Stability analysis of heterogeneous oligopoly games of increasing players with quadratic costs

The paper and the candidate solution derive identical local-stability thresholds for all four heterogeneous Cournot maps (TGB, TGBA, TGBAL, TGBALR) and both prove the strict enlargement of the stability region as the number of firms increases. The paper computes Jacobians at the symmetric positive equilibrium and applies Schur–Cohn/Jury conditions, then uses a PCAD-based regional sign analysis to reduce stability to a single inequality in each model, yielding the same closed-form thresholds reported by the model solution for s = k√c: √2 (TGB), 9(101l−200)/[2(252l−505)] (TGBA), 2√6(226l−441)/(512l−1017) (TGBAL), and 10172√2/5737 (TGBALR) . The candidate independently rederives the same Jacobians and characteristic polynomials and identifies the binding Jury inequality p(−1)>0 as decisive in each case, leading to the same thresholds and inclusion chain. Minor issues in the candidate’s exposition (a sign slip in one difference-of-thresholds argument and calling the quartic Jury test ‘four inequalities’) do not affect the conclusions.