'Chicken' and verification

Professor Ian Bellany

It was Bertrand Russell in 1959 at the age of 87 and whose knowledge of the habits of bored American teenagers might have been thought to be somewhat slight - James Mill yes, James Dean no - who is nonetheless credited with introducing the game of chicken into game theory (or perhaps vice versa). Two drivers speed towards each other, their cars straddling the white line in the middle of the road. The first one to swerve loses and is called 'chicken'. Plainly the way to play this game is always to be doing the opposite of what the other player does. In such a case neither player wishes he or she had played differently. But this is not a recipe for winning. That needs something else - you need to be the first to make a binding commitment never to swerve.

Chicken is very widespread. Voting is a game of chicken. If a lot of other people vote you are well advised to have stayed at home since the chance of your vote being decisive in such a case is virtually zero; on the other hand if virtually everyone else stayed at home, your best bet would be to vote, when your vote would have some reasonable chance (reasonable in terms of the cost to you of the act of voting) of affecting the outcome.

Chicken and verification

The verification of arms control agreements is a game of chicken. The inspecting body can choose between subjecting a state party to close inspection or trusting the state party. The state party can choose between not violating the agreement and cheating on it. More generally each side can choose either to cooperate or defect. In the event of an untrusting or defecting close inspection, the state party prefers to be trustworthily and cooperatively 'clean'; in the event of something more perfunctory and trusting on the part of the inspectorate the state will prefer to have cheated or defected. Note we are talking here of a worthwhile arms control agreement which has a risk of failure in that it is trying to bind at least some of the states parties to act contrary to their normal impulses.

If we as interested observers want the inspecting body to win, then all we need ask it to do is commit itself always to carry out comprehensively thorough inspections. But this is easier to say than to do, since we may ask to whom or what are these commitments made. Russell's chicken contestant can in theory mortgage the family home to place a huge bet on herself to win the game and have lawyers solemnly attest to the fact before the contest is due to occur. Possibly it is not too far fetched to imagine, sitting above the individual inspecting organisations attached to multilateral arms control treaties, a new independent regulating body, an 'OFSTED', with the job of ensuring that the CTBT or the CWC (or even an updated BWC) gets inspected properly. Alternatively, or even additionally to supervision from above there could be supervision from below, with NGO's active in holding informal audits of the inspecting body's performance, on behalf of 'world public opinion'.

But this is only half an answer since it begs the question of what is meant by 'properly'. In the case of the CTBT there are two sorts of verification - routine remote sensing plus special on-site inspections to follow up suspicious events. But for the inspectorate, non-routine verification is expensive at the margin. Coming on top of the sunk cost of a network of remote sensing stations, on-site inspections are expensive to arrange and carry out. They are also normally expensive for states parties to have to submit to even when they have absolutely nothing (in terms of the agreement) to hide. Moreover, experience shows that international funding for international undertakings, including arms control inspection agencies, can never be relied on to be more than barely sufficient, if that.

How much (inspection) is enough?

Fortunately there is a way both to keep costs down and inspect properly. If the inspectorate could commit itself to routine remote sensing and to follow up only a proportion of the suspicious events, it could still guarantee itself to win the game, provided its follow-up inspections on site were not too infrequent. And we can use the chicken game again to indicate what may be meant by the right level of frequency for follow-up inspections.

Inspectorate       Inspect Trust State party Adhere - (Network Cost + Inconvenience Cost), - Network Cost,   Cheat - (Network Cost + Inconvenience Cost + 'fine' for cheating), (Positive Gain -Network Cost),

The four boxes on the lower right of the diagram represent the payoff to a state party in four imaginable situations (in this case the payoffs are actually costs, being negative and shown as such and in the form of outgoings except possibly for the sum in the South East box). The North West box shows only two costs, the basic contribution to the sensor network plus the inconvenience cost of undergoing an on-site inspection. The North East box shows only one cost, the contribution to the network. The South West box is like the N-W box except that there is an additional cost called a 'fine' - the cost to the state party of the consequences for the state party of being caught cheating on the agreement (it is assumed for simplicity that there is no cheating so subtle as to be capable of deceiving an on-site inspection). The South East box is like the N-E box, with the big difference that the cost can become a net gain made up of a 'positive gain' in the form of the benefit the state gains through cheating on the treaty and not being found out, less the cost of subscribing to the network.

Some simple arithmetic (see Annex) indicates that no rational state party would prefer cheating to adherence to the treaty terms as long as the inspectorate in (any one year, say) carries out inspections of suspicious events with a probability greater than:

(Positive gain )/(Positive gain PLUS Fine) or: G/(G + F)

Obviously, for a country such as Denmark in the case of the CTB the positive gain is pretty well zero (if that) and there would be no point in bothering to carry out an on-site inspection there more than once every hundred (say) suspicious events. But the world is not made of Denmarks and the frequency of on-site inspection is set not by the best case but by the worst.

Conclusions

How can we make use of this awkward reality which follows from the prior necessity to treat states as equals? Well, the predicted frequency of follow-up of suspicious events for every state is given by the predicted frequency for the state party whose probability quotient is biggest. And this is for that state taken to have the most to gain from cheating RELATIVE to the damage it would expect to have inflicted on it from other treaty parties as a consequence of being found out (see graph, where a state with a relative gain (G/F) of 3 - supposing for the moment that we can actually put a figure on such things - sets the frequency of on-site inspection of suspicious events at 75%).

Can we say more? Well, in reality we cannot put actual figures to the ratio of the gain a state might hope to make with getting away with cheating on the agreement to the costs of the 'fine' it would face (in the form, say, of international economic sanctions) if it were found out. But we can make some qualitative judgements.

For instance, we can see that powerful states parties are not really the problem (not in this context, but of course no multilateral arms control agreement stands much chance unless it has the backing of the most powerful states to begin with). Already powerful, they would not have much to gain from cheating even if the impact of any feasible 'fine' would also be small. Most weak states are not the problem either. Their gain from cheating could be sizeable but vulnerability to the 'fine' would also normally be sizeable. No, the criterion is set by those weak states which enjoy some kind of immunity to 'fines'. These are states which are really semi-detached members of the international system, for example states engaging very little in international trade (which may be a reason for weakness in the first place), or states which stand aloof from or are kept out of other sorts of functional international organisation, such as alliances.

Now this consideration brings us to our final point. When such semi-detached small states sign up to a new arms control treaty, they are making at the least a gesture that a history of semi-detachment may be behind them. So the arms control treaty's inspecting authorities, once the last such semi-detached state has been corralled within the treaty and in effect been allowed to set the severity of the inspection regime, should be alert to the possibility that any socialising effect treaty membership might have on such states could be more broadly beneficial. If treaty membership is followed for the states in question by fuller participation within the international system generally (which the case of North Korea and the NPT shows need not necessarily happen, of course), they automatically acquire 'more to lose' from being found in breach of the treaty. This automatically makes the original inspection regime too severe and justifies its being eased (provided of course in the meantime the states parties had all remained in good standing).

The same point can just as easily and less consolingly be turned on its head. Any successful arms control treaty but without universal participation at whose door once semi-detached states decide belatedly to knock for admission cannot simply admit them like prodigal sons. Either, on allowing them inside it must tighten up on its inspection procedures for all states parties, which seems impracticable, or, more feasibly, the newcomers should be asked to spend a probationary period outside full treaty membership whilst they establish their credentials as more fully integrated members of the international system.

Annex

Suppose the inspectorate inspects suspicious events with a probability q. Then the state party adhering to the treaty receives a total payoff (allocating symbols in the obvious way) of: -q(N + I) - (1 - q)(N) whilst a state party cheating obtains: -q(N + I + F) + (1 - q)(G - N) A state party is indifferent between cheating and not cheating when these two expressions are equal, which in turn happens when: q = G/(G + F) And the rational state party will choose not to cheat whenever q is greater than this amount.