Why US concerns itself over Taiwan | A game theory perspective

Why does a country halfway around the globe risk itself to the possibilities of an all out war over an island that’s roughly 10,000+ kms away from it? On the off chance this doesn’t ring a bell or context cues were missed — Yes, we are talking about the US- CHINA standoff over Taiwan.

One oversimplified response could be the west’s eternal tussle with communist countries and their increasing influence— but I think US made its peace with China being communist as long as it opens it self for business — with the 1972 visit by United States President Richard Nixon that ended 25 years of zero communication or diplomatic ties between the two countries and was the key step in normalizing relations between the U.S. and the PRC.

Another starry eyed quick answer to this could be the United States standing up for perseverance of democracy, liberty and equality throughout the world. But if one has analyzed US intervention in world politics post WW2 — one would find instances of diabolical nature where preserving democracy was neither a stepping stone nor the end result of such interventions (eg: Albania, Argentina , Afghanistan etc) in fact there have been instance where US has supported dictators , fascists and in fact overthrown governments — which incited decades of violence.

So what drives Western countries, specifically the US’s zeal to push China back when it comes to Taiwan. Before we try to get into that please try and understand — “A commitment by a sovereign state is credible only when that state’s self-interest dictates honoring it”. Simply put, in international politics, there are no permanent friends or enemies, only permanent interests.

So let’s try and find a rational response of the US to Chinese aggression on Taiwan which preserves its self interest the most. And what better way to do it other than game theory.

But just like any other economics theory — let me list the assumptions first:

1. Like any other example of game theory the model just considers a few of the many possible outcomes. It’s therefore very possible that this analysis will neglect some important aspects of the current crisis but this blog isn’t intended as a complete rendering of what’s happening over the taiwanese strait but a model for simpler understanding
2. Although the responses to any kind of aggression can vary across a spectrum ranging from sanctions to full blown nuclear war — we are going to simplify response to either status quo or aggression
3. 0 utility stands for neutral outcome , +1 for good ones and -1 for bad outcomes
4. And at last, obviously all the actors in this exercise are rational and self interest driven i.e. want to go for maximum utility

Now, let’s get right to it — Chinese strategy concerning Taiwan can have one of two dimensions: status quo or aggression. If China chooses the status quo we are right where we started — basically nothing happens — (0,0) utility for both the parties . But things start to get interesting when China chooses aggression.

Now, in turn — American response to Chinese Aggression could be either appeasement or aggression. Appeasement could have various options like doing nothing to making some concessions to China in the South Chinese Sea etc to diffuse the situation. But either way the appeasement outcome returns us back to status quo ultimately with a +1 utility for China whereas , -1 for US.

But what if America chooses to meet Chinese strategy with aggression ? Now in turn China has 2 options to choose from — either a) back down or b) continue with aggression .

If China chooses option A we are back to status quo with a (0,0) utility for both the parties whereas if China chooses option B — both parties come to war and this is the worst outcome possible — hence the utility from such an outcome marks (-20,-20) as the utility for both the parties.

Now let’s look at this game from the US’s perspective if it chooses aggression as the dominant strategy it risks an eventual utility of (-20) whereas if it chooses appeasement as its dominant strategy it’s payout — even in worst case scenario would be (-1).

Hmm, So game theory dictates that the dominant strategy for US to Chinese aggression is APPEASEMENT. This clearly does not reflect what is happening — so Is America really going out on one foot to preserve democracy and liberty — the altruistic way?

NO, this model holds good as long as Chinese aggression is a one off case and its implications are limited to one region only. China for all practical purposes is a dictatorship and Chinese leader Chairman Xi Jinping is here to stay — while the western leaders have to face elections every 4 to 5 years and have to give in to popular mandate — Xi Jinping has the liberty to fixate on one issue and push for it continuously.

Secondly , ramifications from Taiwanese annexations by China would impact disputes in South China Sea — a region of tremendous economic and geostrategic importance. One-third of the world’s maritime shipping passes through it, carrying over US$3 trillion in trade each year. Huge oil and natural gas reserves are believed to lie beneath its seabed

But HOW ? How does Taiwanese outcome affect the South China Sea and its confrontations with other nations like Japan. This is where the concept of expected payout comes into play — utility from an outcome in itself doesn’t mean anything unless we don’t know the probability of that outcome.

EXPECTED PAYOFF = PLAYER’S UTILITY * PROBABILITY OF THAT OUTCOME

Let’s go back to the previous flow chart mentioning strategies and their utility for a second. Imagine for a second that the chances of China choosing aggression is 5 percent after America too refuses to back down. In such a scenario expected pay off for America choosing aggression as a dominant strategy for any kind of Chinese aggression becomes .

AMERICAN PAYOFF DURING AGGRESSION : (-20) * 0.05 = (-1)

Since this was anyways the worst outcome if the US chose to go for appeasement — US will choose to go for aggression as long as the probability of China not backing down is less than 5 percent.

But when you look at it from a broader perspective, if US chooses to back down over Taiwan — probability of future Chinese aggression increases — China is likely to go for more such instances in future when it knows that US will back down to its aggression — in other words the 0.05 probability will further rise and such instances will be repeated in future.

This shouldn’t come as a surprise when Russia chose to annex Crimea from Ukraine in 2014 — West responded with a degree of appeasement wherein NATO refused to meet them in the field and now Russia is once again threatening to invade Ukraine — keeping in mind NATO backed down rather easily last time . Whether Russia might be overplaying this card can only be decided with the extent to which it pushes the west and the response that comes out of it.

America — while deciding its strategies for China — has learned from its Russian experience and it would be unwise to look at the Taiwan issue in a vacuum . It has both temporal and spatial ramification throughout the region at places which can seriously affect world trade and American interests.

But having found out American interests in the region and the dominant strategy US is pursuing it with — we can’t and more importantly shouldn’t discount American efforts throughout the decades via aids and even military interventions in helping restore peaceful transition and democracies throughout the world.

“Capitalism is the astounding belief that the most wickedest of men will do the most wickedest of things for the greatest good of everyone.”