Comparative statics is a well established research field where one analyzes how  changes in parameters of a strategic game affect the resulting equilibria. Examples of such parameter changes include tax/subsidy changes or production cost shifts in oligopoly models. While classic comparative statics is mainly concerned with qualitative approaches (e.g., deciding whether a marginal parameter change improves or hurts equilibrium profits or welfare), we aim at quantifying the possible extend of such an effect . We apply our quantitative approach to the multimarket oligopoly model introduced by Bulow, Geanakoplos and Klemperer (1985). In this model, there are two firms competing on two markets with one firm having a monopoly on one market. Bulow et al. describe the counterintuitive example of a positive price shock in the firm's monopoly market resulting in a reduction of the firm's equilibrium profit. We quantify for the first time the worst-case profit reduction for the case of two markets with affine price functions and firms with convex cost technologies . We show that the relative loss of the monopoly firm is at most 25\% no matter how many firms compete on the second market. In particular, we show for the setting of Bulow et al. involving affine price functions and only one additional firm on the second market that the worst case loss in profit is bounded by 6.25\%. We further investigate a dual effect: How much can a firm gain from a negative price shock in its monopoly market? Our results imply that this gain is at most 33\% . We complement our bounds by concrete examples of markets where these bounds are attained .
Comparative statics is a well established research field where one analyzes how marginal changes in parameters of a strategic game affect the resulting equilibria. While classic comparative statics is mainly concerned with qualitative approaches (e.g., deciding whether a parameter change improves or hurts equilibrium profits or welfare), we provide a framework to expose the extend (not monotonicity) of a discrete (not marginal) parameter change, with the additional benefit that our results can even be used when there is uncertainty about the exact model instance . We apply our quantitative approach to the multimarket oligopoly model introduced by Bulow, Geanakoplos and Klemperer (1985). They describe the counterintuitive example of a positive price shock in the firm's monopoly market resulting in a reduction of the firm's equilibrium profit. We quantify for the first time the worst case profit reduction for multimarket oligopolies with an arbitrary number of markets exhibiting arbitrary positive price shocks. For markets with affine price functions and firms with convex cost technologies , we show that the relative loss of any firm is at most 25\% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on consumer surplus. We find tight bounds also for these measures showing that total profit and consumer surplus decreases by at most 25\% and 16.6\%, respectively .
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Examples of such parameter changes include tax/subsidy changes or production cost shifts in oligopoly models.
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marginal
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aim at quantifying the possible extend of such an effect
provide a framework to expose the extend (not monotonicity) of a discrete (not marginal) parameter change, with the additional benefit that our results can even be used when there is uncertainty about the exact model instance
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In this model, there are two firms competing on two markets with one firm having a monopoly on one market. Bulow et al.
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the case of two markets
multimarket oligopolies with an arbitrary number of markets exhibiting arbitrary positive price shocks. For markets
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the monopoly
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on the second market. In particular, we show for the setting of Bulow et al. involving affine price functions and only one additional firm on the second market that the worst case loss in profit is bounded by 6.25\%. We further investigate a dual effect: How much can a firm gain from a negative price shock in its monopoly market? Our results imply that this gain is at most 33\% . We complement our bounds by concrete examples of markets where these bounds are attained
in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on consumer surplus. We find tight bounds also for these measures showing that total profit and consumer surplus decreases by at most 25\% and 16.6\%, respectively