Vertical mergers and the nature of the firm (part 1)

What are the benefits of vertical integration? To understand why firms sometimes vertically merge, we need to look at two issues: (i) contractual relations between upstream and downstream firms, and (ii) the mechanics of decision-making within a vertically integrated firm. In particular, we need to consider why there may be obstacles to efficient contracting in the absence of integration, and in what areas of decision-making these obstacles are likely to arise. We also need to consider how control over business decisions is reallocated following vertical merger. These questions are linked to work on the nature and boundaries of the firm.

Contractual limitations and the nature of the firm

A firm may be defined as the basic unit for organising production, which performs the crucial role of linking labour and product markets. Reasons why the supply of the products of labour tends to become organised in this way include specialisation, economies of scale, economies of scope and the reduction of search costs. These reasons also indicate what the firm consists of, beyond an abstract point of trade between workers and consumers. The reduction of search costs, for example, is achieved by means of the firm’s reputation and location, one of a class of intangible assets belonging to the firm, which may also include the names of its products ('brands') and other forms of goodwill.

Since the production of goods or services typically uses tangible assets in addition to labour, the firm will also have access to assets used in production. These may include the premises where work takes place, and/or where trade is carried on with consumers. Search costs arising from information asymmetries relate not only to the interaction between workers and consumers, but also to the interaction between different types of worker, once specialisation of function comes into play within a single firm. This suggests that another ‘asset’ which the firm controls is the organisational structure which makes the necessary co-ordination possible.

The work of Sanford Grossman, Oliver Hart and John Moore has helped to confirm this identification of the firm with control over business assets. The assets in question may be assets required for production or, more abstractly, intangibles such as goodwill without which workers would find it difficult to trade with consumers. Specifically, control over assets is identified with ‘residual decision rights’ — those rights which have not been explicitly contracted away. Grossman and Hart (1986) point out that

control or ownership is never absolute. For example a firm that owns a machine may not be able to sell it without the permission of the lenders for which the machine serves as collateral; more generally, a firm may give another firm specific authority over its machines. However, ownership gives the owner all rights to use the machine that he has not voluntarily given away or that the government or some other party has not taken by force. (p.694)

The crucial characteristic which distinguishes the firm’s workers from external parties with whom the firm contracts for supplementary inputs is the dependence of workers on the firm’s assets, rather than their legal relations with the firm. Thus workers who are notionally self-employed may be de facto employees if they need to employ assets over which the firm has control. The relationship between a firm’s control over assets and its control over workers is explained further in Hart and Moore (1990).

We suppose that the sole right possessed by the owner of an asset is his ability to exclude others from the use of that asset. ... [C]ontrol over a physical asset in this sense can lead indirectly to control over human assets. For example, if a group of workers requires the use of an asset to be productive, then the fact that the owner, party 1 say, has the power to exclude some or all of these workers from the asset later on (i.e. he can fire them selectively) will cause the workers to act partially in party 1’s interest. (p.1121)

Reasons why vertical separation may be suboptimal

Say that vertical separation can under certain circumstances lead to suboptimal outcomes. We need to ask why it is not possible for firms to to use contracts rather than merger to eliminate these inefficiencies. First, consider the question of production decisions. It has been argued that these may be sufficiently complex such that they cannot be specified completely ex ante.

[It] may be difficult, if not impossible, to describe precisely the input characteristics required in the future even though these characteristics might be easily described ex post. If a contract for future delivery only vaguely describes the characteristics of the good to be delivered, the supplier may have strong incentives ex post to deliver an ineffective input. Then, despite the presence of the contract, the parties will essentially be left to bargain over the procurement of the input that is really needed. For instance, IBM may not be capable of describing what sort of microchip it wants Intel to deliver five years from now for a computer that it is currently developing, even though in due time it will be able to describe its needs precisely. In this case, IBM may not gain much from writing a long-term future delivery contract with Intel. (Bolton and Whinston 1993, p.127)

Secondly, it has been argued that cost and income streams cannot necessarily be transferred by contract because of the difficulties of verifying such streams. Hart and Tirole (1990) point to the weakness of any agreement which attempts to contract away all or part of an owner’s return stream, such as a compensation package for a manager based on observed profits, or other types of profit-sharing.

Profit-sharing may be difficult to implement in the absence of integration ... because independent units can divert money and misrepresent profits. ... [C]onsider an independent unit, A, that has signed a profit-sharing agreement with firm B. One way A can misrepresent and divert its profits is by purchasing an input at an inflated price from another company in which A’s owners have an interest. It may be hard for B to write an enforceable contract ex ante to prevent such a diversion, even though B may be well aware of the practice ex post (the information that the input is overpriced is observable but not verifiable). On the other hand, if A and B are integrated, B can refuse ex post A’s manager’s request to spend company resources on the expensive input, thus effectively blocking the transaction. This is because B now possesses residual rights of control over company A’s resources by virtue of integration. (pp.206-207)

These points help explain why there may be advantages to vertical integration which cannot be duplicated even by sufficiently complex contracts between separated upstream and downstream firms. The next post will look in greater detail at the internal mechanics of an integrated firm, and consider whether similar limitations may affect relations between upstream and downstream units even after a merger has taken place.

REFERENCES
Bolton, P. and Whinston, M. (1993), ‘Incomplete contracts, vertical integration, and supply assurance’, Review of Economic Studies, 60, 121-148.
Grossman, S. and Hart, O. (1986), ‘The costs and benefits of ownership: A theory of vertical and lateral integration’, Journal of Political Economy, 94, 691-719.
Hart, O. and Moore, J. (1990), ‘Property rights and the nature of the firm’, Journal of Political Economy, 98, 1119-1158.
Hart, O. and Tirole, J. (1990), ‘Vertical integration and market foreclosure’, Brookings Papers on Economic Activity (Special Issue), 205-276.

Two and a half millennia after Parmenides

Raymond Tallis has written an interesting article about the Pre-Socratic philosopher Parmenides in the latest Prospect, as a taster for his forthcoming book on the same topic.

The Pre-Socratics suffer from our having relatively little information about them, and the fact that little of their material survives. They were also in the invidious position of having to invent philosophy from scratch, and of speaking to an audience unfamiliar with the flavour and purpose of philosophical thought. We should therefore not be surprised if their statements, while at times profound, are on the simplistic side.

There is a temptation to read more into Pre-Socratic utterances than is justified. It isn't possible to conclude very much from the fragments we have, beyond the fact that there were intellectuals in that period of history having interesting philosophical thoughts. Interpreting an individual's complete philosophical outlook from what survives has a tendency to move from speculation into fantasy. Whole academic papers are written on the question of whether some fragment of Heraclitus should be interpreted one way or the other. (The interpretation sometimes hinges on how a single word in a particular fragment should be translated.)

While Tallis makes some thought-provoking points, he falls into the same trap.

[In Parmenides' thought] human consciousness had a crucial encounter with itself. This was, I believe, a decisive moment in the long awakening of the human species to its own nature. From this self-encounter resulted the cognitive self-criticism, the profound critical sense that gave birth to the unfolding intellectual dramas of metaphysics and science that have in the last century or so approached an impasse.

Well, perhaps, and Tallis is not alone in wishing to make grandiose claims on his behalf — Nietzsche did it, ditto a number of more recent professional philosophers. But it seems highly speculative. While Plato said nice things about Parmenides, this in itself is not conclusive proof that the latter was indeed the essential foundation for the former, let alone the basis of Plato's metaphysics, as some have suggested.

Parmenides' key idea is usually thought to have been that change is an illusion: ultimately, everything that exists continues to exist. This is an insight comparable to Heraclitus's that you cannot step into the same river twice: a useful reminder about the 'boggliness' of reality, and that common sense concepts don't work very well when you try to analyse the fundamental nature of things. Notably, it is also — on the face of it — saying the opposite from the one about stepping into a river. Conclusion? The Pre-Socratics had some interesting ideas, but it's questionable whether they amounted to full-blown philosophical theories, let alone scientific ones. Still, it is good to be reminded that the metaphysical debate about change versus continuity goes back to the 5th century BC.

Tallis is on more questionable ground when he starts to make claims about Parmenides' contribution to epistemology. While it was useful to state that knowledge comes from analysis rather than perception, and to draw a distinction between appearance and reality, as Parmenides did, Tallis surely goes too far when he says that

In his short poem, thought and knowledge encounter themselves head on for the first time. This is such a huge advance in self-consciousness that it is no exaggeration to call it an "awakening." …The pre-Socratic revolution in thought that Parmenides brought to its climax is, I believe, a more compelling epistemological break than any that Foucault claimed to discover in post-Renaissance humanism.

Tallis asks why this development happened when it did. His answers involve giving political developments priority over intellectual ones — a common move, but a speculative one, and based on the ideological assumption that individuals cannot make innovations without being prompted to do so by their social environment.

Why, hundreds of thousands of years after human beings woke to the outside world as an object of knowledge separate from themselves, did they awaken to knowledge itself? What was it that fostered this collision of human consciousness with itself, such that thought came to think about itself and knowledge inquired into its own basis? …

The pre-Socratic awakening was the result of a unique concatenation of circumstances in place by the 7th century BC. In his classic investigation The Origin of Greek Thought, published half a century ago, J P Vernant connects the pre-Socratic awakening with the rise of the polis, or city state. …

Another driver to the explicitness of thought that made the Parmenidean self-encounter of human consciousness more likely was the rise of cities. … There is one more important driver: writing. This is an extraordinary technology: it stores human consciousness outside of the human body.

Such assertions may seem axiomatic in a post-structuralist culture, but they are highly theory-laden. There is no less evidence for the opposite claim, i.e. that socio-political developments were inspired by philosophical ones. In following the standard line, Tallis comes close to the reductionist thesis that consciousness, or at least thinking about consciousness, is a product of social forces.

Tallis's article becomes more interesting at the end when it turns away from its ostensible subject, and talks about our present intellectual situation.

Over the last century, there has been a growing feeling that in crucial areas of knowledge, we have reached an impasse. For instance, the endeavour to turn the scientific gaze on our own consciousness has run into a brick wall. Although you wouldn't know it from the excitement surrounding brain science, we have made no progress in understanding how it is that we are conscious and are aware of being located in a world that we in part construct and in part encounter as a given. ...

Dismissing the importance of subjective experiences, or "qualia"—a common ploy among the champions of neurophilosophy such as Daniel Dennett—keeps the impression of progress alive, but this is cheating. Biological science—evolutionary theory and so on—is increasingly assimilating itself to physics, chemistry and mathematics. Gene-eyed evolutionary theory and the rise of molecular biology forge closer connections between the biosphere and what Richard Dawkins has called "the blind forces of physics." Not only does this deepen the tension between an objective understanding of ourselves as organisms and our sense of being conscious agents, it exposes the biological sciences to the difficulties our understanding of the physical world is encountering. At the apex of contemporary physics, we have two mighty theories—quantum mechanics and the general theory of relativity—which are incompatible. The attempt to unite the two theories in "superstring theory" has produced a sterile landscape of largely untestable theories … Quantum mechanics, as Richard Feynman repeatedly pointed out, is incomprehensible, for all its extraordinary effectiveness.

He concludes by making the curious suggestion that a solution to these problems can somehow be found in Parmenides’ original insights.

We need to return to the Parmenidean moment to see whether, without losing all the gains that post-Parmenidean thought has brought us, there might be another cognitive journey from that which western thought has taken.

Tallis is right to point to the impasse and sterility which many fundamental areas of science and philosophy have reached. Hanging this observation on the utterances of a minor philosophical figure some two and half millennia ago, however, seems a little contrived. A more persuasive connection between the two periods might have been made as follows, but would probably have been too ideologically incorrect for Prospect Magazine.

'We need to recognise that the revolutionary insights of the Pre-Socratics were made by independent thinkers operating outside an institutional environment, supported by private capital. If we wish to continue to make significant progress, we need to consider whether a different political route from the one which we have taken might be required to restore to us the cultural advantages of classical Greece.'

The theory of the second-best

One of the few provable useful results in economics is the one about markets producing an optimal outcome.

If all goods and services in an economy are traded via perfectly competitive free markets, the resulting outcome is efficient (i.e. Pareto-efficient), i.e. there is no other possible arrangement of available resources in which some would be better off and no one would be worse off.

By contrast, an “inefficient” outcome is one where the position of some can be improved without making anyone else’s position worse, e.g. where the benefits of exchange have not been fully exploited.

This is potentially a very useful result, because if we want to ensure that things are as good as they could be (ignoring redistribution issues) we need not first calculate everyone’s happiness under various different conditions. All we need do is set up perfectly competitive (PC) markets and let people trade amongst themselves. This is just as well, since it is impossible in practice to know what people’s happiness level is under different conditions, or to find out all possible preferences between different outcomes for every individual. We may not even need to do anything as active as “setting up markets” since they tend to develop spontaneously.

If we currently don’t have conditions of PC markets, the way to get to efficiency is simple, in theory: do whatever it takes to get to precisely those conditions.

The problem is that, in practice — for various reasons, e.g. political — we may not be able to get to PC conditions. We may therefore have to choose between other, suboptimal alternatives, and try to decide which of those is preferable from the point of view of efficiency.

What does economics have to tell us about how to optimise efficiency, if we cannot achieve perfect competition)? There are two ways of dealing with the "problem of the second best" for policy purposes. The first favours government intervention, the second does not.

1) If we had information about the preferences of every individual in the economy, we could calculate what the range of possible optimal states are, given the constraints we have to work with. (Call these states “second-best solutions".) In that case, it might turn out that, if the economy departs from PC in one specific area but is PC elsewhere, we will only be able to get to a second-best solution by departing from PC in other areas as well. In fact, it can be shown that for very simple scenarios, that is the case — i.e. it is better to deviate from perfect competition in all areas rather than just in some.

This is sometimes taken to prove that in certain cases government intervention is better than laissez-faire as a way of generating the best possible outcome, given the constraints. But note that this conclusion depends on knowing everybody’s preferences, which in practice is impossible. The great benefit of the strict-PC model — of being certain that the outcome will be efficient, without having to know anything about people’s preferences — does not apply here.

2) The other way of treating the problem of the second best is to advocate agnosticism. If we do not have perfect PC conditions and cannot get to them, and we do not know everyone’s preferences, then we can’t know whether any particular policy change will move things in the direction of greater efficiency. Even if a policy change appears to be moving things in the direction of PC conditions, it might easily result in less overall efficiency.

Now there are two ways to interpret treatment (2), either of which might be appropriate depending on the circumstances.

(2a) One is to be conservative, in the sense of being cautious about doing anything, especially major changes. They might do harm on balance, rather than good. This generates the opposite conclusion to that of (1), in the sense that you should avoid tinkering further with an already imperfect system in case you make it worse.

(2b) The other way to react is to adopt a muddle-through approach, for which there is no strict justification, but which might be the best one can do, on a sort of hopeful common-sense basis. This could be taken to mean, we should try to aim at the nearest thing to PC in all markets, being careful to ensure that no major areas are omitted.

The one thing second-best theory can definitely tell us is the following: one should be wary of policy changes which involve partial marketisation of a given area. E.g. if the intergenerational market for private capital (= inheritance) is heavily distorted by estate duties, it is not necessarily a good idea to marketise (i.e. remove subsidies from) cultural institutions such as universities or opera houses.

Also — though one does not really need second-best theory for this — it may well be misguided to impose artificial marketisation, e.g. by making academics or medical professionals try to prove they are generating “value for money”. There is no hard support from economic theory for the idea that anything other than a genuine market (where the genuine end users are able to vote with their wallets) will generate any benefit whatsoever.

The standard textbook interpretation of the point about second-best (originally made by Richard Lipsey and Kelvin Lancaster *) is (1) above, i.e. the version which appears to favour government intervention. This interpretation is at best biased, and at worst simply false, but is very common. Dani Rodrik, for example, uses it when he says that

the First Fundamental Theorem of Welfare Economics is proof, in view of its long list of prerequisites, that market outcome can be improved by well-designed interventions.

This is not exactly false, but does seem to exaggerate the case in favour of intervention. The best that could be said is:

The First Fundamental Theorem of Welfare Economics is proof, in view of its long list of prerequisites, that interventions may not necessarily make things worse.

In March I made this point on the Talk page of the Wikipedia article, where the same misinterpretation was being used.

This entry is incomplete as it stands, and in a way which generates a political bias i.e. in favour of state intervention.

Another way of looking at the Lipsey/Lancaster point is as follows. If you are not at a Pareto-optimal point for the economy, you don't know whether any change that doesn't actually take you onto an optimal point is going to improve efficiency (i.e. make everyone better off). Even when you move in what appears to be the direction of greater efficiency, e.g. by changing all controllable parameters to an average of where you are now and where a Pareto optimum is, you might be making things less efficient i.e. making everyone worse off.

So another moral (apart from the one given) is that, when you have a market that is already regulated or otherwise distorted, it is not necessarily a good idea to move in the direction of less distortion. You can be sure that if you can get to a Pareto optimum, that is a good thing (at least in terms of efficiency); apart from that, you can't be certain of the effects of different policy changes. This is a consequence of the severely restricted conclusions of Pareto theory.

In fact, the moral given in the entry is questionable as stated. It isn't really the case that intervention to move things in a direction different from the pro-market one is sometimes a good idea. It's just that such a move might be a good thing, only neither the government nor anyone else can ever know if it would or not.

In a paper published in June, Professor Lipsey himself came out in favour of the second interpretation.

The upshot is that in practical situations, as opposed to theoretical models, we do not know the necessary and sufficient conditions for achieving an economy-wide, first-best allocation of resources. Achieving an economy-wide second best optimum allocation looks even more difficult than achieving the first best. Without a model of the economy’s general equilibrium that contains most let alone all of the above sources, we cannot specify the existing situation formally and so cannot calculate the second best optimum setting for any one source that is subject to policy change. This is an important point since much of the literature that is critical of second best theory assumes that economists know a distortion when they see one and know that the ideal policy is to remove the distortion directly, something that is necessarily welfare improving only in the imaginary one-distortion world.

* R. Lipsey and K. Lancaster (1956), 'The General Theory of Second Best', Review of Economic Studies 24, 11-32.

(originally published on the mediocracy blog)

Credible threats, moral hazard and Northern Rock

Continuing last week's post on game theory

Entry deterrence

'Entry deterrence' is an example of trying to manipulate a rival player's moves. In this case, it involves an incumbent firm trying to prevent the entry of potential rivals into a market.

Successful entry deterrence depends on avoiding the non-credible threat problem. If you want to make things too difficult for a potential entrant to bother entering, you have to do so in a way which binds you, i.e. you have to commit to a particular strategy. This has to involve ex ante (i.e. prior to the other player’s move) and irreversible action which prima facie is suboptimal for player 1 (and therefore is said to be ‘strategic’, i.e. undertaken only for the purposes of affecting the other player’s behaviour) but which ultimately pays because it succeeds in deterring entry.

Excess (in the sense of surplus) capacity is not an effective way of deterring entry; in fact it represents a non-credible-threat. An incumbent would never expand capacity in response to entry, he would always contract. (Unless there is imperfect information, in which case he may try to convince the other player he is irrational.) However, over-investment in capacity may succeed in deterring entry. This is the Dixit* model in which the incumbent invests irreversibly to expand the capacity at which he can produce at low marginal cost, beyond what he would do left to himself. The point is that this results in a post-entry equilibrium in which his output is higher than what it would have been, and the entrant’s lower — indeed, so low that the latter can’t cover its fixed cost.

Moral Hazard

'Moral hazard' arises when player A wishes to contract with player B for the performance of a variable task by B, the outcome of which will depend partly on (i) B's effort and partly on (ii) random factors, and where it is impossible to ascertain how much the outcome is due to (i) versus (ii). The problem is that B does not have as much incentive to perform as would be optimal. In the case of theft insurance, for example, the insured does not have the ideal level of incentive to protect his property because the insurer cannot monitor what he does, and he will therefore tend to under-protect it.

There is a connection between credible threats and moral hazard. To avoid moral hazard, A wants B to believe there will be penalties for indulging in 'immoral' behaviour. However, the threat to penalise errant behaviour has to be credible. Either the penalty has to be unavoidable, e.g. criminal legal sanctions, or it has to be somehow in A's interests to apply it. The problem is that the application of a punishment is not usually intrinsically beneficial for the punisher. One possible way out is through reputation: if A's reputation for truth-telling and toughness is valuable to A, then A announcing publicly that a penalty will be imposed could lead to a cost for A if he then fails to implement. In this way, the threat to punish would become credible.

Applying this to the Bank of England, a threat not to bail out a bank in trouble except in very limited circumstances is at risk of not being credible and therefore of not being effectual, unless reneging on the threat can be regarded as somehow costly for the Bank. However, it is not clear how the Bank, or any of its agents, could suffer from the failure to penalise an errant lender. Possibly when the Bank was still relatively controlled by the government (pre-1997), the desire of the ruling party to be re-elected could have provided such an incentive.

When there is imperfect information about whether the failure to carry out a threat is costly for the threatener, it is possible for the threat to be credible by exploiting uncertainty. However, once a player has reneged on his threat without obvious negative repercussions, the possibility of future credible threats is more or less eliminated.

* Dixit, A. (1980) 'The Role of Investment in Entry Deterrence', Economic Journal 90, 95-106.

A short introduction to game theory

In game theory, we are usually looking for one or more equilibria (ideally only one), which we regard as representing the likely outcome of a particular situation. The principal criteria which an equilibrium is expected to satisfy are the Nash equilibrium condition and 'subgame perfection'.

Dominant strategies

We can write the strategy of player i as s_i. By strategy we mean a particular move or policy, e.g. “produce low output” (collude), or “cooperate if and only if the other player did so the previous round” (trigger).

We can write the payoff to player 1
if player 1 plays s₁ and player 2 plays s₂
as u₁(s₁,s₂).

If u₁(s₁^A,s₂) < u₁(s₁^B, s₂) for all possible s₂ and some s₁^B
(i.e. whatever player 2 does, it is possible for player 1 to do better than s₁^A)
then s₁^A is a dominated strategy.

If a strategy remains after iterative removal of all dominated strategies, it is a rationalisable strategy.

If there is only one rationalisable strategy, it is the dominant strategy (e.g. “defect” in the Prisoner's Dilemma game).

Nash Equilibrium

For n players, (s₁*,s₂*,…,s_n*) is a Nash equilibrium (NE) if and only if:
u_i(s₁*,s₂*,…,s_i*,…,s_n*) ³ u_i(s₁*,s₂*,…,s_i,…,s_n*) for all s_i and all i.

All NEs consist of rationalisable strategies, but not all combinations of rationalisable strategies are NEs.

All combinations of dominant strategies are NEs, but not all NEs consist of dominant strategies.

Mixed strategy equilibrium

A mixed strategy is a probability distribution over strategies. I.e. a given player is playing each of his possible strategies with some probability. For example, firm A produces high output with 40% probability and low output with 60%, and firm B similarly mixes these strategies, but in the ratio 70:30. The game may be one-shot, so the point isn’t necessarily that the players alternate between strategies.

In this case the NE consists of optimal probability choices by each player given the probability choices of other players.

Once you allow for mixed strategies then every (finite) game has at least one NE.

Non-cooperative game

In a cooperative game, the rules permit binding agreements prior to play. (Hence collusion would be possible in a one-shot cooperative game.) In practice, we are usually concerned with games in which this is not possible, i.e. a non-coooperative game.

Games of complete information

• Players’ payoffs as functions of other players' moves are common knowledge.
• Each player knows that other players are 'rational' (i.e. payoff-maximising), and knows that they know that he is rational.

Static and dynamic games

In a static (or ‘one-shot’) game, players move simultaneously and only once. In a dynamic game, players either move alternately, or more than once, or both. Bertrand and Cournot models of oligopoly competition are both static games, while the Stackelberg model (firm B moves after firm A) is a dynamic game.

An equilibrium for a dynamic game must satisfy subgame perfection.

Normal and extensive forms

A game expressed in ‘normal form’ is in the form of a payoff matrix, as shown below for the Prisoner's Dilemma game.

A game expressed in ‘extensive form’ shows the ‘tree’ of the possible move paths depending on what each player does at each stage. A dynamic game can only be shown in extensive form.

Repeated games

The same agents repeatedly playing a given one-shot game (“form game”) in sequence is called a supergame. A supergame can consist of either a finite, or an infinite, repetition of a form game. Or we could have a game with a certain probability p of being repeated, i.e. a probability 1 – p of breakdown.

A strategy in this context can be contingent on what other players have done in previous moves.

Subgame perfection

For a dynamic game, some Nash equilibria are not acceptable as solutions because one or more players will want to, and be able to, avoid those outcomes. The subgame perfection criterion demands that, at each stage of the game, the strategy followed is still optimal from that point on.

Non-credible threat

A 'non-credible threat' is a strategy that one player is trying to use to manipulate the behaviour of another (usually via the second move in a sequential game), which forms part of a Nash equilibrium but one that is not subgame perfect.

The strategy is one which is being claimed in some way by the threatening player (e.g. by means of a signal that he is capable of using it) but which is not credible: although the threatened player’s optimal response to the strategy is to do what the threatening player wants, the former knows that by moving first in a different way, the latter will adopt another strategy to generate a different Nash equilibrium.

In a sense, there is no ‘credible threat’ — the term ‘threat’ implies that player 1 will do something specifically designed to harm player 2 if player 2 doesn’t comply, but such a threat would never be carried out in a finite game with perfect information because such a move would not be optimal for player 2. Player 2 will always ‘accommodate’ when it comes to it.

[Next week: applying game theory to Northern Rock & the Bank of England]