Abstract: |
Companies are continuously confronted by challenges that could impact future resource availability, given the rising complexity of global supply markets.
Population expansion and economic development are expected to increase overall resource consumption, perhaps resulting in a scarcity of resources to meet future demand.
Reality shows that companies must address not only potential future resource scarcity difficulties (e.g., as a result of a government policy change), but also the fact that scarcity conditions are frequently unpredictable (e.g., will a new policy affect supply, and if so, when?). For example, as the demand for electric vehicles grows, the raw minerals necessary to produce electric batteries, such as cobalt and lithium, are predicted to become scarce. Alternative materials may become available, however these basic materials are also employed in the manufacture of other gadgets.
Supply chains in economic environments with limited resources can be evaluated by comparing to rivers with a limited amount of water.
Cooperative game theory is frequently used in water resource economics to analyze water resource allocation. In the theoretical literature, this is referred to as the "river sharing problem."
The current paper assumes that when a group of players considers breaking away from the rest of society, they are unsure of the partition that the players outside S will form. As a result, on the set of all possible partitions, they assign various probability distributions. These probabilistic beliefs do not always correspond to the behavior of outsiders, beliefs do not have to be consistent with actual choices. Given the beliefs, regardless of how they emerge, one can compute the expected value of S and define the core of the resulting cooperative game.
We consider agreements with a single supplier to share scarce resources. Along the supply chain, a number of agents extract the quantity of the scarce resource for use in the production of their own products. Agents each have their own method of evaluating scarce resources, with some having greater needs and higher marginal utility than others. Concave and single-peaked benefit functions are used to represent these heterogeneous valuations, with the peak consumption corresponding to an agent's satiation point. The satiation point is depicted, at which over consumption may result in an increase in storage costs.
If the marginal benefits for agents located further downstream are higher, it may be profitable for a coalition to transfer some quantity from one component to another. As a result, the value of a coalition may be greater than the sum of its constituents' values. However, it may be profitable for the agents outside of S to pass some resources from one component to the next, leaving some resources for the agents in S to consume. As a result, the value of a coalition S is determined by both its components and the behavior of the agents outside of S. In other words, the behavior of the agents outside of S has an effect on the value of the coalition S. |