System-Wide Incentives to Trace Food Processing: A Cooperative-Game Analysisa

This paper uses cooperative game theory to analyze the incentives for firms to adopt product tracing in a three-tier food processing system with multiple farmers, one manufacturer, and one retailer. Firms that adopt the tracing system can either form a single coalition or create multiple coalitions, while non-adopters make decisions independently. Our analysis identifies equilibrium outcomes for all possible coalition structures, showing that collaboration between the manufacturer and retailer boosts system-wide efficiency, and fewer coalitions lead to greater overall benefits. We develop a coalition game in characteristic value form and prove that the game’s core is always non-empty. The Center of Gravity of the Imputation Set-based value (CIS-value) is a core element of our game and it matches the nucleolus when the system includes at least three farmers. However, the CIS-value does not always ensure non-negative allocations for all coalition members. To resolve this, we introduce the Evenly-Split Value (ES-value), which stays within the core and guarantees positive allocations for every member of the tracing coalition.