Corporate Strategy and Policy

University Degree Business and Administrative studies

Note on the failure of established firms

Business historians have often pointed out that established firms have a tendency to last long, very long. A look at the list of the largest 10 companies in the US in 1920 and in 1970 would reveal seventy percent common names. This is what the economists call “the persistence of monopoly”. To some it suggests major departure from the ideal of competition that is supposed to drive down “abnormal profits” in the long run. To others it indicates large welfare cost requiring antitrust intervention.

In 1982 Gilbert and Newbury (1982) published a now classic paper in the American Economic Review in which they showed, under quite general conditions, that a firm having a patent giving it a monopoly right for a limited period of time will always have greater incentive than anybody else to extend its monopoly by obtaining the patent for the next generation of technology. To some it may sound obvious, but, and here you must believe me, in reality, is far from so. The question is important and has strong implications. For instance, in the past, some economists have argued that monopolists were conservative rather than innovative (the two terms have almost been used as antonyms in the past) and that innovation was driven by new rather than established firms. Here is the basic Gilbert & Newbury model.

Consider a sequential game between a monopolist with an about-to-expire patent and a potential entrant. The cost of entry for the entrant is $10 million. The monopoly profit is $100 m. In case of successful entry, each firm will make duopoly profit of $40 m (the entrant will make a net profit of $30 m). If the monopolist spends $10 m, it can obtain a new patent with certainty that will extend its monopoly. The monopolist gets to play first. If it patents, there will be no entry and the potential entrant makes zero profit. That is, the top left quadrant in the table below is redundant. The payoff matrix is as follows (monopolist’s payoff is in italics):

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The unique equilibrium of the game is Patent/do not enter. That is, the monopolist always obtains the new patent and the potential entrant always fails to enter. This may explain such cases of persistent monopolies as Polaroid that had monopolized the instant photography business for half a century by repeatedly obtaining newer and newer patents for improved products and processes. (I will leave it to you to think about how much of such a model may be applicable in cases such as Intel and Microsoft).

Gilbert and Newbury’s model was developed in a deterministic framework. That is, there ...

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Gilbert and Newbury’s model was developed in a deterministic framework. That is, there was no uncertainty associated with getting the patent. But they had argued that the addition of uncertainty into the model would not affect their results qualitatively. That claim turned out to be false. In another classic paper in AER, Reinganum (1983) showed that in the case of uncertainty, the monopolist has less incentive to invest in the new technology. Her original model is quite complex (it involves solving a stochastic differential game). Here I will try to give you a flavour of the argument with a simple, single period, non-cooperative game.

We look at the same industry that we looked at in the earlier game. But now obtaining patent is no longer certain for the monopolist. Thus the payoff matrix of the previous game is no longer applicable. Suppose a race is on for obtaining the patent. The incumbent and the potential entrant are the participants in the race. We consider the game at time T and look at the payoffs during a very thin slice of time dt. Let us assume, for simplicity, that upto this time both firms have spent similar amount of money on R&D and are equally likely to win the patent. Again, for simplicity, we limit the strategy space for players, so that, each has only two choices: it can either spend $ 0.1 m on R&D during the period, in which case its probability of success in obtaining the patent during the period dt will be 0.01, or spend $0.05 m on R&D during the period, in which case its probability of success during dt will be 0.005. If the incumbent wins, it keeps its monopoly profit of $100 m. If the entrant wins, or if both succeed in getting the patent simultaneously, each gets duopoly profit of $40 m. If nobody gets a patent during dt, the race continues. We ignore the present value of future expenditure on R&D. (Also remember that past expenditure on R&D is in the nature of sunk cost, it will not influence the future payoff calculations and decisions in this case). The cost of entry for the entrant is $10 m.

A payoff matrix for the game during dt is shown in the table below. Let me explain how I have calculated the payoff in one particular case, that is, when both firms spend ) $0.1 m on R&D. (This is the top left quadrant). Let us calculate the payoff for the incumbent. The probability that only the incumbent will succeed is 0.01. The probability that only the entrant will succeed is also 0.01. The probability that both will succeed simultaneously is 0.0001 (this assumes independence of outcomes), and the probability that no one will succeed during the period is 0.9799. Thus, incumbent’s expected profit is (0.01x100 + 0.01x40 + 0.0001x40 + 0.9799x100 –0.1) = Rs. 99.294. You can calculate the payoffs in the other cases.

You can also calculate the payoffs for the entrant. What is interesting is that it is not even necessary to calculate the payoffs for the entrant in this particular case. For the set of numbers I have chosen here, the incumbent has a dominant strategy. Or, as is more commonly spoken in the game theory literature, the strategy of spending $0.05 m on R&D dominates the other one of spending $0.1 m on R&D. It does not seem optimal for the incumbent to spend the higher amount on R&D. Through induction, one could even argue that not spending any amount would dominate that of spending the smallest amount on R&D. That is, the incumbent would not enter the patent race at all. The new entrant alone has the incentive to invest in R&D and obtain the patent for the new generation of technology.

You can also see the reason behind this result. The major source of incumbent’s inertia is the fact that its expected profit in the next period is larger the smaller the probability of anybody getting the patent during the period. This is a form of “winner’s curse” or a first mover “disadvantage”. Although the above result depends on the particular numbers I have chosen, Reinganum’s result is quite general and only requires that the innovation be uncertain. Henderson and Clarke (1990) is an extension of this basic concept.

References:

Gilbert, Richard, J. and David M.G. Newbery (1982) “Preemptive patenting and the persistence of monopoly,” AER, 72, 3: pp. 514-526.

Reinganum, Jennifer F. (1983) “Uncertain innovation and the persistence of monopoly,” AER, 73, 4: pp. 741-8.

Henderson, Rebecca and Kim B. Clarke (1990) “Architectural innovation: The reconfiguration of existing,” ASQ, 35, 1, PP. 9-30.