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On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies

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  • Anne-Christine Barthel

    (West Texas A&M University)

  • Eric Hoffmann

    (West Texas A&M University)

Abstract

This paper takes a novel approach to studying the existence and stability of Nash equilibria in N-firm Cournot–Bertrand oligopolies. First, we show that such games can be monotonically embedded into a game of strategic heterogeneity, so that each firm best responds to the choices of all other firms in a monotonic way. We then show that this monotonicity can be exploited to derive conditions which guarantee the existence of a unique, dominance solvable Nash equilibrium which is stable under all adaptive dynamics. These conditions constitute a strict improvement over existing results in the literature. Finally, we examine the effect on these conditions resulting from additional firms entering the market.

Suggested Citation

  • Anne-Christine Barthel & Eric Hoffmann, 2020. "On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies," Theory and Decision, Springer, vol. 88(4), pages 471-491, May.
    • Handle: RePEc:kap:theord:v:88:y:2020:i:4:d:10.1007_s11238-019-09739-y
    DOI: 10.1007/s11238-019-09739-y
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