Solving the Korean crisis with game theory

People have asked me whether game theory can offer any insights for finding a solution of the North Korean nuclear crisis. Let me suggest that the answer may be Yes, as I will try to explain here in a nontechnical note without mathematical analysis. Based on a few general points that one can learn from game-theoretic analysis, I will explain why an effective strategy for encouraging moderation and political change in North Korea may be possible only with a long-term American commitment to recognize and respect China’s vital security interest in North Korea.

The first lesson that students learn from game theory is that we should try to think about any conflict situation from the perspectives of all the parties involved. Game theory also teaches us that a strategy for inducing others to behave better should include, not only a threat to punish their bad behavior, but also a promise to reward their good behavior. If we have a problem in making such threats and promises credible, then it may be necessary to stake our reputation on them, so that we would lose our ability to influence others in the future if we did not act as promised in this situation. But game-theoretic analysis often finds that a party can increase its current power to influence others by accepting such commitments that could reduce its own freedom of action in the future.

Several years ago, I argued that American military threats against Iran only tended to increase Iran’s motivation to acquire its own nuclear deterrent; and so an effective strategy for deterring Iran from acquiring nuclear weapons had to include an offer of better relations between America and Iran if Iran complied with international standards of nuclear nonproliferation. But I would be less optimistic that North Korea’s nuclear ambitions could be deterred by such an offer of detente. The rulers of North Korea must fear that their grip on power may require perpetual military tension with South Korea and its American ally, because peaceful relations could enable the people of North Korea to discover the vastly greater prosperity and freedom that Koreans enjoy in the South.

As a result, North Korea has become a perennial source of international tensions, and it has invested heavily in destructive military capabilities, so that any military operation against North Korea would be extremely dangerous for its neighbors. Economic sanctions have remained as the primary instrument for deterring North Korean provocations, but such sanctions cannot be effective without China’s full cooperation. In the past, a lack of such cooperation has undermined America’s efforts to use sanctions for inducing better behavior by North Korea.

Thus, an effective American strategy for managing the Korean crisis depends on finding a way to induce better Chinese cooperation with international sanctions against North Korea. Threats to extend trade sanctions against China are unlikely to induce full cooperation, and such a trade war would be at least as harmful to America as to China. But it is a mistake to think only about threats when searching for strategies to induce others to cooperate. Americans need to think also about promises that America could offer to make China prefer full cooperation with sanctions against North Korean violations of nuclear nonproliferation agreements.

It might seem surprising that China has not been a stronger supporter of sanctions against North Korea’s nuclear program. After all, no country would want an unreliable neighbor to acquire nuclear weapons. So what has limited China’s willingness to cooperate with America against North Korea? We must look at the situation from China’s perspective to understand what kind of promises could elicit the Chinese cooperation that is essential for solving the Korean crisis.

When we ask how the Korean situation looks from China’s perspective, we should recognize, first and foremost, that Korea was the starting point of the Japanese invasion of China in the early 20th century. Once Japan had achieved military dominance of Korea in 1905, Korea served as Japan’s base for invading China until the end of World War II in 1945. Of course the leaders of China know that their country is one of the most powerful nations in the world today, but people in China cannot forget the devastating Japanese invasion that entered China through Korea. We must understand that the people of China remember this history and demand that their leaders, who are responsible for their country’s security, must never permit the conditions for such an invasion to happen ever again.

But any threat that can effectively deter the rulers of North Korea must entail some risk of causing them to lose their grip on power. And any process of political change in North Korea, once it begins, could naturally open the way to a reunification of the peninsula under the government of South Korea, which already hosts American military forces. In that case, what would prevent American forces from moving north to the Chinese border? Such a possibility was intolerable to China in 1950, and we should understand that it is still intolerable for China today. This fear has made China resist any threat that could destabilize the North Korean regime.

Thus, to get China’s effective cooperation against North Korean militarism, America needs to provide some assurance that political change in North Korea would not expose China to any risk of foreign military forces on the Chinese border there. Indeed, one could argue that an American failure to recognize Chinese security concerns has been a factor in the Korean crisis since 1950, when America first tried to settle the crisis by moving its forces north to the border with China. Since then, China has seen only one clear way to ensure that powerful foreign forces should never return to its Korean border, and that is by maintaining the xenophobic regime of Kim Il Sung and his heirs as a buffer against all other powers. So any possibility of political change in North Korea will be strongly resisted by China unless it gets some credible assurance that its vital long-term security interests there would be respected even in the event of a regime change.

The fact that America and its NATO allies actually did move their forces eastward toward Russia after the end of Communism in Eastern Europe constitutes an unhelpful precedent which must be addressed. But there is nothing in North Korean history to resemble America’s long historical connection with Poland and other parts of Eastern Europe. Strong statements by American diplomats and leaders of both parties could give China some confidence that America would not use regime change to expand its power into northern Korea.

In the old language of 19th-century realpolitik, the key is for America to recognize the northern half of the Korean peninsula as being in China’s sphere of influence. Today, of course, agreements among great powers to recognize each others’ spheres of influence would be generally viewed as inconsistent with the principle of political self-determination for the people of every country. But in this case, a promise by America and its allies to respect a long-term Chinese sphere of influence in northern Korea could be actually the essential key to creating some possibility for the people of North Korea to change the political course of their country.

Thus, a credible commitment to keep American forces out of northern Korea could be the basis for a strategy to achieve long-term American policy objectives in Korea with Chinese cooperation. Some observers might consider such a commitment as a concession by America, but a game theorist would recognize it as a concession which could actually strengthen America’s ability to influence the situation.

See also the sequel “On the problem of commitment in Korea.”


9 Responses to “Solving the Korean crisis with game theory”

  1. Kien Choong Says:

    Sir – I think you are right that, to elicit China’s cooperation, the US has to credibly address China’s long-term security concerns. However, would US assurance about China’s long-term security be credible? I know US diplomats disavow any US intention to change China, but China (and North Korea) can place little confidence in US assurance given US actions (for example, in relation to Iran and Russia).

    That said, I do think there is a “game theoretic solution” to the North Korean crisis. This would be my approach:
    – First, the two Koreas, China and the US ought to agree in principle that as a long term goal: (a) the US military will eventually withdraw completely from Korea (and possibly all of Japan too if North Korea insists); and (b) there would be no nuclear weapons in the Korean peninsular (and Japan, if North Korea insists), with China and the US jointly guaranteeing the security of the two Koreas.
    – Assuming agreement on the long-term goal, the US and South Korea should adopt a “tit-for-tat with forgiveness” strategy towards North Korea (and China). For example, I would publicly announce a (say) 2 year plan to: (a) cease military exercises involving the US military in the Korean peninsular, and (b) reduce US military presence. Implementation of the 2 year plan would be conditional on North Korea suspending any further missile launches and nuclear tests.

    Suppose N Korea does suspend launches/tests, then the US and S Korea would faithfully implement the 2 year plan. Importantly, implementation ought not to be suspended for any other reason not stipulated – e.g., to punish N Korea for engaging in money laundering. All conditions for implementing the 2 year plan ought to be expressly stipulated in advance.

    Suppose N Korea continues to perform launches/tests, then the US and S Korea would simply suspend implementing the 2 year plan (and perhaps even reverse implementation). Be clear about the reason for the suspension (reversal) (this is the “stick”), but also announce that implementation of the 2 year plan would resume if N Korea desists from launches/tests for (say) 6 months.

    The goal here is to build confidence and trust. At present, neither N Korea nor the US/SK have confidence in each other. A “tit-for-tat with forgiveness” strategy is a way to build that confidence and trust. Each party must be able to demonstrate (by action) that their respective commitments are genuine.

    I imagine that the tit-for-tat (with forgiveness) strategy will continue for many years, possibly even 100 years. But that is OK. I see no need to achieve denuclearisation (by N Korea) and demilitarisation (by the US) immediately. There is no rush. The continuous effort by the two opposing parties to test each other to see if their commitments are genuine, will itself reduce the risk of nuclear conflict.

    I am reasonably confident that the tit-for-tat (with forgiveness) strategy will work eventually. My confidence is based on the fact that in biology, we know that evolutionary stable strategies are invariably some kind of tit-for-tat (with forgiveness) strategy. Such strategies however play out over many generations. We just have to be patient.


  2. Flat Eric Says:

    I think it might be even easier than that. A unified Korea, under South Korean leadership would have little reason to want a continued US military presence. Fear of China? Maybe, but it seems to me much more likely that a unified Korea, pre-occupied with reconstruction of the North for several decades, would fairly happily drift into a satellite relationship to China (and become more hostile to Japan).

    A deal for China in which it assists in bringing about Korean unification seems quite likely, therefore, naturally to result in US troops moving further away from China. I agree, of course, that a US commitment along those lines would be helpful.

    On a slightly different note, what would be the game-theoretic analysis of a speech by a US President that, on the one hand, threatens a state with war if it does not agree to limit its nuclear programme but also, on the other, announces that the US no longer regards itself as committed to a similar deal it previously struck with another state (Iran)? Solve for the equilibrium, as they say…

  3. Stas Kolenikov Says:

    The West chronically suffers from lack of understanding of the non-Western mentality, which in a way is a lack of imagination. The only two serious attacks on American soil by external forces, Pearl Harbor and WTC 9/11, led to (relatively) great losses for America, and got the country dragged into revengeful wars in both cases. Both resulted from Americans lacking imagination to envision a scenario that somebody would sacrifice their lives to maximize destruction (although that’s the most reasonable military strategy to expect from an adversary). I am not saying that Chinese or North Koreans or Russians would be blasting themselves in the near future to attack America — Russia seems to be making more progress with moving the armies of twitter bots rather than men with rifles, for one thing. But getting into other people’s brains and understanding what *their* payoffs are in the game *they* are playing is critically important: game theory assumes you know what your opponent is thinking.

    But you don’t — neither in case of diplomacy with North Korea, nor with Iran, nor with Russia (the best that the West could offer was “a bulldog fight under a rug”). And since America is generally scared to allow co-ethnics figure in decision making (W.A.S.P. only at top level of military/security, please; no Irish… I mean, Iranian… need apply), this lack of understanding will only be carried on into the future.

    Myerson offers a glimpse of that understanding when he says that (in his opinion) China isn’t thinking in terms maximizing the economic benefits or whatever natural, to the Western eye, objective function might be. He says that China is thinking in terms of its 5,000 year history, of which the WWII invasion is not an event of the nation’s quarter-life past (as it is for the 200-year young America), but something that happened a few geological minutes ago. As long as NK rhetoric is aimed strictly to the east (and the U.S. happily reciprocates, from President’s private twitter to the UN podium), China may indeed feel safer with the buffer that the NK is. At least his argument is different from “surely they want to create an elected government and run a modern economy with booming stock market” as the narrative usually goes with most other American geopolitical projects (although it did work once with the Marshall Plan).

    With all due respect, America is not known for maintaining its commitments. The President’s talk of reducing contributions to NATO and pulling out of Iran accord are but the most vivid examples. No amount of words and, I am afraid, no amount of ink on paper at this point could possibly convince China — so I end up sharing your scepticism.

    (First posted on Konstantin Sonin’s blog where he referenced this post.)

  4. typhoidX Says:

    Judging from a Chinese perspective, the main problem with this proposal is that this is not a REAL exchange or concession. China would be giving up its buffer zone, in return for vague promises of “influence” or “no US troops north of the 38th”. The author has correctly pointed out that such promises are of little value, given the NATO expansion precedence, or the more recent reneging on the Paris Accords. If the present US regime withdraws from JCPOA, it would further reinforce that such US promises are simply hollow.

    IF there is to be a GENUINE geopolitical exchange, then there must be REAL concessions from the US. An example would be exchanging the DPRK for Taiwan – reunification of Korea in return for the reunification of China. The PRC would cooperate with the US, impose whatever sanctions that the US desires, & leave the future of North Korea to be solely decided by the RoK & the US. In exchange, the US would reciprocate in Taiwan. In fact, under such an arrangement, I think the Chinese would even agree to accept a US military presence in North Korea following Korean reunification, since the PRC’s long-term security & strategic position would already be sufficiently enhanced with Taiwan under control, that they’ll make such a concession in NE Asia.

    • Kien Choong Says:

      Any reunification of China (with Taiwan) would require Taiwan’s consent; it is not for the US to bestow.

      That said, the US could stop supplying arms to Taiwan, which the US should not be doing anyway. Imagine if China were to send arms to Cuba or Iran. Or suppose the American South had won the Civil War; would the North be happy for China to supply arms to the American South?

      In any event, Beijing’s position on Taiwan is clear. It is happy for the Taiwanese to govern themselves autonomously. What China doesn’t want is for Taiwan to be a base for a foreign power to invade China. Hence, China would ideally want to control Taiwan’s military – ie, Taiwan is free to maintain its own military, but Taiwan’s military should ultimately report to Beijing.

      • Kien Choong Says:

        China’s reunification with Taiwan must have the consent of the Taiwanese people, and the challenge is for Beijing to win the confidence of the Taiwanese people. (Any reunification by force will not last.)

        Taiwanese politicians ought to resist any temptation to exploit fear of China. The challenge for Taipei is to at least discuss and negotiate the terms of unification with Beijing and see if there is a “win-win” outcome. If I were Taipei, I would insist that China’s constitution (as well as the constitution of the Communist Party) be amended to give Taipei a right to review any law or policy of China’s that affects Taiwan. I would also insist that a special “Constitutional Court” made up of Chinese and Taiwanese judges be established to adjudicate any disputes between Beijing and Taipei. Meanwhile, Taiwan would retain full control of its military indefinitely. Over time, as Taiwan becomes confident that Beijing will respect Taiwan’s legitimate interests, the Taiwanese armed forces will eventually be integrated into China’s armed forces.

  5. Links 10/6/17 - Daily Economic Buzz Says:

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  6. Juliette Récamier Says:

    Mr Myerson—

    Thank you for this piece. One feels the situation could really be split into components rather neatly, don’t you think?

    Firstly, there’s the fundamental question of Kim Jong Un’s rationality. If KJU is irrational then indeed we are in a no-holds-barred situation which does not present itself willingly for analysis. But surely, the burden of proof is on those who would make that assumption, and not otherwise? For “he is not like us, regular good folks” is not the same as “he is irrational”, and KJU has done nothing so far that couldn’t be explained away by his genuine desire to use his growing but still limited leverage against his largest geopolitical foe. Furthermore, he has been around (very much in power, in fact) for almost the last six years; that alone has to support very strongly not just the assumption of his rationality, but his foresight and his ability to play the system.

    An inevitable complication still remains, of course: even a rational player in a real world may behave unpredictably; he may misinterpret a signal because of information asymmetry or any other misrepresentation or bias; how can this be factored into the equation? Here we need to understand that DPRK leadership’s payoff in any situation that differs in a noticeable way from the status quo is unquantifiably negative. To put it very simply, KJU and his generals can expect to be either killed or imprisoned if things, as it were, go south; and this is not a development this clique will—or any other group of people would—seriously entertain. Constrained by this indefinitely negative payoff, which is known to all players, KJU cannot in reality issue any credible [existential] threats UNLESS he perceives his situation as no longer sustainable.

    Secondly, we might observe that the trio of China, DPRK and South Korea seem to be locked in a local Nash equilibrium. Indeed, if any of these players should dramatically alter their do-nothing/status quo strategies, then their payoff is almost inevitably going to worsen. South Korea has no economic incentive to merge with the North; the few estimates of the cost of such a potential reunification that have emerged are truly horrifying (to say nothing of North’s ability to lay waste to Seoul and its surroundings should a forceful coup be attempted). (Of course this eschews the deeper, almost sacral, importance of reunification, but one cynically wonders whether it is really behaviourally important for South Koreans.) North, then, has no incentive whatsoever to loosen its grip on its people (at least not overnight) lest their whole house of cards implode unexpectedly owing to internal discord. Finally, China also has no axe to grind in getting rid of KJU because, regardless of what lip service America pays to the notions of regional balance, not advancing north of the 38th parallel, etc., none of the promises made by the USA in this particular geography will, or can, ever be credible. Consciously forgo an opportunity to have a dynamite stick under the belly of the second biggest beast in the world? why on Earth?..

    North Korea has to endure, therefore, either 1) intact (easiest to implement but ultimately less predictable) or 2) as a buffer state wholly controlled by China (more difficult to implement but ultimately more reliable). The second option implies a transitional process, however, which may not be dismissed as a mere technicality because it implies a fundamental and systemic change from Juche to something, well, more humane.

    Thirdly and finally, the last biggest actor—USA—is arguably also a bit of a wildcard (especially with Mr Trump at the helm; one can only hope he remains constrained by all the revered checks and balances, chief of which, it appears, is Mr Tillerson), but we can probably safely assume USA will not start a nuclear war on a whim. Otherwise, we can discern several distinct strategic vectors here:
    1. Allow no credible threat from DPRK to emerge. This being a noble cause, a decent casus belli would justify even a military action against DPRK; but no such casus belli seems to have presented itself so far.
    2. Allow further military exposure only if there’s an assured prize. Here the situation is less clear-cut: on one hand, we should all agree the military lobby almost universally are a trigger-happy bunch, and in the USA especially so; on the other, the stakes here aren’t really that big and might even prove negative. (Think Marshall Plan but in Asia all over again, on top of the ongoing, low-efficiency War on Terror.)
    3. Undermine China’s global competitiveness. This is a very obvious motivator and as such it will never sit well with China.

    Out of the three above, therefore, only no. 1 is readily actionable. And coupled with our points one and two, it follows that the only realistically acceptable development is a situation where KJU willingly “abdicates” (and is never seen again, having been allowed to escape with his wealth and life) and is then replaced by a wholly Chinese candidate (such a candidate need not necessarily be Han, of course, all I mean is he needs to be installed by China), while the USA and South Korea are privy to such a turn of events but have otherwise no say in it.

    Having said that, it is not clear how such a development would occur. For KJU to become desperate enough to abandon his family’s wretched playground and yet not to try to burn as much of this world as he can while he does so would require a sequence of very deft diplomatic moves on the sides of China and USA—but from observing the present state of affairs, one is far from convinced that current policymakers are up to the challenge.

    I wonder if this is, by and large, in tune with your thinking?

  7. Links, 10 October 2017 | illiquid ideas Says:

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