Game Theory and International Trade

One of the most enjoyable moments while teaching Principles of Economics is the “aha!” moment that inevitably materializes when students “get” the concept of the Prisoner’s Dilemma. I rely upon a clip from “Golden Balls”, a UK game show that made use of PD games, along with the game The Evolution of Trust while teaching game theory for the first time, and also refer to Games Indians Play.

But an area in which I could get better is in showing students how game theory is used outside of these applications that are of an introductory nature. Dixit and Nalebuff’s book is of great help in this regard, and should be read by everybody regardless of whether or not you have a background in economics.

In today’s post I want to cover a chapter in a recent book that also does a good job in this regard. The book is titled “Rebuilding the Post-Pandemic Economy” and the name of the chapter is “America and International Trade Cooperation”


Consider the workhorse economic model of international trade agreements. Trade agreements are valuable because they solve what is known, in game theoretic terms, as the prisoner’s dilemma.
In such a game, each player has two choices—“cooperate” or “do not cooperate.” (The values in each box are the payoffs to each player if that is where they jointly end up.) To start, suppose there is no coordination between the players, so that each chooses its best response. The equilibrium outcome will be that each chooses “do not cooperate,” and the payoff to each is 1. But the problem with this outcome is obvious. Even though neither of them has a unilateral incentive to change its behavior, if they
both agreed to, each can be made better off and receive a payoff of 3.

Bown, Chad P., “America and International Trade Cooperation” in Rebuilding the Post-Pandemic
Economy, ed. Melissa S. Kearney and Amy Ganz (Washington D.C.: Aspen Institute Press, 2021).
Available at https://www.economicstrategygroup.org/publication/bown/
Source: From the chapter referred to above

If you have learnt game theory, it should be easy for you to understand why (1,1) is the Nash Equilibrium. If you have not learnt game theory, now’s a good time to start!


What Chad is getting at is this: “Broadly speaking, these prisoner’s dilemma models can be used to characterize the WTO and its core rules.” Countries that choose to not cooperate are boxing themselves into a corner (if you’ll excuse the pun), whereas countries that choose to cooperate and enter into a trade agreement are likely to see much better outcomes.

Ah, but hang on. Two very tricky questions arise. One, better for whom, exactly? And two, what if a country signs a trade agreement but then reneges? Let’s deal with both of these in turn.


Better for whom, exactly? This isn’t a superficial, rhetorical question, and nor is it a question that is even trying to imply that international trade is “bad”. It is a question that has had an impact on US Presidential elections (and political outcomes with real repercussions elsewhere in the world), and it is also a therefore a question that has engaged the minds of some of the best economists out there in recent years. See, for example, this article, or if you’re up for it, read this paper.

Globalization hasn’t reduced inequality, it may have increased it. As with all contentious issues, so also with this one – you’ll have passionate people arguing both sides of this story, armed to the teeth with data, models and theories. My own position is that there is, alas, at least an inconvenient iota of truth to the story. (Bonus points if you got the reference)

Listen to this podcast if you want more background information, and this symposium if you want a take by four different economists.

And read this if you want to understand how policymakers, in at least the United States of America are responding to the evolution of our understanding of this issue: better for whom, exactly? Note that you don’t need to agree that the US government has done, is doing or will do enough – all I am saying is that policies such as these are an acknowledgment of sorts that the perception on the ground is that trade hasn’t helped everybody.


And now back to game theory: what if a country signs a trade agreement but then reneges?

Historically, the United States has pushed for relatively low tariffs, applied on a nondiscriminatory basis to all members of the WTO. One interpretation of the Trump administration’s tariff war is the following. Even nearly two decades after its 2001 WTO accession, China had refused to engage in additional tariff liberalization. It was deploying other policies in ways symptomatic of noncooperative play,
imposing costly externalities on trading partners. Thus, the United States imposed trade war tariffs as its best response; as a result, each country is now imposing its noncooperative policy on the other. (Both are economically worse off than if they agreed to cooperate—see again Figure 1—but the United States may now be better than off than it was when it was cooperating but China was not.)

Bown, Chad P., “America and International Trade Cooperation” in Rebuilding the Post-Pandemic
Economy, ed. Melissa S. Kearney and Amy Ganz (Washington D.C.: Aspen Institute Press, 2021).
Available at https://www.economicstrategygroup.org/publication/bown/

As Chad suggests, go back to that first diagram shared above. What Chad is saying is that we need to understand that China agreed to play nice, as did America. And so we’re in (3,3), the upper left cell of the diagram. And this is obviously better than (1,1), the lower right cell.

But what if China said it would play nice, but then went ahead and played “dirty”? Then we’re in (0,5) upper right territory, and that is not a nice place to be in at all. How then should America respond? Please play The Evolution of Trust Game if you haven’t, by the way, and ask yourself which character most closely resembles China.

And then ask yourself how USA should respond, and then read the rest of this excellent chapter.


Also read the Twitter thread that Chad Bown but up about this chapter, and if you don’t listen in already, do listen to Trade Talks. Finally, here is Chad Bown’s Google Scholar page, and here is his PIIE website.

MADDER

If you are even an amateur fan of game theory, you must have come across the term “MAD”:

Mutual assured destruction (MAD) is a doctrine of military strategy and national security policy in which a full-scale use of nuclear weapons by two or more opposing sides would cause the complete annihilation of both the attacker and the defender (see pre-emptive nuclear strike and second strike). It is based on the theory of deterrence, which holds that the threat of using strong weapons against the enemy prevents the enemy’s use of those same weapons. The strategy is a form of Nash equilibrium in which, once armed, neither side has any incentive to initiate a conflict or to disarm.
The term “mutual assured destruction”, commonly abbreviated “MAD”, was coined by Donald Brennan, a strategist working in Herman Kahn’s Hudson Institute in 1962. However, Brennan came up with this acronym ironically, to argue that holding weapons capable of destroying society was irrational.

https://en.wikipedia.org/wiki/Mutual_assured_destruction

As with most theoretical concepts, it has its fair share of exceptions and limitations. Reading the Criticism section of the Wikipedia article is a great way to depress yourself, for example. But today, we depress ourselves a little bit more, by thinking about an article whose cheerful title is “The Math is Bad for MAD“:

Alarmingly, the current modernization of nuclear-missile arsenals by both Russia and China exposes a simple mathematical flaw in the assumptions underlying continued reliance on MAD. Despite our having ~1,400 deployed strategic nuclear warheads, they are postured such that a surprise attack by approximately 70 – 100 Russian or Chinese missiles—a fraction of their total nuclear forces—could soon undermine our “assured” retaliatory capability.

https://www.realcleardefense.com/articles/2021/11/08/the_math_is_bad_for_mad_802552.html

The rest of the article explains how China and Russia could, quite conceivably, undermine the US’ “assured” retaliatory capability. And when I say “quite conceivably”, I am not exaggerating. The authors, Norman Haller and Peter Pry lay out with implacable logic how China and Russia might think through all of the moves in this most dangerous of games, and reach the conclusion that America’s ability to “assure” retaliatory capability is not, in fact, assured. I will not excerpt anything to defend my argument, please read the entire article.

So what, one might ask, is to be done? The authors lay out seven things that America could conceivably do, and evaluate each of them in turn. Again, read the whole thing, it is in your interest to do so. I will, however, excerpt their concluding paragraph:

Finally, U.S. decision-makers should tune out minimalists who ignore the math and advocate replacing the Triad with either a Diad (bombers and submarines only) or, even worse, a Monad (submarines only). Tuned out as well should be MAD proponents who are inattentive to the math and insist that an undefended America is a positive asset.

https://www.realcleardefense.com/articles/2021/11/08/the_math_is_bad_for_mad_802552.html

You may agree with that paragraph, you may not. But you should, as a student of game theory, ask yourself if you can frame your agreement (or otherwise) in game theoretic terms. It is a useful (albeit depressing) exercise in your journey as a student of game theory.

And finally, for your reading pleasure, a further selection of cheer inducing books by one of the authors.

As my favorite bloggers like to say at the end of posts that are as optimistic as this one, have a nice day.

Navin Kabra on Game Theory and Blockchain: Notes

Navin Kabra was on campus yesterday, to talk about blockchain. More specifically, game theoretic aspects of blockchain. The talk was excellent throughout, and lasted well beyond the scheduled 90 minutes (and I mean that as a compliment!)

What follows are my key takeaways of the talk (although I have cheated just a little bit):

Introduction

  • Navin began the talk with a brief summary of the prisoner’s dilemma, the Nash equilibrium, repeated games and iterative games
  • He briefly touched upon the surprising success of the tit-for-tat algorithm
  • He mentioned the Schelling point

The Use Case

  • He then got into the need for a technology such as blockchain. He used land records and trust issues from this area as a use case.
  • When I buy land, or an apartment, from somebody, the following issues emerge:
    • How do I know that the land is yours to sell?
    • How do I know that you are you?
  • Of these, we focused more on the first one: how do I know that the land is yours to sell?
  • Without blockchain, the idea is to go to a centralized repository, and check who owns the land. If it is indeed the person who wants to sell you the land, great. If not, ask the prospective seller to buzz off.
  • But how do I make sure that the prospective seller is who she says she is?
  • One way to prevent this from happening is by using modern cryptography to digitally sign these land records. Navin didn’t mention this in his talk yesterday, but here’s one recommendation to learn more about this topic: The Code Book.
  • But what if the prospective seller has sold the land to somebody else, and gotten that transaction struck off the official record?
  • Enter blockchain

The Basic Idea

  • Take a block of transactions, and apply a seal to them. A digital seal, although the idea is the same as a mohar.
  • But that’s not enough: what we then do is also use an identifier for this block of transactions, that is generated in a unique, but random way, from the previous block of transactions (this is called a hash).
  • If somebody were to hack into this block of transactions and change something, it would therefore change the hash for the next block, rendering the next block untrustworthy.
  • This dependency works across the entire chain of blocks, hence “blockchain”.
  • Better still, this entire chain of blocks is not stored on one central server, but across many different servers – this is the distributed ledger concept.

The Distributed Ledger

  • So why would these different servers (or rather, their owners) want to be a part of this?
  • So here’s the incentive mechanism: servers solve an algorithm that isn’t difficult, but is time consuming. Whoever solves the next chunk of this algorithm gets to seal the next block, and alerts all other servers about having done so.
  • Once all servers get this alert, they all update the chain of blocks so that everybody has the same version of events. This, of course, happens automatically.
  • The server that sealed the latest block gets as reward: bitcoins.

Bitcoins

  • These bitcoins are, in essence, a reward mechanism for making blockchain work.
  • Once folks start trading these bitcoins, especially in exchange for stuff from the real world, the value of bitcoins goes up.
  • We didn’t explicitly speak about this yesterday, but here’s my understanding: It becomes, as with any other currency, a medium of exchange, and also a store of value. (The unit of account bit is more troublesome, and I won’t get into it right now)
  • That reward mechanism is randomized, in the sense that any computer/server is equally likely to crack the next chunk of the algorithm. The more computing power you have, over timethe more you will get a higher share of bitcoins.
  • The number of bitcoins that can be mined is limited, and the number that is released per chunk of algorithm solved may change as a function of the number of computers trying to compete. In other words, the incentive mechanism is built in (I was rather impressed with this)
  • There are ridiculously large buildings in China stocked to the roof with servers whose sole objective is to mine bitcoins.

Game Theoretic Aspects of Blockchain

  • This is as pure an experiment in game theory as one could hope for.
  • You have people, necessarily anonymized, who can’t communicate with each other, who are trying to mine bitcoins
  • Also, you have folks who are, again necessarily anonymized, trying to transact using bitcoins.
  • Should they cooperate with each other or not? What are the implications? Since I’m already at around 750 words right now, I’ll outsource this part. Do read it, it is a very good summary of both game theory as well as its application to blockchain.

Also…

  • I enjoyed the fact that the numbers 42 (check the last bullet point, especially. But also, see this), 1729 were used in the presentation. This had nothing to do with anything, but Easter Eggs are always fun.
  • Also, yesterday I learnt (is YIL a thing? It should be)
  • I (and I think I speak for all the students who were present yesterday) would love to learn more about applications of Bitcoin. If there are folks in Pune who would like to come talk about this at Gokhale Institute, please get in touch! ashish at econforeverybody dot com

 

Finally, a huge thank you to Navin! The talk was hugely informative, thought provoking and easy to understand – and that’s a very rare combination indeed.

Links for 6th May, 2019

  1. “Not long ago, the Liverpool away coach uniform was technical mountain climbing apparel, which had its roots in drug dealers in cold northwest England figuring they didn’t need to freeze to death slinging weed in a park. That meant a lot of North Face gear, which became fashionable. One leader at an LFC firm bought so much high-end gear that when he got a stadium ban several years ago, he actually started climbing mountains around the country, unsure of what else to do with all the stuff he’d bought.”
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    A nice long read on Liverpool: the city and the club. Also a fascinating peek into a place in England that isn’t necessarily English.
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  2. “In my view, reform of government economic administration must take priority. As things stand, it is a prerequisite for the success of any other reform. A weak state cannot deliver anything other than grandiloquent statements of intention. This must change. Without a capable State, there can be no transformation.”
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    Rathin Roy explains in the Business Standard why India hasn’t fulfilled its potential so far, and what needs to be done to change the status quo.
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  3. “How much, in all, does Popovich spend annually on food and wine? That’s hard to say. But he reportedly earns $11 million a year, the highest salary in the league for a head coach. Considering the offerings from his private wine label and that he holds thousands of bottles in his cellar, plots out dozens of high-end dinners per year at some of the country’s most high-end restaurants, drops $20,000 on wine alone at some dinners, and routinely leaves exorbitant tips — well, it’s not a stretch to suggest that Popovich might ultimately drop a seven-figure annual investment on food and wine. “He’s spent more on wine and dinners than my whole [NBA] salary,” former NBA coach Don Nelson says. But in San Antonio — where Popovich has won more with his team than any NBA coach has with a single team in history — the investment, apparently, has been worth it.”
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    Is good dining the means to an end? Read this fascinating article to find out one man’s answer.
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  4. “Gorbachev pushes back at the notion that the Soviet Union’s end was somehow a triumph for the other side. “Americans thought they’d won the Cold War, and this went to their heads,” he says. “What victory? It was our joint victory. We all won.” Well, maybe not entirely — Vladimir V. Putin, pointedly absent from most of the film, is glimpsed in footage of Raisa Gorbachev’s funeral — but you come away from the movie agreeing with Herzog’s assessment, and yearning for Gorbachev’s brand of diplomacy.”
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    A short article about Gorbachev – a documentary about the man. He’s 88 this year, but the article is interesting throughout. And the excerpt is a great way to think about whether you have really understood the concept of a zero-sum-game.
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  5. “The Northern states are densely populated. But this density has clearly not provided the economies of scale to promote rapid economic growth. One problem is that the dense population in the Gangetic plains is not clustered in large cities. Prateek Raj of the Indian Institute of Management in Bengaluru has written about the metropolis vacuum in the Hindi speaking states of Uttar Pradesh, Bihar, Jharkhand, Madhya Pradesh and Chhattisgarh, which together have 500 million residents (bit.ly/2UOS2Kv). “The glaring absence of a major metropolitan center in the region has forced young people to migrate away from the small towns and move to other cities in the West and the South,” he argues.”
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    A lovely read from Niranjan Rajadhakshya about what ails Northern India and how one might tackle the issue. The lack of urbanization is a very real problem in Northern India, among others.

Links for 11th April, 2019

  1. “Who has the upper hand in bargaining for wages and employment benefits? Who dominates markets and who must submit to market forces? Who can move across borders and who is stuck at home? Who can evade taxation and who cannot? Who gets to set the agenda of trade negotiations and who is excluded? Who can vote and who is effectively disenfranchised? We argue that addressing such asymmetries makes sense not only from a distributional standpoint, but also for improving overall economic performance. Economists have a powerful theoretical apparatus that allows them to think about such matters.”
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    Dani Rodrik makes the case for rewriting economics, rather than tinkering with it at the margins, in order to really tackle the problems that the world faces today. An article worth reading – I’d linked to their manifesto earlier.
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  2. “In San Lucar, selfish behavior is unacceptable. But in New York, a city with 8 million people, selfish behavior is the norm. It’s a dog-eat-dog mentality. Policemen are everywhere and sirens are the sound of the city. During rush hour on 5th Avenue, pedestrians fight like soldiers on a battlefield. They step over homeless people, weave through strangers, and J-Walk through red lights.Why are people so cooperative in San Lucar, but so selfish in New York?”
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    If you are a student of game theory, you already know that the answer is game theory. But the article is worth reading because it should prompt you to wonder if there is a deeper answer than the one provided – and Adam Smith might be a good place to begin.
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  3. “First, declining growth is a key, albeit low-frequency, cause of today’s social and economic distress. Second, the unfortunate consequences of the ICT revolution are not inherent properties of technological change. Rather, as Rajan notes, they reflect a “failure of the state and markets to modulate markets.” Though Rajan does not emphasize it, this second point gives us cause for hope. It means that ICT need not doom us to a jobless future; enlightened policymaking still has a role to play.”
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    Angus Deaton reviews Raghuram Rajan’s latest book, and leaves us with a sense of appreciation for the book (and in my case, a desire to read it), but also with a deep sense of foreboding about where we may end up as a society.
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  4. “That leads to a broader point: “tech” is not simply another category, like railroads or telecom. Tech is a means, not an end, but Senator Warren’s approach presumes the latter. That is why she proposes the same set of rules for the sale of toasters and the sale of apps, and everything in between. The truth is that Amazon is a retailer; Apple a combination of hardware maker and platform makers. Google is a search and advertising company, and Facebook a publishing and advertising company. They all have different value chains and different ways of impacting competition, both fairly and unfairly, and to fail to appreciate just how different they are is a great way to make bad laws that not only fail to fix problems but also create entirely new ones.”
    Ben Thompson on how to think about tech (and in a very long article, this excerpt really matters): tech is the means to an end, and therein lies all the difference in the world.
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  5. “You may never have heard of Islamestan, in Chinese Turkestan, or its one-time “king”, Bertram Sheldrake. Islamestan is long gone, swallowed up in the historical shifts of a turbu­lent region, but for a brief and unlikely moment, an English pickle-factory heir ruled, with his wife, Sybil, over the newly independent Muslim country, to the far west of China.”
    Stories don’t get much better than this, and that’s putting it mildly.

Links for 29th March, 2019

  1. “”Because it’s so difficult for people with edge-to-edge bites to produce sounds like f and v, the study’s authors figured they would be unlikely to say them by accident, or to incorporate them into their languages. They checked to see whether they could find this pattern playing out in the real world by comparing the sound systems of languages across the world with the subsistence style of the people who speak those languages. About half of the world’s languages use labiodental sounds, but on average, languages spoken by hunter-gatherer societies turned out to use fewer than one-third the number of labiodental sounds as their agricultural counterparts.”
    An area I know nothing about, but I found this fascinating. How agriculture might have influenced speech, and how therefore we got around to using “F” and “V” sounds in language. It begs the question: how might current society be impacting the evolution of language?
  2. “Something interesting emerges from those figures. As the atmosphere is full of small eddies, so humanity experiences many small deadly quarrels, which result in a few fatalities. But now and again come huge storms, which kill millions. These are just the sort of outbreaks, like the world war Richardson had seen for himself, that people think of as surprising. Yet when Richardson plotted the frequency of wars against the number of deaths caused by each one, he found a constant and predictable relationship. On his graphs, the violence obeyed a “power law”—a constant relationship between the size and frequency of measurements. In his turbulence work, Richardson had found that such a power law governed the relationship between the rate of diffusion of objects in a turbulent stream and their distance from one another. Now he had found evidence of an underlying law in the supposedly unpredictable realm of politics.”
    Well worth the price of admission – the article begins somewhat slowly, but picks up pace and complexity, taking us on a journey through war, weather forecasting, religious background, and much else besides. People who don’t like math, especially, should really read this post.
  3. “Foreign investors believe they can navigate around India’s governance fault lines. Still, South Korea’s chaebol discount could also become a millstone for India if the grip of a handful of private interests on state institutions and economic opportunities tightens. The new boxwallahs will be much harder to shake off than the old cronies.”
    The always excellent Andy Mukherjee on the urgently needed corporate reforms in India. Well worth a read for its own sake, of course, but more importantly, a great read to help you understand what you should read more of when it comes to India’s business history.
  4. “There are undergraduate courses, and then there are great undergraduate courses. Today we have the 49 item course bibliography for Thomas C. Schelling’s “Conflict, Coalition and Strategy” along with its ten-page final examination”
    This is, I’m still gobsmacked to think about it, an undergraduate  course. We at the Gokhale Institute are starting an undergraduate course this year – it’ll be interesting to see if any of these references could be included in that course. I found this fascinating, especially because of the wide variety of subjects from which the list has been drawn up. A lot of bookmarks to be added via this link!
  5. “For, in both Ricardo and Marx, a conflict of interest is visible between social classes. In order to promote the ‘idea’ of a just and harmonius system, the theories (especially the labour theory of value) of Ricardo and Marx were criticised as being limited, and an alternative was proposed. This new theory completely did away with social classes. Individuals were chosen as the primary unit of analysis. Social classes, actually was modified into ‘factors of production’. A very interesting and important methodological shift, with powerful political implications! All the factors of production were assigned equal importance, and it was also shown how both labour and capital recieved incomes according to their contribution to the production process. That is, a capitalist system, with free mobility of labour and capital and with clear property rights (contracts), is essentially a just and stable system.”
    Why should one study economics? Most, if not all, colleges today leave students with the answer to this question being completely backward. We learn, and teach, theories of economics and then ask students to apply them to the world outside. Arguably, even the latter doesn’t happen nearly often enough. But this post helps you understand where theories come from in the first place! They came up in response to the world that was around those theorists – at that time, and at that place. This time, and this place is different – and we, as students of economics, would do well to remember that. Excellent article, and about an economist who isn’t studied enough.