We study the Spohn conditional independence (CI) varieties of an n-player game for one-edge Bayesian networks on n binary random variables. For generic payoff tables we prove that the Spohn CI variety is an irreducible complete intersection curve (Nash conditional independence curve) in the Segre variety (P1)n−2×P3 and we give an explicit formula for its degree and genus. We show that any affine real algebraic variety S⊆Rm defined by k polynomials with k«

We study the Spohn conditional independence (CI) varieties of an n-player game for one-edge Bayesian networks on n binary random variables. For generic payoff tables we prove that the Spohn CI variety is an irreducible complete intersection curve (Nash conditional independence curve) in the Segre variety (P1)n−2×P3 and we give an explicit formula for its degree and genus. We show that any affine real algebraic variety S⊆Rm defined by k polynomials with k»