@Article{Badev_atal_2026_Games_FailedCartel,
AUTHOR = {Badev, Anton and Ivanova, Vanya and Nedelcheva, Diana and Pavlov, Martin and Zlatanov, Boyan},
TITLE = {A Failed Cartel: When Collusive Firms Become Competitors},
JOURNAL = {Games},
VOLUME = {17},
YEAR = {2026},
NUMBER = {5},
ARTICLE-NUMBER = {56},
URL = {https://www.mdpi.com/2073-4336/17/5/56},
ISSN = {2073-4336},
ABSTRACT = {Collusive agreements may break down completely or leave behind a surviving coalition of firms that continues to coordinate its production. We study an exogenously specified partial-cartel structure in which one firm operates independently while the remaining firms maximize their joint profit. We use the term failed cartel to indicate the institutional origin of this market configuration, without claiming that the breakdown, the identity of the outsider, or the persistence of the surviving coalition is determined endogenously. For comparison, we also consider a Cournot–Stackelberg structure in which the former cartel members compete non-cooperatively while anticipating the quantity choice of a common follower. We therefore reformulate the stationary first-order conditions as a fixed-point problem in which the follower’s implicitly defined stationary response b3(x,y), rather than the derivative-generated mapping F3λ3(x,y,z), forms the third component of the corresponding operator. Fixed points of this operator characterize stationary solutions and provide conditional criteria for uniqueness and numerical approximation on an invariant region. When feasibility and the relevant sufficient optimality conditions are satisfied, these stationary solutions determine market equilibria. The linear n-firm analysis compares equilibrium output, prices, profits, market shares, asymmetry, and concentration across the considered market structures. Consumer surplus and total surplus comparisons are provided separately for the illustrative linear quadratic triopoly and are not asserted for general nonlinear demand. A separate isoelastic triopoly with linear costs provides a globally optimal partial-cartel outcome and a verified scalar contraction algorithm, with full-cartel and Cournot benchmarks.},
DOI = {10.3390/g17050056}
}