Weak and Strong Time Consistency in a Differential Oligopoly Game with Capital Accumulation

Journal of Optimization Theory and Applications (Impact Factor: 1.42). 01/2008; 138(1):17-26. DOI: 10.1007/s10957-008-9432-0

ABSTRACT We illustrate a differential oligopoly game with capital accumulation where the accumulation dynamics of productive capacity
is modelled à la Ramsey. The model is solved under the open-loop information structure, to show that it admits an open-loop
Nash equilibrium which is indeed a degenerate feedback one and therefore strongly time consistent, even if, by construction,
the problem under consideration is not a linear state game.

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    ABSTRACT: We propose a simple method for characterising analytically the feedback solution of oligopoly games with capital accumulation à la Solow-Swan. As a result, it becomes possible to contrast the feedback equilibrium against the corresponding one generated by open-loop information. Our method accommodates extensions of the stripped down oligopoly model in several directions. As an example, we expand the setup to include environmental effects and Pigouvian taxation.
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    ABSTRACT: Open-loop Stackelberg equilibria in linear-state games are subgame perfect. This result holds under the hypothesis of unconstrained final state; whereas we need to take into account suitable final-state conditions in order to correctly formalize certain economic problems. A striking contribution of this paper is that it tackles the consistency problem for an open-loop Stackelberg equilibrium in linear-state games with a final-state constraint in the leader’s problem. In this paper, after proving that such a type of equilibrium is not subgame perfect, we introduce a weaker definition of subgame perfectness, which we call ε-subgame perfectness. This new definition can be applied to the open-loop Stackelberg equilibrium of a constrained linear-state game. Finally, we present some explanatory examples to show how the definition of ε-subgame perfectness can be meaningful.
    DGAA Dynamic Games and Applications. 09/2012; 2(3):269–279.
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    ABSTRACT: I characterise the subgame perfect equilibrium of a differential market game with hyperbolic demand where firms are quantity-setters and accumulate capacity over time `a la Ramsey. I show that the open-loop solution is subgame perfect. Then, I analyse the feasibility of horizontal mergers, and compare the result generated by the dynamic setup with the merger incentive associated with the static model. It appears that allowing for the role of time makes mergers more likely to occur than they would on the basis of the static setting.

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