Tag: game theory

On The Economics of Time Wasting in Football

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Or soccer, if you so prefer.

So what is the issue here? If you are a football fan, you know it all too well. But if you are not, here is some background:

The International Football Association Board (Ifab) has ordered referees around the world to clamp down on time-wasting and add on the exact time taken for goal celebrations, substitutions, injuries, red cards, penalties and VAR checks. Referees would previously add 30 seconds for each goal or substitution.
An average of 16 minutes and 34 seconds was added to matches on the opening weekend of the EFL season, with 29 bookings for time-wasting compared with two on the final day of last season. Any player who stands in front of a free-kick to prevent it being taken quickly or kicks the ball away to delay a restart, for example, will be cautioned.

https://www.theguardian.com/football/2023/aug/10/added-time-howard-webb-no-backing-down-referees-ifab

… and you’d think that’s a good thing, right? Even the most casual fan of football is all too aware of the fact that there is a lot of time-wasting that goes on. So anything that helps eradicate it is a good thing, surely?

Well, turns out there’s two ways to “deal” with time-wasting. One, do it hockey style. Field hockey uses a stop-clock, and the clock is, well, stopped when play is stopped. The countdown timer is reactivated when play begins, and we “count down” the amount of time that needs to be played.

The second method, which is the one that football currently favors, is to not use a stopwatch, but rather to count the number of minutes that play has been stopped for, and add those minutes as “extra” time.

So why the second method, and not the first?

Well, economics:

Why is this happening? As ever, follow the money. The drive to increase active “game time” (itself a vapid, ill-defined concept) comes directly from Fifa. And Fifa is essentiality a TV rights distributions agency, its entire model based around increasing screen revenues. What we have here is the laws of the game being employed as a tool to doctor the perceived TV entertainment value of the product; as expressed via a massively overengineered notion of what the referee’s role should be, clumsily grasped value judgments of what entertainment looks like, and how this sport, our own shared treasure, should feel and look.

https://www.theguardian.com/football/blog/2023/aug/17/time-wasting-in-football-is-ugly-maddening-and-absolutely-vital

If you found it difficult to untangle the simple message in that paragraph, here is the quick takeaway: longer games means more advertising opportunities. But it also means more goal-scoring opportunities, which means more entertainment… which means, well, more advertising opportunities.

Is that a cynical hypothesis, or is this backed up by data?

In the 49 games played so far, the average match duration is now 101 minutes and 40 seconds, an increase of three minutes and 36 seconds on last season. This means Premier League games are lasting even longer than matches at last year’s men’s World Cup, where world governing body FIFA pressed the need to give fans better value for money in terms of action.
Even more dramatic is the uplift in effective playing time — the amount of time the ball is in play — with that increasing by four minutes and 25 seconds to 59 minutes and 30 seconds.
These extra minutes have produced more goals, with 151 being scored already this season, 3.1 per game. And 22 of those goals have come in added time, compared to only five at this point of the season last year.

https://theathletic.com/4886737/2023/09/21/premier-league-time-wasting/

So who’s complaining? We have more people watching more goals being scored, and therefore advertising revenue has gone up. Seems like a good thing all round. No?

Ah, but TANSTAAFL.

The move has not been greeted by everyone, though, with several prominent managers and players pointing out this would lead to more fatigue, injuries and potential burnout. European football’s governing body UEFA has refused to implement the new guidelines, opting instead to tell their match officials to keep the game moving.

https://theathletic.com/4886737/2023/09/21/premier-league-time-wasting/

So what should we be optimizing for?

  1. Should players be optimizing for not doing time wasting? What if they see their opponents doing it? How does the game theoretic solution then work out? How does it work out under the stopwatch rule? How does it work out under the added-time rule?
  2. Should the organizers be optimizing for players’ well-being? Or for advertising revenue?
  3. Should player recruitment change to account for the fact that matches will last longer? Should the number of substitutions be increased to account for longer matches? But will that not affect smaller clubs disproportionately?

If you are a fan of the sport, thinking through all this (and more) gives you a way to understand how one decision can impact so many others. Learn to transfer this type of interconnected thinking into other domains.

If you are a fan of economics or public policy, use the tools of your trade to think through the “best” solution. But realize that no solution is perfect, and that somebody, somewhere, will end up complaining. Maybe the players will play for too long, maybe you’ll stymie revenue growth, maybe coaches will come up with strategies to “work around” this problem.

And if you are a fan of both football and economics/public policy tell me what I’m missing!

Signaling, Game Theory, Inflation and Ukraine

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“…as the war approaches its 500th day tomorrow, there is no end in sight. Not this year, or next year or the year after. That should be deeply concerning, especially because, contrary to received wisdom, all those who really matter — the Ukrainians, Russians and the Americans — are actually trying very hard to end it.”

https://unherd.com/2023/07/why-no-one-can-end-the-ukraine-war/

I love reading about geopolitics, but know precious little about the underlying theory, and when I read about it, I approach it with the tools that I know a bit about – the tools of the economist. And so with this essay by Edward Luttwak – how can my knowledge of economics help me read it better? Where does my knowledge of economics not help while reading it? Let’s find out:

  1. Luttwak mentions that Zelenskyy doesn’t want a return to the status quo as of 2014, including taking back Crimea, and says that the current Ukrainian offensive is proof of the fact. In other words, he would like to end the war by getting to the negotiating table. I don’t know enough to agree or disagree, but that does then beg the question about why he doesn’t state his aims clearly. And this is because of two reasons. One of them Luttwak classifies as being military, while the other is personal.
    • The military reason: It’s because saying that “our aims are limited” can demoralize troops. Ukrainians on the battlefrom “must believe that their absolute commitment and self-sacrifice can end the war in victory.” Signaling, in other words.
      Read the whole article, as always, but first begin with this. Then scroll down to the section on “war” and ask how what we’re talking about might fit within that description. If it doesn’t, ask if my hypothesis is wrong – this is not signaling – or if the Wikipedia explanation is in this context incomplete.
    • The personal reason: “The personal reason is that Zelenskyy is a Jew, as is his defence minister, Oleksii Resnikov. And like the countless Jews who fought for their countries up and down Europe in the last century, the pair remain suspect in the eyes of the Ukrainian ultra-nationalists who are commonly antisemitic.
      It is, for them, no small irony that Ukraine should be led in its struggle for existence by two Jews since its founding hero, Bohdan Khmelnytsky, was Hitler’s only predecessor as a genocidally-antisemitic national leader; but instead of opprobrium, he has a city, a region, countless streets and Zelenskyy’s own Presidential Guard brigade named after him. Given the nationalists’ bigoted mistrust of the president, in spite of his stellar leadership from the first night of war, he cannot be seen to be a compromiser.”
  2. The other reason that Zelenskyy doesn’t want a return to the status quo is that an outright victory for Ukraine is actually bad news for it. How? Because an outright victory over Russia almost certainly means a regime change in Russia. That new leader, whoever they may be, “will promise not peace but a more effectively prosecuted war”. Better the known devil, in other words. More people should read The Art of Strategy, by Dixit and Nalebuff, particularly the section on “looking forward and thinking backward”.
  3. So these, Luttwak says, are the reasons for Ukraine preferring a negotiated truce rather than an outright victory. But they can’t clearly and openly state what they prefer, and so they continue to fight.
  4. What about Putin? Why would he want to come to the negotiating table instead of pushing for an outright victory?
    • Because, Luttwak says, he got into this war based on optimistic assessments that the war would be done and dusted in less than a week. That is obviously and painfully not true, and never has been. So why doesn’t he graciously retreat? Well, he can’t afford to. That signals weakness and defeat to Russians, and no dictator can continue to rule after appearing to have made a mistake, and then be seen as retreating from that mistake. Superman doesn’t negotiate or signal weakness, Superman does Superman things. So he can’t win, and he can’t be seen as having ordered a retreat. Signaling again!
      And there are a couple of factors that have helped him continue to carry out his grotesque and tragic charade:
    • First, Russia turns out to have been fairly self-sufficient. “Unlike China, the Russian Federation is autarkic in food and fuel, and manufactures all that is needed to sustain its armed forces and civilian population on a war footing, even if they are short of a few luxuries. So all Putin needed to keep fighting till his enemies lost patience was manpower, and to keep his conscripts out of combat.”
    • Second, he has enough roubles to throw at his soldiers. “Right now, joining the Russian army earns one a ₽600,000 sign-up bonus, ₽204,000 a month ($2,296 today), and stellar death benefits: ₽5,000,000 from the President himself an additional 2-3 million from the regional government and a monthly widow’s pension of ₽25,000 a month. Enough have joined to provide the forces that dug and fortified the long trench lines now holding up Ukraine’s offensive, along with almost 200,000 of the recalled reservists, who get the same pay and benefits.”
  5. So wait, that still doesn’t answer the question: why would he want to negotiate? One simple word: inflation.
    “Nabiullina is the formidable head of Russia’s Central Bank. Already very highly respected before the war, she is now the hero of Russian public finance for having successfully controlled inflation — better, in fact, than the Bank of England or the US Federal Reserve. The word is that she is tapering the printing of roubles, not for fear of a greater national debt (Russia’s is much lower than that of the US or UK) but of inflation. For Putin, too, that is a greater threat than anything his troops can encounter on the battlefield. Inflation will quickly drown Russia’s poor, many of whom are scattered across the endless steppe of Russia with very few opportunities to earn their way around rising prices.”
    And so he can’t clearly and openly state what he prefers, and so he continues to fight.
  6. And continuing with a game-theoretic approach, we can also understand why the US doesn’t want Russia to lose this war. There’s no grand conspiracy here, only simple logic: “the Biden administration (fully backed by most Republicans) does not want Russia destabilised by this war. For it knows only too well that Russian power alone keeps the Chinese from absorbing the vast spaces of Mongolia, Kazakhstan, the Kyrgyz Republic, Uzbekistan and Tajikistan — and that Russian weapons still flow to the only countries that actually fight the Chinese in recurring incidents: India on land and Vietnam at sea.”
  7. And so we reach a startling conclusion. Ukraine would like to end the war, but can’t afford to be seen as wanting to end it. Russia would like to end the war, but can’t afford to be seen as wanting to end it. The USA would like this war to end, but not at the cost of a destabilized Russia. And so it can’t end – it is actually “optimal” for the war to continue to grind on, so long as it doesn’t escalate further.

In other words, the good news is that the Ukraine war is, a polite, “limited war”, just like those of the 18th century that were later envied in the terrible 20th century of all-out, unlimited wars. But the bad news is that as long as only the Ukrainians are under fire, none of the other protagonists has an impellent reason to end the fighting. So like the 18th-century Seven Years’ War, it risks dragging on for at least another 500 days.

https://unherd.com/2023/07/why-no-one-can-end-the-ukraine-war/

A very happy Monday to all of you.

On Enshittification

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The writer and activist Cory Doctorow has coined a memorable term for this tendency for platforms to fall apart: enshittification. “Here is how platforms die,” he wrote in January. “First, they are good to their users; then they abuse their users to make things better for their business customers; finally, they abuse those business customers to claw back all the value for themselves.”

https://timharford.com/2023/03/the-enshittification-of-apps-is-real-but-is-it-bad/

What a lovely word, enshittification. I’m sure you’ve experienced the feeling of your own favorite app/online service going down Route Enshittification, pedal to the metal. Tim Harford refers to Facebook, Instagram, Twitter and Tiktok going down this route, with his own personal experience being a witness to the slow and – as he explains later on in the blogpost – inevitable degeneration of Amazon.

The problem, Harford says, is due to two important concepts that are (at least tangentially) from the field of microeconomics: network effects and switching costs.

What are network effects? The quote isn’t my own, and I’ve forgotten where I’ve filched it from, but here’s the easiest way to understand network effects:

“The first person to buy a fax machine was an idiot. The second was a genius.”

What this means is that just the one fax machine isn’t a useful thing, at all. You need another fax machine to send a fax to. Ditto with email addresses, if you’re looking for a more modern example (well, more modern than fax machines, at any rate!). People from the technology/marketing side of things are probably more familiar with Metcalfe’s Law:

In 1985, the economist George Gilder named the idea Metcalfe’s law. It’s probably the most celebrated equation of its kind since Gordon Moore’s observation about computer chips. Metcalfe says his motivation was not science but commerce. “It was a sales tool,” he says. “People were building small networks and not finding them useful. So I ginned up a slide on an Alto that showed that the cost of a network goes up linearly with the number of nodes, but the number of possible connections goes up as the square. Our salesforce took this 35-millimeter slide and told people the reason they weren’t useful is that they weren’t big enough. The remedy, of course, was buying more of our networks.”

https://www.wired.com/story/plaintext-the-man-who-discovered-network-effects-isnt-sorry/

And what are switching costs? As the phrase itself suggests, they’re the cost of switching from one service provider to another. I’ve had a lot of reasons to be deeply unhappy with my bank over the past year or so. I’m really tempted to switch. But the very thought of having to jump through a million hoops to do so, not to mention having to think through all of the ways my life has become immeasurably intertwined with my curren’t bank’s systems, makes me not want to go ahead with it. The only option that leaves me with regard to my current bank is to bleat at them in outraged fashion once I defeat their IVR. But anyways, that’s switching costs.

Now, combine these two things – network effects and switching costs, and the result, Tim Harford says, is enshittification:

Both switching costs and network effects tend to lead to enshittification because platform providers see early adopters as an investment in future profits. Platforms run at a loss for years, subsidising consumers — and sometimes suppliers — in an effort to grow as quickly as possible. When switching costs are at play, the logic is that companies attract customers who they can later exploit. When network effects apply, companies are trying to attract customers because they will draw in others to be exploited. Either way, exploitation is the goal, and the profit-maximising playbook will recommend bargains followed by rip-offs.

https://timharford.com/2023/03/the-enshittification-of-apps-is-real-but-is-it-bad/

Well, TMKK?

  1. As Tim writes in his post, as a smart, trained-in-microeconomics consumer, go to town on all the deals that a start-up offers you. Before the enshittification process starts, and while the app is in the “let’s get network effects to work for us” stage, make sure you double down on acquiring all the freebies on offer
  2. Don’t get attached to the awesomeness of a brand. Get attached to the early stage marketing offers of all brands. Remember, economics is “the dismal science”, and the dismal conclusion from Tim’s post is that all brands will eventually enshittify themselves.
  3. Read Tim’s post, all of it. Ask yourself if you’re in favor of eliminating switching costs. Remember that the opportunity cost of eliminating switching costs is that apps won’t bother with trying to build out network effects. That means a) no mad offers at the outset, but also, b) weaker network effects on your app. There is, unfortunately, no such thing as a free lunch!

The Game Theory of Bazball

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The term has its own Wikipedia article now!

Bazball is an informal cricketing term coined during the 2022 English cricket season. Bazball commonly refers to the style of play of the England national cricket team after the appointments of Brendon McCullum as Test cricket head coach, and Ben Stokes as England Test cricket captain, by English cricket managing director Rob Key, in May 2022. The Bazball style and mindset is said to have an emphasis on taking positive decisions in attack and defence, whether batting or in the field.

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

The article is worth reading in full, especially if you are a fan of cricket. But how does one think about Bazball if one is both a fan of cricket and of game theory?

  1. First, you can have fun defining what Bazball is, but what it has brought to the table where England is concerned is not up for debate. 10 wins out of 11 since the era has started, a victory in Pakistan that is still hard to believe, and the second fastest declaration in history – and there’s a lot many more records to look up apart from these. Whatever it is, it is working – so far.
  2. One way to think about Bazball is to argue that it is the same style of play that has worked so well for England in the case of limited overs cricket. So why not bring the same fearless approach into test cricket too? And on the basis of the evidence thus far, why not indeed?
  3. You could argue that Brendon McCullum is in effect hastening what would have been an inevitable process in the medium/long term. Is it safe to say that Cheteshwar Pujara is the last of his breed when it comes to Indian batsmen? Will all test playing nations have batsmen who are more naturally aggressive in five to ten years time? If yes, England just got there sooner under Stokes and McCullum.
  4. So the other teams must play catch-up, correct? They must respond by utilizing the same no-fear-no-holds-barred approach. Bazball, in other words, but the amped-up version. Beat ’em by getting better than ’em at their own game. That’d be one option, sure…
  5. But there were two ways to out-Pep Pep at the start of the previous decade. I’m talking football now, but you could either try and get even better at possession based football than the OG’s, or you could go the Mourinho route. Think about the Barcelona Inter Milan semis, for example. Similarly, you could try and out-Baz Bazball, or you could go in the opposite direction and play ultra defensively.
  6. If you want to go the out-Baz Bazball route, it’ll be great for the spectators, and one will get to see high-octane series with a lot of risks being taken by both teams. But there will be teams that will lose a game too many by adopting the extremely risky route, and such teams might adapt by toning down their level of risk tolerance. You’ll see risk-taking approaches go through cycles before hitting upon some sort of an equilibrium.
  7. If you want to go the conservative route instead, you might push teams that go down the Bazball route taken even more risks in response. This may work, in which case these teams will be even more incentivized to go further down the high-risk path. Or it may not, in which case these teams may tone down down their gung-ho approach a bit. But again, you’ll see risk-taking approaches go through cycles.
  8. Football has gone through many such cycles in its past, and this is a great book to read in this regard.
  9. As a fan of cricket, and as a student of game theory, it will be fascinating to see how this plays out in cricket, especially in the context of shortening attention-spans, the increasing popularity of T20 leagues, and the preferences of players to play ‘T20 style’.
  10. Get game theory out of the classroom, and into whatever fields you like to think about. Sports is just one example. But a subject like game theory comes alive when it helps you understand real-life situations better. And as a cricket fan, I can think of very few examples better than analyzing Bazball and its game theoretic implications!

A Tale of Two Sports

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Sport 1:

The Associate nations won four out of 11 matches against the Test-playing sides in this tournament. These are the most they have won in any edition of the men’s T20 World Cup. There were also a few close games in the seven they lost; two matches were decided within a margin of less than 20 runs, and the other two with less than ten balls to spare. This was clearly an improvement on the previous editions.
The 2021 T20 World Cup had 15 matches where the Associate nations were matched-up against Full Members, and they ended up winning just two games – both during the first round. Among the 13 games won by the Full Members, six were by a margin of 45-plus runs and another five games by seven or more wickets or 25-plus balls to spare.

https://www.espncricinfo.com/story/t20-world-cup-2022-stats-struggle-for-boundaries-a-tournament-of-upsets-and-englands-pace-highs-1344880

Sport 2:

Perhaps one of the most striking aspects of the World Cup has been the willingness of the so-called weaker teams to advance further up the pitch to win the ball in opposition territory.
A defining part of Saudi Arabia’s shock 2-1 win over Argentina was the remarkably high defensive line, which not only rattled the opposition but also caught them offside a total of 10 times – leading to three disallowed goals. Japan’s second-half turnaround against Germany was built around a similar high press. In one of the more under-the-radar results, Tunisia’s well-earned draw against Denmark came from the same risky approach.
Teams that chose to sit back and wait for counter-attacking opportunities alone – like Iran, Costa Rica, and Serbia – all faced big defeats.

https://indianexpress.com/article/sports/football/fifa-world-cup-learnings-from-the-first-round-of-matches-8288832/
  1. Small sample size, I know. But leave aside statistical rigor for the moment. Would it be right to assume that weaker teams are gradually getting better over time? Is this a hypothesis worth examining? Why has men’s tennis been telling us a very different story for the past two decades?
  2. The IE article talks about the specific tactics and strategies that have benefited the weaker teams in the football World Cup. What (if any) common strategies and tactics, have there been to the weaker teams that did well in the T20 World Cup?
  3. How might (and how should) the stronger teams adapt to these new strategies by the weaker teams when it comes to football? What about the stronger cricket teams?
  4. Playing the riskier strategy seems to be, counter-intuitively, the better (not necessarily safer!) thing to do, and you could argue that this is true for weaker nations in both sports. What does this say about the nature of both sports today? How much of this can be explained using game theory (what should be your rational strategy as the coach of a weaker team in a tournament such as this? What should be your rational strategy, given your best guess re: the previous question, as the coach of a stronger team in a tournament such as this?)
  5. Whatever our answers to these questions, how do they help us understand the world around us better today? Do they help us understand, say, geopolitical conflicts better? Corporate takeovers? If yes, how? If not, why not?

One of the random questions I recieved in class yesterday was about me asking five random questions to the students for a change instead. I had fun being on the other side for a change, and I’m going to enjoy pondering over these questions over the weekend.

Simon Sinek on Game Theory and War

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Quick update: I’ll be on leave this week, regular posts will resume on the 31st of October. Happy Diwali, everybody !

Game Theory and International Trade

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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

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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

Ashish1 Comment

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 time, the 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

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  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.