Game theory and the South China Sea conflict
When is it better not to be No 1? Whether it's in sports, academia or business, we are conditioned to believe that success means being first. We make decisions and adopt strategies geared towards putting us in a dominant position.
But there are contests where it may not be possible or even desirable to arrive at a dominant position - in the competition among companies for market share and resources, for example, or in the arms race among countries. A company's overly dominant market share invites anti-monopoly lawsuits, as Microsoft learned to its cost. Countries trying to dominate their region escalate tensions and instability, as with current disputes over the South China Sea discussed by the foreign ministers of China, the US and Southeast Asian countries in Cambodia last week.
Far better for all concerned (and for world peace) is to arrive at a situation where no player is inclined to make unilateral decisions that would change the status quo, knowing the set of decisions that other players could make. Enter game theory. Pioneered by the Hungarian-American polymath John von Neumann in the 1940s, game theory is the mathematics of how players decide strategies in different situations in the face of competing strategies acted out by other players. It is essentially a methodology to understand conflict and co-operation.
Posing questions in the context of a simplified model reveals the essential features of a conflict, shorn of its confusing real-life complications. In its simplest form, game theory assumes that players make rational decisions to maximise their benefits, possess all the available information and are fully aware of the decisions that can be made by other players.
Let's apply an elementary version of game theory to the conflicting territorial claims in our region.
China and Japan claim sovereignty over the Diaoyu Islands in the East China Sea. China and Vietnam claim sovereignty over the Spratly and Paracel islands in the South China Sea. Each country has offered few conciliatory gestures while taking action seen as provocative by the other.
China recently established the Sansha prefectural-level city to administer the Spratlys, Paracels, undersea atoll Macclesfield Bank and surrounding waters. Hanoi passed a law requiring foreign ships traversing the disputed waters to notify Vietnamese authorities. To assert its sovereignty over the Diaoyus, the Japanese government is considering buying them from a private owner.
Looking at the situation through the lens of game theory, we assume that each country can pursue a provocative or a conciliatory policy. In pursuing either action, each is acting rationally to maximise its interests and has full information on the benefit to itself and to the other country. The benefit for each country depends on the policy taken by both countries, an essential feature of conflict as described by game theory. (See diagram)
Blue represents China's policy and the benefit of that policy; red represents Vietnam's (or Japan's) policy and its benefit. When China is provocative and Vietnam conciliatory, China gains Z unit of benefit and Vietnam gets nothing.
Conversely, when Vietnam is provocative and China conciliatory, Vietnam gains Z unit of benefit and China gets nothing. When both countries are provocative, both get Y units of benefit. When both are conciliatory, both get X units of benefit.
This model reasonably hypotheses that when a country takes a provocative position, it hopes to intimidate the other country, reaping all the benefit. But when both countries adopt the same policy, the benefit will be less than that obtained when one country dominates. Thus Z is greater than either X or Y.
China will increase its benefit by moving to a provocative position regardless of what Vietnam does, increasing its benefit from X to Z if Vietnam is conciliatory and from 0 to Y if Vietnam is provocative.
For Vietnam, the situation is exactly the same. It will increase its benefit by moving to a provocative position regardless of what China does, increasing its benefit from X to Z if China is conciliatory and from 0 to Y if China is provocative.
Consequently, both countries will take a provocative position if they are not in one already, resulting in a benefit of Y units to each. The game results in what is known as a Nash equilibrium, named after the brilliant mathematician and Nobel laureate in economics John Nash: neither country will be inclined to change its position because such a move will lead to a deterioration of its benefit. This is the situation we see so far, with all South China Sea claimants taking a provocative position.
But is this a satisfactory equilibrium? No, because the benefit of conciliation X is greater than that of provocation Y. A provocative policy requires military preparation, and may disrupt transport and impact the flow of trade. So the benefit of both countries acting conciliatory is greater than when both are provocative.
Then why has the policy of provocation, which results in unsatisfying outcomes for both countries, become the equilibrium? If both countries have taken conciliatory positions, they are not inclined to change, for that will lead to a deterioration of their position. They will have reached another Nash equilibrium solution that is superior.
The problem is, this simple model does not allow for co-ordination and consultation between the countries. Instead, each country acts independently as if separated in different rooms, examining its own position in reaction to what the other country may do. Had they sat down together to consider the consequences of each policy, both would have rationally chosen conciliation, resulting in the highest benefit to both.
The obvious conclusion is that in the absence of consultation, countries may choose policies that create fewer benefits for all. On the other hand, co-operation will result in higher benefits for all - common sense that is not so common in the heat of nationalistic fervour.
This very simple game-theory model does not consider all the complexities in the interaction among countries. Benefits cannot be reduced to a single number, policy is not based on a single action, action is not static but evolves over time, and national leaders do not necessarily act rationally. Nor have we considered the elephant in the room, the US, lurching in the background.
After years of stalling, China has finally signalled a willingness to discuss with its Southeast Asian neighbours a 'code of conduct' in the South China Sea with limited enforceability - a small but conciliatory gesture perhaps?
Tom Yam is a Hong Kong-based management consultant with a doctorate in electrical engineering and an MBA from the Wharton School, University of Pennsylvania. He has worked at AT&T, Ernst & Young and IBM