Fifty years ago, the economist Thomas Schelling applied the new mathematical tools of game theory in fields ranging from everyday disagreements to international politics. Prof Schelling’s work was inspiration for Stanley Kubrick’s Dr Strangelove. It won him a Nobel Prize in 2005.
Negotiation over divisive issues has never seemed so central to news events. A Democratic president is engaged in repeated budget confrontations with a Republican House of Representatives. The international community struggles to address Syria. And I have been thinking how, if Scotland were to vote for independence, the process of negotiation would unfold.
What the parties to a negotiation will accept is principally determined by their perceptions of the outcomes for each if they fail to reach agreement.President Barack Obama’s position today is immeasurably different from his position before November last year. Then he was seeking re-election; a shutdown of the US government would have left him as a failed one-term president. Now he will never face voters again. His concern is his legacy. Before he could not risk facing opponents down. Now he can.
By his actions, Bashar al-Assad has in effect ruled out any option for himself other than doing whatever is necessary to remain dictator of Syria. He has made what Prof Schelling termed a “credible” commitment: readiness to fight to the death must be accepted as a fact because it makes sense for him to implement that threat. The paradox of commitment, well described in the phrase “burning one’s boats”, is that limiting your options – in this case by arousing the revulsion of the world – may actually strengthen your position.
However, when Mario Draghi, president of the European Central Bank, says his institution will do “whatever it takes” to save the euro, his statement falls far short of a credible commitment: it makes sense for him to make the statement, but whether it makes sense to act on it depends on what, or how much, it actually does take.
Once the default positions of the parties are defined, successful negotiation is possible if – and only if – there is a possible outcome which is better for all the parties which must consent to the solution than a disagreement. The more players there are, the harder it is to achieve such an outcome.
Where there are gains that can be realised from agreement, the issue may move to how these can be shared. This kind of problem may be starkly posed as an “ultimatum game” – a scenario where the instructor offers two students a dollar if they can agree on how to share it. If you play the game for real, the participants often quickly agree to take 50 cents each. A sense of fairness plays a large role in our decisions, and many people will prefer to let the dollar slip through their fingers than accept a derisory offer from the other player.
But this “fair” outcome depends on the players having the same perceptions of the game and its possible outcomes, and the most common source of breakdown of negotiation is that they do not. The likelihood of a fair outcome is also influenced by the symmetry of the position of the two students, and the assumption that the game is played only once. If you play time and again, it is more likely that your strategy will be co-operative. Absent these conditions, matters become more complex.
Negotiations over Scottish independence are framed by the observation that neither the rest of the UK nor the EU has anything significant to gain from such negotiation – or any wish to conduct such negotiation at all. That gives them a strong bargaining position; in fact, they should expect to exact a large part of the gains Scotland perceives from independence as the price of their consent.
Yet matters are not quite so simple. If the people of Scotland vote for independence, an agreement on its terms must be reached. The status quo has ceased to be an option for the UK; there is no alternative to a negotiated settlement. But there are fundamental differences on the relevant timescale. A Scottish government loses credibility if it cannot proceed rapidly to resolution: a Westminster government can allow discussions to continue indefinitely. That leaves Scottish negotiators with few cards in their hand.