394 research outputs found
Robust Quantitative Comparative Statics for a Multimarket Paradox
We introduce a quantitative approach to comparative statics that allows to
bound the maximum effect of an exogenous parameter change on a system's
equilibrium. The motivation for this approach is a well known paradox in
multimarket Cournot competition, where a positive price shock on a monopoly
market may actually reduce the monopolist's profit. We use our approach to
quantify for the first time the worst case profit reduction for multimarket
oligopolies exposed to arbitrary positive price shocks. For markets with affine
price functions and firms with convex cost technologies, we show that the
relative profit 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 social welfare. We find tight
bounds also for these measures showing that total profit and social welfare
decreases by at most 25% and 16.6%, respectively. Finally, we show that in our
model, mixed, correlated and coarse correlated equilibria are essentially
unique, thus, all our bounds apply to these game solutions as well.Comment: 23 pages, 1 figur
- âŠ