An interdisciplinary study introduced a two‑player knapsack game to probe how institutions influence resource allocation. Each player can choose a subset of available resources, but their choices are limited by private capacity limits. The game adds a competitive loss parameter λk that specifies the fraction of a resource’s value lost when both players use it. Allocation coefficients αik decide how the remaining value is split, so that αak+αbk = 1. A second pair of parameters, βk and γk, captures institutional asymmetry by giving different benefits or costs to the two players.

The model finds that changes in allocation coefficients redistribute payoffs without altering total welfare, whereas institutional parameters modify welfare through their net effect. Crucially, two institutional arrangements can produce the same overall welfare yet generate different Nash equilibria. In some cases, sharing a resource is socially preferable but strategically unstable: the non‑priority player can improve their payoff by abandoning the shared resource. In other instances, exclusive allocation yields higher welfare but shared use remains strategically stable.

These results highlight that social efficiency and strategic stability need not coincide when institutions affect how resources are shared. The findings caution against assuming that maximizing total welfare automatically aligns with stable user behavior.

(*Figure: Graph illustrating welfare equivalence versus Nash equilibria distinction under varying institutional parameters was displayed.*)