Game-theoretic characterization and dynamic formation of stable hypergraphs

Source abstract

This paper studies stability of hypergraphs and their dynamic formation under four utility scenarios combining benefits (with/without decay) and costs (with/without overlap adjustment). We derive parametric stability conditions for five canonical structures: grand, empty, star, line, and circle. Results include: grand and empty hypergraph stability depends on a cost threshold; star and line hypergraph stability requires micro-low and macro-high cost balance; circle hypergraph is stable only for three players with decay in benefits. Simulations confirm that benefit decay shifts structures from few large associations to many small overlapping ones, while overlap cost adjustment has a limited effect.