The South China Sea Game: Does the FONOP Make Things Worse?

The decision of the United States to conduct Freedom of Navigation Operations (FONOPs) around the artificial islands in the South China Sea, which China uses for justifying her sovereigny claims in this area, has somewhat increased tensions between the two countries. The newspaper Global Times known for its notorious nationalism commented on the employment of the American destroyer USS Lassen in the disputed waters:

In face of the US harassment, Beijing should deal with Washington tactfully and prepare for the worst. This can convince the White House that China, despite its unwillingness, is not frightened to fight a war with the US in the region, and is determined to safeguard its national interests and dignity.

I am not particularly interested in the possibility of a major showdown between the Americans and Chinese. A more interesting question to ask is whether the FONOP made it harder to resolve the dispute peacefully to the benefit of all. By resolving the dispute I mean first of all a significant moderation of Chinese sovereignty claims.

There are two conventional wisdoms in the study of coercion that are two sides of the same coin. First, "rocking the boat" can make a threat more creadible. By saying that the U.S. will "sail, fly and operate wherever international law allows" AND indeed doing it, Washington is demonstrating resolve. Second, demonstrations of resolve make it harder for the target to back down. If I set the bridge on fire showing that I am prepared to fight and not willing to retreat, I leave my opponent with only two choices: fight of perrish. That is to say that it is much harder for China to moderate her claims now without losing face and honor.

We can try to approach the issue as an extensive form game in which two players make their moves sequentially. China makes the first move in the game having two choices: make excessive claims (A) or make moderate, cooperative claims (B). Because the payoff from a unilateral control of the SCS (U_A) clearly outweighs that of a multilateral control (U_B), China plays "excessive" claims.

A if U_A > U_B

B if U_A < U_B

Now, it is the U.S.'s turn. The question is how many choises the U.S. has responding to China's playing A. She can stand on the sidelines and oppose the claims of the Chinese. Another question is how to oppose. Washington can raise the stakes, e.g. through naval demonstrations as recently happened, or try to find a win-win solution by diplomatic means. So, there are essentially three choices: stand on the sidelines (XA), moderate (diplomatic) opposition (YA) and outright opposition (ZA).

Does it mean that by choosing "outright opposition", the U.S. make it harder for Beijing to back down? The answer is yes because China would not only suffer costs of of not having an unrestricted success to important maritime routes (C_B). She would also suffer reputational costs (C_R). Why did the U.S. then opt for a naval demonstration? The answer may be that the U.S. simply does not believe that China's appetite can be satisfied by moderation (strategy YA). That is, diplomacy only makes it easier for China to achieve the desired objective on the cheap, for unrestricted control over the SCS is a dominant strategy for China.

So, if China plays A and the U.S. responds with XA, China simply goes forward with construction works in the SCS and eventually starts to control the area. No costs are imposed on China. There is no reason for using strategy B (backing down from excessive claims)

U_A = B_A - C_A , where B_A is benefits from controlling the Sea and C_A costs associated with such foreign policy. In this case, C_A = 0; U_A = B_A.

If China plays A and the U.S. responds with YA, China gets some costs imposed for non-compliance C_A (C_A means here costs imposed for using strategy A).

U_A = B_A - C_A. Here, I assume that C_A > 0, but B_A > C_A.

U_B = B_B - C_B, where U_B is a payoff for aquiecsing to the U.S. demands, B_B and C_B benefits and costs of this decision respectively. I assume that B_B and C_B are fairly equal: China gets a moderate benefit (multilateral control of the SCS) by suffering only minor costs for backing down from her previous demands. U_B ≈ 0, U_A > U_B. Therefore, there is no reason for China to aquiesce to the U.S. demands and she continues her policy.

Finally, if China plays A and the U.S. responds with ZA, the costs for non-compliance C_A are dramatically increased. They might equal or even exceed the benefits of unilateral control.

So, if C_A > B_A, U_A < 0.

But although the payoff for strategy A can be negative, the payoff for backing down is even less because in addition to C_B (costs for foregoing unilateral control over the SCS) we now have also C_R ( reputational costs China would suffer at home and also internationally).

U_B = B_B - C_B - C_R < 0 < U_A.

This leads me to conclude that the U.S. had no choice but to escalate.

P.S. I was not able to make a so-called tree for this extensive game because it is impossible to upload pictures in the entry. I hope the "math" is not confusing. Not a big fan of it and by far not a specialist. I kind of think it makes my argument more precise.

I tweet at @IvanSamolovov