In this paper, we propose and compare three heterogeneous Cournotian duopolies, in which players adopt best response mechanisms based on different degrees of rationality. The economic setting we assume is described by an isoelastic demand function with constant marginal costs. In particular, we study the effect of the rationality degree on stability and convergence speed to the equilibrium output. We study conditions required to converge to the Nash equilibrium and the possible route to destabilization when such conditions are violated, showing that a more elevated degree of rationality of a single player does not always guarantee an improved stability. We show that the considered duopolies exhibit either a flip or a Neimark–Sacker bifurcation. In particular, in heterogeneous oligopolies models, the Neimark–Sacker bifurcation usually arises in the presence of a player adopting gradient-like decisional mechanisms, and not best response heuristic, as shown in the present case. Moreover, we show that the cost ratio crucially influences not only the size of the stability region, but also the speed of convergence toward the equilibrium.

Cavalli, F., Naimzada, Nonlinear dynamics and convergence speed of heterogeneous Cournot duopolies involving best response mechanisms with different degrees of rationality, <<NONLINEAR DYNAMICS>>, 2015; 81 (1-2): 967-979. [doi:10.1007/s11071-015-2044-y] [http://hdl.handle.net/10807/85476]

Nonlinear dynamics and convergence speed of heterogeneous Cournot duopolies involving best response mechanisms with different degrees of rationality

Cavalli, Fausto
;
2015

Abstract

In this paper, we propose and compare three heterogeneous Cournotian duopolies, in which players adopt best response mechanisms based on different degrees of rationality. The economic setting we assume is described by an isoelastic demand function with constant marginal costs. In particular, we study the effect of the rationality degree on stability and convergence speed to the equilibrium output. We study conditions required to converge to the Nash equilibrium and the possible route to destabilization when such conditions are violated, showing that a more elevated degree of rationality of a single player does not always guarantee an improved stability. We show that the considered duopolies exhibit either a flip or a Neimark–Sacker bifurcation. In particular, in heterogeneous oligopolies models, the Neimark–Sacker bifurcation usually arises in the presence of a player adopting gradient-like decisional mechanisms, and not best response heuristic, as shown in the present case. Moreover, we show that the cost ratio crucially influences not only the size of the stability region, but also the speed of convergence toward the equilibrium.
Inglese
Cavalli, F., Naimzada, Nonlinear dynamics and convergence speed of heterogeneous Cournot duopolies involving best response mechanisms with different degrees of rationality, <<NONLINEAR DYNAMICS>>, 2015; 81 (1-2): 967-979. [doi:10.1007/s11071-015-2044-y] [http://hdl.handle.net/10807/85476]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/85476
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 12
social impact