Abstract
In a two-stage oligopoly, with investment in the first stage and quantity or price competition in the second stage, there is a “Common Wisdom” Theorem which states that we find over-investment if the goods are substitutes and competition is in strategic substitutes, or if goods are complements and competition is in strategic complements, and that we find under-investment if we have complements and strategic substitutes or substitutes and strategic complements. The existing literature, however, lacks a proof of this theorem and, in particular, it lacks a systematic comparison of the different benchmarks for over- and under-investment. A “naive” benchmark is the cost efficient investment with respect to the subgame perfect (closed loop) equilibrium quantities. Alternative benchmarks (which are more often proposed) are the open loop equilibrium investment or the welfare maximizing investment. The chosen benchmark is critical because the Common Wisdom Theorem applies (under certain conventional conditions) only for the naive benchmark. The other two benchmarks give rise to subcases.
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Bolle, F. Over- and under-investment according to different benchmarks. J Econ 104, 219–238 (2011). https://doi.org/10.1007/s00712-011-0218-8
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DOI: https://doi.org/10.1007/s00712-011-0218-8