-Agent Coordination, Non-Sub Additive Games, Disaster Response, Humanitarian Supply Chain.Abstract
Indonesia is one of the world's most disaster-prone countries, experiencing thousands of natural hazard events annually across its archipelago. Effective disaster response requires coordination among diverse stakeholders government agencies (BNPB/BPBD), non-governmental organizations (including PMI), private sector logistics providers, military (TNI), and community organizations. However, collaboration is often hindered by conflicting incentives, coordination costs, and resource constraints. This paper develops a cooperative game theory framework to analyze stakeholder collaboration in Indonesian humanitarian logistics, explicitly modeling coordination costs as functions of coalition size and heterogeneity, allowing for non-sub additive outcomes where larger coalitions may be less efficient. Using empirically-informed parameters derived from BNPB operational data, disaster response literature, and expert-informed estimates, we calibrate the framework to the Indonesian context. All numerical parameters (standalone costs c_i, efficiency parameters e_i, coordination cost coefficients β₀, β₁, β₂, and resulting Shapley values) presented in this paper are constructed for illustrative and methodological demonstration purposes. They are informed by existing literature and BNPB data patterns but do not represent actual expenditure data from any specific disaster event. The primary contribution of this paper is the mathematical framework itself and its application to the Indonesian multi-stakeholder context, not the specific numerical findings. Empirical validation with real transaction-level data from Indonesian disaster responses is required before the framework can inform actual policy decisions. Key illustrative findings from our calibrated model include: (1) the private sector generates the highest marginal value (Shapley value share: approximately 34% of total savings), supporting prioritization of public-private partnerships; (2) grand coalitions (5 players) may exhibit non-sub additive outcomes when coordination costs exceed marginal benefits; (3) community organizations may require subsidy mechanisms to participate effectively; (4) capacity building for community organizations (increasing efficiency from baseline to 0.65) raises their Shapley value significantly. The framework offers a rigorous analytical tool for disaster policymakers in Indonesia and contributes to humanitarian logistics theory by extending cooperative game theory to a new context with explicit non-sub additive modeling and empirical grounding in Indonesian disaster response patterns.
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