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→Part I
Whether the innovation is cheap or not is not first order germane. The important question is the appropriability regime. I will assume that the cheap innovation (making the phone red) is appropriable (i.e. there are no property rights associated with the colour red), and that the battery life innovation is patentable and that strong (perfect) IPR protection exists.
Then the red phone would indicate an introduction of differing qualities that are imitable at some (possibly zero) cost. This gives a Hotelling (1929) or Salop (1979) like model, assuming that customers have some preferences over quality. Perhaps a line from White to Red could indicate the distribution of customer preferences, the cost of innovation could be the cost of entry on the line, and the transport cost could present represent the lost utility of a customer away from thier ideal colour. We begin the game with two firms situated on White, one of which gets to 'spawn' another firm that locates on Red. The White-only competitor may spawn an entrant or other new entrants may enter the market.
Absent new entry, if there was only one firm at White and one at Red we would expect them to price to compete against each other exactly in the Hotelling model (given these location choices). However, the Bertrand competition at the White end of the line reduces price to marginal cost, and only customer whose valuation of a White above marginal cost can buy from them. This gives the player at Red, potentially at least, the rest of the market without competiting with players at White - the customer whose valuation of White is marginal cost would have to have a valuation of Red greater than or equal to marginal cost for the entire market to be served. However, as the Red player is a monopolist over this area he would rather price above marginal cost and earn positive profits which he does.
