APPLICATION OF COOPERATIVE GAME THEORY: SOLVING THE PROBLEM OF TRAVELING BETWEEN FIVE CITIES IN JAVA - Muhammad Aditya Tri Ariyanto; Rubono Setiawan (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2026)
Intercity travel between Surabaya, Madiun, Surakarta, Semarang, Cirebon, and Jakarta is increasingly facilitated by integrated infrastructure such as toll roads, railways, and airports. Among travelers, forming informal coalitions with others heading in the same direction has become a practical way to reduce individual travel expenses. This study aims to analyze the cost-efficiency of coalition-based intercity travel compared to solo travel, utilizing cooperative game theory to determine fair contribution values among travelers. This study aims to analyze the cost-efficiency of coalition-based intercity travel compared to solo travel, utilizing cooperative game theory to determine fair contribution values among travelers. A case study was conducted in an urban setting involving individuals who travel intercity using various transportation modes. Data were collected through semi-structured interviews. The study applied the Shapley value method within cooperative game theory to model and evaluate each participant’s contribution in a travel coalition. An algorithm was developed to calculate Shapley values for different coalition scenarios. Initial expenditures were: Player A (IDR 210,000), B (IDR 240,000), C (IDR 60,000), D (IDR 400,000), and E (IDR 165,000). First calculation (5-player coalition): A spent IDR 122,750, B IDR 147,750, C IDR 77,750, D IDR -52,250, and E IDR 104,000. Player C opted out, as joining the coalition would cost more than traveling individually (IDR 60,000). Second calculation (4-player coalition): A spent IDR 113,750, B IDR 133,750, D IDR 53,750, and E IDR 98,750. The study’s findings are based on a small sample with specific subject criteria and cannot be generalized to broader intercity travel scenarios. This research demonstrates the practical application of game theory—specifically the Shapley value—in modeling travel coalitions and optimizing cost distribution, offering insights for policy makers and transport planners in collaborative travel schemes.