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Nuclear Deterrence and Profit Maximisation


Hugh Oliver

By

August 10th, 2013


Hugh Oliver examines how the worlds of commerce and the military often collide. Through the use of the Nash equilibrium, Oliver shows how the USSR used a credible threat to deter the US from invading Cuba during the Cold War.


In October 1962, the world watched on anxiously as the US and the USSR became precariously poised on the verge of mutually assured destruction during a confrontation known as the Cuban Missile Crisis. This tense 13-day period is considered by many as the point during the Cold War in which the two superpowers came closest to full scale nuclear warfare.

So why didn’t they?

And how is this relevant to economics?

In economic terms a Nash equilibrium materialised between the US and the USSR. Put simply, a Nash equilibrium occurs whereby each side is doing the ‘best’ they possibly can given what their opponent is doing. Neither side has an incentive to deviate from their current position taking into account the actions of their opponent.

Given the US had attempted to overthrow the communist government of Cuba on two occasions (the Bay of Pigs and Operation Mongoose) the USSR began to look for ways to deter further US invasions. The solution? The then USSR leader Nikita Khrushchev covertly arranged for the positioning of Soviet nuclear missiles in Cuba in order to prevent a US invasion into Cuba. Previously, the US faced no deterrents from the USSR in terms of entering Cuba. They possessed a larger nuclear arsenal, greater military resources, and faced a relatively smaller threat from Soviet nuclear missiles – which were purportedly inaccurate at best.

Once the US realised that missiles had been placed in Cuba, the threat of nuclear warfare and mutually assured destruction conditional on a US led invasion into Cuba become chillingly clear. The US faced a strong deterrent to invading Cuba. Aside from cooperation, the US had two courses of action. Firstly it could enter Cuba and risk full scale nuclear warfare which would have involved mutually assured destruction. Secondly the US could stay out of Cuba and avoid a nuclear catastrophe. The solution was simple. Acting rationally, the US refrained from invading Cuba. In turn, the US was doing the best it possibly could given what the USSR was doing. Given the USSR had deployed nuclear missiles in close proximity to US boundaries, the US’s most practical course of action was to stay out of Cuba to avoid antagonising the USSR and triggering nuclear warfare. Similarly, the USSR, by maintaining the nuclear missiles in Cuba and deterring the US invasion was doing the best they possibly could given the US’s desire to overthrow the Cuban government and stifle the spread of communism.

It is important to note that for the Nash equilibrium to occur at a point where the US was deterred from invading Cuba, the USSR needed to cultivate a credible threat. Thus, for the USSR to merely assert that they would respond with nuclear weapons would be insufficient to invoke sufficient fear of nuclear warfare to deter the US from invading Cuba. In the ‘Strategy of Conflict,’ Thomas Schelling highlights the importance of taking actual ‘moves’ in order to convey credible threats. According to Schelling, ‘moves’ convey ‘manifest costs, risks, or a reduced range of subsequent choice,’ and possess an ‘evidence content’ of a ‘different character’ from mere speech alone.[1] Accordingly, the USSR’s placement of nuclear missiles in Cuba was sufficient to demonstrate that any subsequent threats made by the USSR were credible – and not merely empty.

With the US unwilling to initiate nuclear conflict, the Kennedy administration ultimately refrained from invading Cuba. Thus, through the placement of nuclear missiles in Cuba, the USSR was able to deter a US invasion into Cuba.

So how does nuclear deterrence relate to profit maximisation?

When an incumbent firm (i.e. firm already in the market) monopolises a particular market, it is in its best interest to sustain low levels of competition so as to enable it to charge a higher price and generate a higher profit. A reduction in the level of competition can be achieved by convincing any prospective entrant that entry into a market will be unprofitable. One means of achieving this – and a means directly analogous to the Cuban Missile Crisis – is by convincing a prospective entrant that entering the market will prompt the incumbent firm to instigate competitive warfare by lowering the price through an expansion of quantity produced.

The end result? Given the prospective entrant will face competitive warfare should it enter the market, the potential for incurring large losses upon entry operates as a strong deterrent to market entry.

In turn, the trick lies in convincing the prospective entrant that the threat to lower the price is a credible threat. Assuming the USSR is analogous to the incumbent firm, and the US analogous to a prospective market entrant (i.e. invading Cuba = entering market), the incumbent firm will have to make a definitive ‘move’ to deter market entry. Merely threatening or asserting to lower the price will lack a credible basis if it is against the incumbent firm’s best interests.

For example, if a prospective entrant ‘B’ faced the following payoff matrix, it could rationally infer that even if it did enter the market, the incumbent firm ‘A’ would still be better off maintaining a high price and accommodating firm B. If firm A lowered the price following B’s entry into the market, A would lose $150 million in profit (500-350). Accordingly, A’s threat to lower the price is not credible. B’s rational move is to enter the market, wherein a Nash equilibrium occurs at (500, 100).

Table 1[2]

Untitledfinal

So how does firm A create a credible threat to lower the price?

Firm A must make an ‘irrevocable commitment’ that alters its incentives in favour of competitive warfare should entry occur.[3] By making an ‘irrevocable commitment’ in the form of investing in the production of excess capacity, firm A now has the extra capacity to increase output and therein fare better in competitive warfare.[4] Subsequent threats to lower price now appear completely credible. Firm A can now engage in competitive warfare should entry occur. By analogy, when the USSR made extensive investments in nuclear technology and deployed nuclear missiles in Cuba, the threat of nuclear warfare conditional on a US invasion to Cuba was completely credible. The USSR was well placed to engage in nuclear warfare given it had placed missiles in such close proximity to the USA. Similarly, firm A’s threat is no longer empty – as can be seen by the payoff matrix below, should B enter the market, ‘A’ now has the ability to lower the price i.e. initiate competitive warfare.

Table 2[5]

Untitled

Ultimately, an incumbent firm, by making a definitive commitment to invest in the production of excess capacity, will fare better in competitive warfare should B enter the market. Accordingly, as firm A has the ability to lower the price conditional on B’s entry into the market, and given the potential losses that will accrue to B should it enter, B would likely be deterred from market entry. In effect, the incumbent firm has engineered a new Nash equilibrium in which B’s best course of option is to stay out of the market. Should B enter, A’s threat to drop the price so that B incurs a loss is completely credible. Given A has invested in extra production capacity, it is now in a strong position to instigate competitive warfare. Thus, the Nash equilibrium has been manipulated favourably by the incumbent to reduce competition by deterring market entry. The incumbent can enjoy the corresponding rise in market share and therein profitability.



[1] Schelling, T, ‘The Strategy of Conflict,’ Harvard University Press,(1960).

[2] Pindyck, R, and, Rubinfeld, D, ‘Microeconomics (8th edition),’ Pearson (2012) – values changed from original.

[3] Ibid.

[4] Ibid.

[5] Ibid – values changed from original.

The views expressed within this article are those of the author and do not represent the views of the ESSA Committee or the Society's sponsors. Use of any content from this article should clearly attribute the work to the author and not to ESSA or its sponsors.

  • Dave Sharpe

    Hey Hugh, i like the analogy. I think i might be finally getting my head around Game Theory. As i was reading your article i couldnt help think Coles/Woolies v Aldi as a current market example. What do you think? Cheers Dave S

    • Hugh Oliver

      Thanks Dave,

      The price wars between Coles, Woolworths and Aldi are an excellent current market example. Also relevant on that note are the ‘milk wars’ which have occurred between Woolworths and Coles in what appears to be fierce competition with predatory pricing undertones. Both supermarkets have created their own brand of milk, lowered the price to $1 per litre, and have been able to capture a a greater proportion of the market than they would otherwise. It’s not to say that Woolworths and Coles are able to completely eradicate the competition. Australian dairy farmers are still able to remain profitable by marketing their products on quality and relying on customer loyalty.

      However, individual Australian farmers will never be able to match large supermarket chains in terms of market share and dominance. Woolworths and Coles have been able to sacrifice some short term profitability in order to reduce competition and therein enjoy higher levels of profitability from reduced competition in the long term. In theory, sustaining such low prices has the potential to push farmers already in the market out of the market (shakeout strategy) whilst deterring prospective producers of milk given the potential to suffer huge losses upon entry (strategic entry deterrence). Any threats made by Coles or Woolworths to initiate competitive warfare are completely credible given they have taken actual steps to develop and market their own private brands.

      It is also worth noting that a reputation for aggressive pricing behaviour can in itself confer a competitive advantage. For example, a dairy farmer contemplating entry into the market in the future might be deterred purely on the basis that Coles and Woolworths have a reputation for waging price wars. Thus, although I have argued in my article that threat credibility depends on actual ‘moves,’ these supermarket chains could theoretically deter prospective market entrants by merely asserting that they would lower the price of milk in the future without taking any further ‘moves’ to substantiate such a threat.

      • Dave Sharpe

        Thanks for taking the time to respond Hugh. You seem to have some really good insights into these issues. From where i am sitting i think the ACCC should take a harder look at the predatory practices of the supermarket chains. What do you think? Any insights into how and whether the ACCC take a “Game Theory” approach/view to competition in the marketplace? Cheers Dave

        • Dave Sharpe

          Any thoughts on my questions Hugh ?

          • Hugh Oliver

            Hi Dave,

            Sorry for the delay!!! Great question!

            Ultimately, I don’t believe there is any fixed formula or approach that the ACCC can adopt in determining whether or not predatory pricing is occurring within the supermarket industry. Determining predatory pricing is inevitably a matter of degree that varies according to the circumstances. Nor can I really conceive game theory as being particularly practical in analysing the issue of predatory pricing in the supermarket industry. A lot of game theory is very theoretical and involves unrealistic assumptions that are difficult to satisfy in practice. Additionally, I’m not sure how it would apply in determining whether or not pricing is predatory or merely competitive.

            I think the best approach for answering this question lies in a close analysis of the various cost structures of respective firms within the supermarket industry. To illustrate, if we take the Milk Wars as an example, the ACCC could look at the cost structures of Australia Dairy Farmers and than compare these to the cost structures of the major supermarkets, Woolworths and Coles. If it was determined that the price of Milk ($1) was below the marginal cost (cost of producing an additional unit of milk) for a Dairy Farmer, it could potentially be inferred that the pricing was predatory in nature. Placing the price so low that a dairy farmer could not recoup the costs of producing the milk would appear to be anti-competitive. Moreover, both Woolworths and Coles could remain profitable by maintaining milk at a higher price. In turn, lowering the price ostensibly to promote competition but in fact intending drive existing producers from the market would seem to be predatory.

  • Owen Wakely

    Hugh, another interesting article and perspective. How do you propose the Nash equilibrium operates in settings where there is incomplete information on one or both sides? Also can you see a scenario where Firm A makes an “irrevocable commitment” in response to a perceived threat and builds out additional production capacity but that burden of excess capacity becomes in itself a competitive disadvantage, leaving the new entrant (without the legacy capacity of Firm A) to swoop in with a means of production that is lower cost at a later date? At a more contemporary level, do you think the Burger Wars between Burger King and McDonalds are a useful analogy?

    Keep up the good work Hugh. Owen

    • Hugh Oliver

      Hi Owen,

      Thanks for your response.

      In terms of the first part of your response, the point at which the Nash equilibrium occurs implies that the respective players know each other’s planned strategies. Thus, their information is complete in this sense. Obviously, this can be a difficult condition to fulfil in reality. Conversely, when analysing situations in which there is incomplete information on one or both sides, a Bayesian game is more appropriate as it assumes that the knowledge of the other players is incomplete. A Nash equilibrium does not appear to operate under these circumstances.

      With respect to the second part of your response, it is undoubtedly possible that an incumbent firm could make an ‘irrevocable commitment’ by expanding its production capacity which would ultimately translate into a competitive disadvantage due to the reason you outlined above. Such an ‘irrevocable commitment’ would likely result in a competitive disadvantage if that excess productive capacity quickly became obsolete, say due to a rapid growth in the production technology of that particular industry. In turn, a new entrant could capitalise on the growth in technology to refine a more cost effective production process and therein enter the market at a later stage. Nevertheless, I find it difficult to envisage many scenarios in which changes in production technology occur so rapidly as to render an incumbent firm’s current excess production capacity redundant in the short term. Having said that, such a scenario could theoretically occur in the airline industry whereby there has been a recent move towards substituting labour for capital. Hypothetically, imagine if one of the major airlines signed a union contract to employ a large quantity of labour for an extended period of time i.e. expand its production capacity. Given the phasing out of relatively more expensive labour for relatively cheaper capital i.e. consumer self check ins etc, the airline who has signed the contract would now be stuck with relatively more expensive labour. A prospective airline could take advantage of the incumbent airline’s ‘irrevocable commitment’ (contract) in excess production capacity (additional labour) by utilising more capital relative to labour, thus saving money by using relatively cheaper capital. In such a case, the excess production capacity (surplus labour) has become somewhat obsolete thereby enabling the prospective airline to take advantage of new capital technology to enter the market with a means of production at a lower cost, placing the incumbent airline at a competitive disadvantage due to its outdated productive capacities.

      In regards to the final part of your response, the Burger Wars between Burger King and McDonalds are definitely a good analogy. The use of marketing to cultivate brand loyalty and the heavy advertising expenditure required to attain that brand loyalty operates as a strong deterrent to market entry. Many prospective entrants are unable to match the economies of scale derived from spreading that advertising expenditure over a large output. In fact, advertising in order to develop brand loyalty is one of the more common ways incumbent firms attempt to deter market entry from new firms.

  • Owen Wakely

    Thanks Hugh. I understand where you are coming from in terms of the Nash equilibrium, thanks for clarifying that. I am not sure there was complete information on both sides during the Cuban crisis but perhaps a series of positions taken and strategies based upon evolving but incomplete information and implied intent.

    I like the airline industry analogy. Also i think semiconductor industry is another interesting example you could explore. For example smart phone and computer manufacturers are often locked into certain production cycles and processes that may carry in effect the characteristics of an irrevocable commitment in terms of capex and sunk costs and impact on overall earnings and profitability. This is why i think firms like Apple are looking to “own” all aspects of the manufacture of their products right from sourcing of raw materials through to final assembly. Just food for thought Hugh.

    By the way the new look ESSA web site is great. Much easier to navigate and more engaging.

    regards. Owen

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