2005-10-21

Applying 'Game theory' to the Taiwan Strait problem, Google image and Anti-Secession Law

It is now widely known that you can see everything with google's satellite maps.

All major air-force bases in Taiwan can be viewed in google (see this, this or this for more pictures of air-bases in Hsinchu (with parked F-104), Chiayi, Pingtung, Tainan), taken maybe 1-2 years ago. Same for any other location on earth (e.g., San Diego Naval Base's Swatiska) except a few censored locations like the White House.

But more interesing is a 1:1 model of the Taichung Ching Chuan Gang (台中清泉岗) base built in NW China (the 2 white labels in the China map on the first picture indicates locations). In zooomed pictures below, the yellow ones are that of Taichung Ching Chuna Gang, grey ones from Badanjilin (巴丹吉林), in the desert in NW China.


  • There is nothing surprising and no need to be paranoid. Military exercise and model target can be found in Taiwan and any other parts of the world as well. If we can see this in google, the Pentagon and the armed forces in mainland and Taiwan all knew it long, long ago (and other sites). This is just to demonstrate the power google has given to the public.
  • In fact, one can say the GPS and targeting technology of the PLA is very primitive. Because sophisticared modern technology (used by US in gulf wars) will deem such mega target for training irrelevant, hence no need to build such target model
  • There may be a small connection to the controversial Arms Deal in Taiwan, in that the submarines and anti-subs are quite irrelevant in defending against an amphibious assaults. Michael Thurton was right that air control is more important than subs. But destruction of airports will neutralize this advantage. Taiwan only has so many airports, and the PAC-3 will always be outnumbered by PLA missiles. So it is not optimistic for Taiwan.

In realpolitik, peace is secured by deterrance and balance of power. Fortunately, nowadays the stakes for war are much higher thanks to globalization. A decent defense for Taiwan, and a decent attack power of the PLA could both help to secure peace across the strait.


According to the game theory exercise that earned this year's Nobel Prize, it is all about deterrant against any move that might escalate conflict. I will digress on Schelling's theory as per LofC's request. Schelling's theory can be illustrated with a simply analogy.

  1. Say if two people go into a duel with sword, the loser might suffer severy injury but may not die. So it is very common in the pre-gun era to go into sword duel (apart from other psychological, social and legal reasons)
  2. With the invention of a deadly weapon called gun, the stake becomes much higher. but one still can hope to kill the other in one shot and be opportunistis. The skilled shooter (or cheater) often is willing to take chance.
  3. However, if each person also holds a remote control, which will detonate a bomb that could kill both. He could press the remote at his last breath. There is no point going into a duel any more
  4. The remote controlled bomb is basically Schelling's theory of "deadly second strike". What Schelling did was to simply extend the basic von Neumann game theory of matrix (table) computation (A tabulation of score with columns and rows representing options of the 2 parties, single move game) into a time series analysis (more than one move for each party), and translate it from mathematics into layman's language. Threat of destruction prevents destruction from happening.
  5. One caveat, Game Theory analysis assume perfect information and best options choseon by both side. Incomplete information on one side will lead to entirely different choice and outcome (the movie Dr. Strangelove was probably made to help the US and USSR to make the right choices and disclosures)

To formulate a "game theory" model, we need to list the options of both players in a 2-dimensional matrix, mainland's options as column entries and Taiwan's row entries. The more the number of options we can contemplate, the larger this matrix is. We then proceed to assign values of each cell in the matrix: option m(x) vs option t(y), based on the result of option x from mainland and option y from Taiwan. A mathematical analysis can then be performed to find out which option (combination, with a probability mix) will generate the maximum value for the palyer (m or t), assuming the opponent is also applying the best strategic option mix available. This is the classical von Neumann model in the normal form. To apply Schelling's theory we need to apply many of these matrices as the follwing "turns" of the game. One may also needs to incorporate the options and responses of the US. The analysis could get immensely complicated.

  • Technical note: the first entry is the score for player 1 and the second entry the score for player 2
  • An example will be Play 1's best option is to apply option (x1,x2,x3) with probability (60%,40%,0%) and that for play 2 (30%,20%,50%)

Since among the scenarios there are some which involve conflict and probably even war. This is definitely a non-zero-sum game. (but not neccessarily negative sum, see my next post)

Fortunately, we can significantly simplify the problem if we know the scores of certain options are immensely higher than others. e.g. my earlier post about an extremely simplified case of long term sum of scores. The conlusion is to extend the status quo and put off confrontation.

For Taiwan this means to maintain its so-called "de facto independence", and avoid any action toward a "nominal independence". Even hardliner Lee Tenghui understands this. Unfortunately some within DPP and TSU (and enthusiastic foreigners) do not.

For the mainland, it needs to take a soft approach so as not to push Taiwan further away, while establishing significant barrier to any move away from status quo. Firing missiles in 1996 with no clear understanding of the consequence was idiotic. Recent moves to appeal for the opposition party is a good change. Quite counter-intuitively, the "Anti-Seccession" Law of PRC (for the American version, see here - salon.com requites you to view an ad for a "site pass", Salon has a great business concept which I will come back to in another post) also serves the same purpose, as Lee Kuan Yew correctly pointed out. If a unilateral move by Taiwan toward "nominal" (vs the so-called "de facto") independence will automatically trigger PLA reaction, the likelihood of such scenario will be greatly reduced, hence also the chance of a war. Leaking of the Badanjilin target model, interntionally or unintentionally, reinforces such threat and may help the statud quo.

Unfortunately, the ASL is vaguely worded, especially the Article 8 "that possibilities for a peaceful reunification should be completely exhausted (和平统一的可能性完全丧失)". Who is there to interpret "possibility"? What kind of idiot lawyer drafted this? Even if Taiwan declared independence today, I would argue, there is still possibility for unification in, say, 100 years later.

CCP inserted this clause to give itself more leeway as to how to define what would 'trigger' ASL. DPP is now questioning the claim of "no declaration no invasion", since CCP effectively retained the right to attack even without a formal declaration of indepedence. From the DPP's perspective, if you can attack me even if I behave, what is the point of listening to you.

This reflects extreme stupidity and complacency from CCP's side. Because only a threat which follows certain explicit and well-defined trigger is a real threat. By compromising to give itself a leeway, CCP has significantly sabotaged this threat.

Now go back to the game theory model. If the elements of the matrices are "disconnected", so that we can isolate certain sub-matrices (sub-square, or sub-rectangles, in mathematical language, it is "block-diagonalizable"). The analysis is simple, because we can use small sub-blocks of ASL and it won't entangle with other options. We could hence conclude that ASL helps to achieve the goal of maintaining status quo. However, if the sub-matrix interacts with the rest of the elements (in technical term, off-diagonal blocks are non-zero), the problem becomes more complicated. This is exactly what the last clause of ASL has done. So, please take that line away in the next NPC.

The above discussion is under the premise that status quo is the best long term objective. But if we try to think out of the box, this is not neccessarily so. I would discuss about this in my next post, which will start from a quote you heard in the movie Crouching Tiger Hidden Dragon.

8 comments:

Budding Sinologist said...

"submarines and anti-subs are quite irrelevant in defending against an amphibious assaults."

It seems I'm losing this battle as more and more people seem to be buying into this idea of yours and Turton's, but I would disagree.

Naval superiority (local naval superiority at minimum) is necessary for any hope of success in an amphibious invasion. Subs are vital to achieving naval superiority or denying it to one's enemy. Taiwanese submarines could attack troop transports as could the rest of Taiwan's navy, unless it is sunk by uncontested Chinese submarines.

I'm not doubting that air superiority is important, but as you point out that isn't a panacea. I don't think the ROC military wants all of its eggs in one basket.

dylan said...

Your comments about the importance of the clause leaving it entirely subject to Beijing's interpretation whether "possibilities for a peaceful reunification" are "completely exhausted" are spot on. And I think that clause highlights the fact that we are really talking about a two-level game on both sides of the Strait. Both CSB and HJT have domestic considerations and their external game is affected by the status of the internal game.

Sun Bin said...

dylan,

Yes, I believe HJT does not have full control (see recently posts from the88s, which are excellent), not yet. Many factions need to be appeased, including the military and the hawks. That is why the policies are always compromised (eg 2.1% instead of 5% appreciation of RMB in July). When such compromises are made, it often blurs, or even damages the original objective.

Michael Turton said...

Naval superiority (local naval superiority at minimum) is necessary for any hope of success in an amphibious invasion. Subs are vital to achieving naval superiority or denying it to one's enemy. Taiwanese submarines could attack troop transports as could the rest of Taiwan's navy, unless it is sunk by uncontested Chinese submarines.

Subs cause losses, which a determined enemy will take. Just like we did in our all invasions. Air power makes invasions possible/impossible. Period.

I can't imagine a scenario where Taiwan has subs + no air control and can still stop the Chinese from coming over.

Michael

Sun Bin said...

Budding Sinologist,

You would have been absolutely right, if the amphibious assault comes from a wide open sea on the east coast.

But it only takes a few dozen planes to carpet search the Taiwan strait. As soon as a sub is located, it is as dead as a turtle.

Having said that, I have to admit I have tried to simplify the scenarios. For example, there are a lot of diplomatic problems if US provides Taiwan with other training or attack weapons that Michael proposed. I focus on the strategic implication, the implications and conclusion should be fairly independent on small difference in detailed deployment.

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尤其是這一篇談「清泉崗」機場的文章鄙人極感興趣。
早先聽說大陸上有這麼一個仿建的機場,但一直不知何所在,看了您的報導後才茅塞頓開。
崗以「清泉」為名乃在紀念抗日戰爭時期一位國民党將軍「邱清泉」先生,這位將軍後來在「徐蚌會戰」(淮海戰役)中兵敗自殺殉國。
台灣有很多人對這個機場很有興趣,我也想「仿建」您的「布落格」,希望您不要介意!

Sun Bin said...

thanks.

please feel free to use the info or image from my post. i have also post some links to your site which you may find useful. i would also suggest you search on baidu.com (which would automatically search for both simplified and traditional chinese characters)

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