Why sharing resources can benefit the whole but fail the individual

A resource problem with unequal rules

Why might someone abandon a shared resource even when sharing generates more total benefit? Jorge David Castaño-Yepes, Marcela Herrera and Javier Parra-Domínguez investigate this question in a theoretical preprint submitted to arXiv on 9 November 2026. The supplied record does not establish peer review.

Their framework is a two-player version of the knapsack problem. In the familiar optimization problem, someone chooses objects with different weights and values without exceeding a carrying limit. Here, each player independently selects resources subject to an individual capacity constraint. A resource’s weight represents the capacity it requires, while its value represents its benefit.

The strategic complication is overlap: both players can select the same resource, and what each receives then depends on the rules governing shared use.

Separating loss, division and privilege

The model distinguishes three mechanisms. First, competition destroys a specified fraction of a shared resource’s value. Second, an allocation rule divides the remaining value between the players. Third, an institutional rule gives one player priority, potentially adding a benefit for that player and imposing a cost on the other.

These priority effects apply only when both players select the resource. Exclusive selection gives the selecting player its full value.

The authors define social welfare as the sum of the two players’ payoffs. This is a specific mathematical measure, not a comprehensive assessment of fairness or social well-being.

Adding the payoffs reveals a useful distinction. For a fixed allocation, changing how the remaining value is divided does not directly change the total. The institutional benefit and cost affect that total only through their difference. Equal additional benefits and costs cancel in aggregate, even though they change what each player receives.

That cancellation does not make the rules strategically irrelevant. Players choose according to their own payoffs. Two institutional arrangements can therefore assign the same combined payoff to every feasible allocation while creating different incentives—and potentially different equilibria.

When sharing becomes unattractive

The authors derive two separate tests for a shared resource, holding all other selections fixed.

Sharing produces at least as much combined payoff as exclusive allocation when the institutional benefit minus the institutional cost covers the value destroyed by competition.

But the disadvantaged player has a different test: does their share of the remaining resource value cover their institutional cost? If not, dropping the resource increases their own payoff.

These conditions can disagree. Sharing can be collectively preferable yet vulnerable to withdrawal. Conversely, neither player may benefit from simply abandoning a shared resource even though exclusive allocation would produce greater combined welfare.

These are restricted comparisons, not complete equilibrium tests. A Nash equilibrium is an allocation in which neither player can improve their payoff by switching to any other feasible resource bundle. Checking whether someone would drop one resource is insufficient to establish that broader stability.

What the numerical examples show

Alongside the mathematical derivations, the researchers enumerate small, constructed games. In one example, there are five resources and each player has capacity seven. Each has 22 feasible selections, giving 484 possible paired allocations.

Twelve allocations attain the maximum combined payoff of 18 by assigning every resource exclusively. Yet only one of the four pure-strategy Nash equilibria reaches that maximum. The other three yield combined payoffs of 17.8, 17.5 and 17.8.

Changing capacity also changes strategic possibilities. When both capacities rise from seven to ten, the maximum attainable welfare remains 18, but the game has a single pure-strategy equilibrium with welfare 17.3. In this example, more capacity does not ensure an efficient equilibrium.

A theoretical result, not a policy forecast

The evidence consists of mathematical analysis and illustrative numerical scenarios, rather than measurements of actual institutions. Its conclusions depend on the specified two-player payoff rules and capacity constraints; the examples do not establish how frequently these outcomes occur outside the model.

The central lesson is nevertheless clear within the framework: assessing total benefit alone misses the incentives needed to sustain an allocation. Rules governing who receives benefits and who bears costs can change stable outcomes even when their direct effect on combined welfare cancels out.