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The objective of this paper is to provide two-stage game models explaining the ‘Generic Competition Paradox’ that demonstrates an increase of brand-name drug price in response to generic entry. Under the assumption that there are two groups of consumers who are segmented by their insurance status, high insurance coverage and low insurance coverage consumers, the models indicate that the decisive factor is the market share of the high insurance coverage consumer and the size of cross-substitute factor relative to certain characteristics of market demand. The paper analyses both the case of only true generic entry and the case of pseudo-generic and true generic entry. The models prove that a brand-name price will increase when both the market share of high insurance coverage consumer and the factor of cross-substitute are small. Also, the ‘Generic Competition Paradox’ more likely occurs in the market where less pseudo-generic products are produced.