A threat may become believable because its author cannot guarantee that the danger will remain a threat. The earlier Commitment showed a player gaining strength by surrendering a future choice; The Credibility asked whether the response promised would actually be chosen when its moment arrived. Brinkmanship takes that inquiry into a situation neither party entirely commands. The threatened catastrophe can be something both would avoid if offered a final, dependable choice. What alters the encounter is the possibility that events will reach it without that choice being available. Schelling’s contribution was to distinguish a commitment to inflict a loss from a situation exposing both sides to a chance of suffering it. The opponent need not believe that you welcome the worst outcome. He must believe that the course being taken could bring it about despite your wish to escape.
The credibility of such a threat rests on an actual limit to control. Announcing that one might do something ruinous leaves the other player to ask whether one would still choose it; greater theatrical uncertainty does not by itself change the answer. In Schelling’s account, accident, imperfect communication, third parties and the workings of collective decision can instead make the outcome uncertain even to the person issuing the threat. His image of the brink is a slope on which a person can slip, with the other party bound to share the fall. A sure footing and a choice whether to jump would present a different problem. The uncertainty here concerns the unfolding of events, and may persist even when each side knows that the other would prefer to avoid disaster. That gives the threat its distinctive force, and gives the force its cost.1
A small invented game makes the opponent’s calculation visible. Suppose conceding a disputed claim gives a player a payoff of zero. Resisting gives six if the encounter ends safely and minus a hundred if it ends in disaster. The player values these payoffs by their mathematical expectation, and timely concession is assumed to end the danger. With a one-in-ten chance of disaster, resistance is worth nine-tenths of six minus one-tenth of a hundred: minus 4.6. Concession therefore pays more. At zero risk, resistance is worth six and the conclusion reverses. The threshold lies where six times the probability of safety equals a hundred times the probability of disaster, a disaster probability of three fifty-thirds, about 5.66 per cent. The figures represent stipulated preferences and chances. They show how a feared possibility can change a choice without making the worst outcome certain; they supply no estimate of an actual crisis.2
The person creating the danger must face a calculation too. Extend the invented game: initiating the risky encounter costs one; the other’s concession brings eight; safe resistance brings nothing; disaster costs the initiator a hundred as well. If concession is assured, initiating yields seven rather than the zero available by abandoning the demand. If resistance follows, the same one-in-ten danger instead gives an expected payoff of minus eleven, including the initiation cost. These figures explain why willingness to begin need not mean willingness to suffer the ending. They also expose the importance of the game’s timing. We have stipulated that, once begun, the danger cannot be cancelled unilaterally during the response interval. If the initiator can certainly and costlessly remove it before any harm, and prefers doing so to accepting the risk, the opponent can reason through that escape. The claimed probability then needs a different foundation. A probability written into a payoff table cannot make a hollow threat credible.3
The time allowed for compliance can matter as much as the apparent size of the threat. Schelling distinguishes deterring an action from compelling a change already demanded: in the latter case, danger may continue while the other side prepares to respond. Our tidy illustration gave concession the power to end risk before anything happened. An actual process may allow no such clean interval. Even small repeated chances can accumulate: with an invented independent one-per-cent chance in each of a hundred periods, the probability of at least one disaster is about 63.4 per cent. Survival through one period is compatible with the danger having been real. A threat can thus injure both parties before its recipient has time or capacity to satisfy it. Increasing the danger may increase the pressure while destroying the very prospect of a settlement that would make the pressure worthwhile.4
An account of strategic force therefore leaves open the judgment of what should be done with it. A danger can be credible and impose costs on people who have no voice in the dispute. It can be taken seriously by an opponent who nevertheless lacks the power to comply. And the two sides can disagree about the chance itself, the meaning of an action or the route back to safety. Schelling’s imperfect decision process includes miscommunication and delegated authority, so the supposed master of the threat may know less about its operation than the word strategy suggests. Institutions that make intentions clearer, keep channels open or permit an orderly retreat can change the encounter by making control more reliable. In judging those arrangements, the losses they prevent belong in the account alongside any leverage they remove.5
The brink answers the plate’s question by locating credibility in the danger that remains after the threatener’s preference for safety has been admitted. Binding oneself to a certain response is one way of changing another person’s calculation. Becoming partly unable to govern a dangerous process is another, and the difference survives even when both begin with a deliberate act. Its promise is that a shared peril may induce accommodation; its burden is that the peril must be capable of defeating the intention that created it. The earlier plates asked how expectations and commitments shape a game. This one adds the possibility that a player shapes it by surrendering some mastery of the result. The next asks what follows when that power to shape the encounter is turned toward its rules: how a game might be designed so that the conduct it rewards serves the purpose for which it was made.