When Different Market Concentration Indices Agree

Market concentration ratios are popular statistics for characterizing the extent of marketdominance in an imperfectly competitive market, but these ratios may not agree whencomparing two markets. Neither do they necessarily agree with the Herfindahl-Hirschman orentropy indices. This letter compares two Cournot oligopoly markets in which firms haveconstant unit costs. It is shown that the majorization pre-ordering on normalized marketingmargin vectors is both necessary and sufficient for all aforementioned indices to agree on whichis the more concentrated market.[...]