Midfield General

The Game Theory of the Game

When the United States meets Germany, will either side try to win?

Sports are supposed to be simple. Two teams, one goal -- may the best men (or women) win. Tournaments can complicate matters though.

All of a sudden, instead of the single goal of winning a game, teams have a bigger objective: take home the trophy. And that's where things start to get complicated, as they are for Germany and the United States in Brazil, where they face off in a third and final group match on Thursday, June 26.

In single-elimination tournaments like the NCAA's March Madness or the NFL playoffs, the strategy is still straightforward enough -- win and advance, or lose and go home. But in the World Cup and other round-robin competitions, especially when there's a transition from group stages to knockout rounds, the intrigue begins. In Brazil, with four teams vying for two spots, the third round of the group stage offers a host of competing incentives, and the aims of the protagonists can be far from clear. Luckily, we have game theory to help us understand what is and isn't at stake for the two sides.

You remember game theory -- you probably had a junior high teacher who taught you about the Prisoner's Dilemma, or you went and saw A Beautiful Mind (though you'd probably understand Nash equilibrium better if you hadn't, but I digress). In general, the idea is that if you examine what decision-makers have to gain by making different choices, you can predict what they will do. So, let's take a look at what the United States and Germany will be considering.

The first thing that stands out is how different this game is from a normal match for Germany. Given the respective point totals and tiebreakers in the group, Germany is all but assured of going through. Win, lose, or draw -- Germany will play in the Round of 16. However, with a win or a draw they will also win the group; with a loss they will come in second. Germany is playing only to determine what their path to the final looks like.

Come first, and Germany will face a path that consists first of the runner-up in Group H (a decidedly lower-ranked team like Algeria seems likely), followed by France and possibly Brazil before the finals. Again, this will happen whether Germany wins or draws against the United States; unlike in most soccer matches, there is literally zero difference between the results here. But if Germany comes second, it will likely face Belgium, possibly Argentina, and then whichever victor emerges from the Netherlands, Mexico, Greece, and Costa Rica.

For the United States, the story is slightly different. Win, and they'll top the group with the path that entails; draw, and they come in second. If they lose, their future rests on what happens between Portugal and Ghana in the other game, and they could be eliminated. So, while there may be slight differences for the United States between winning and drawing, there's a huge difference between drawing and losing. Just like Germany, the United States faces a very different set of incentives from what you'd normally see in a soccer match.

That's how this one game lines up, but remember: Thursday's match is only one part of the bigger picture. If the result makes no difference for Germany's chances to win the tournament -- that is, if the two paths are roughly equivalent -- then coach Joachim Löw should also consider other things. Does resting his stars, giving them time to recover while offering his reserves a chance to stay sharp, increase his team's chances of winning the entire tournament? Or is the opposite is true -- that playing his best team together for another match will increase their cohesion and generate even bigger benefits?

Such considerations could extend to tactics within the game as well. Might Germany decide not to use its energetic pressing defense, if there was even the possibility it might hurt them down the line? If the sole purpose of the tactic is to expend energy and win the game, it's difficult to see why they would press. But again, if Löw thinks that pressing might help to train his players, or that deviating from his usual gameplan might do more harm to his players' psyches than good to their fitness, perhaps he will continue as before. If the outcome of the match truly makes little difference to Germany's chances in the tournament, then considerations like these -- which might seem marginal in a knockout match -- might be important enough to sway him.

The United States has no such luxury. For coach Jürgen Klinsmann and his squad, the goal is clear: they must do everything in their power not to lose. There will be no room for adventurous forays that could leave the defense exposed. Counterattacking will be the order of the day. If Löw's decisions help them to keep the game under control, so much the better.

If it sounds like a draw might suit both teams, then you've been paying attention. And it's not the first time such a thing has happened. In the 2004 European Championship, Sweden and Denmark played a 2-2 draw that saw both advance from the group stage only by having superior goal difference to Italy. They even managed to save the last goal for the 89th minute -- quite a risk if the fix was in.

Of course, all of this assumes that the primary goal of both teams is to advance as far as possible in the tournament. But there's one more dynamic at work. Löw was Klinsmann's assistant when he took his home country of Germany to the semifinals of the World Cup in 2006. Afterwards, some said Löw was the real brains of the operation. Löw took over the national team and Klinsmann moved to California. The two rivals might just send their players out hell bent for leather, even if it means running them into the ground, just to prove a point.

It's also important to consider exactly whom the players will be playing for in Recife. If it's for themselves, they may strive to score audacious goals even if the coaches tell them to play it safe. If it's for the people who bought tickets from FIFA, then they'll try to play entertaining soccer even if its means risking elimination. Only if it's for their own fans will they stick to the smart strategies above.

When fans arrive at the stadium for a World Cup match, they usually expect both teams to do everything possible to win. Yet thanks to the structure of the tournament, Thursday's match will be between a team trying not to lose, and one to whom the result is largely incidental. German and American fans may nod their heads solemnly as their teams play out the corresponding strategies. For the neutral, it's likely to be a snooze.

Marcus Brandt / AFP / Getty Images

Democracy Lab

The Participation Gap

Why the problem of inequality isn’t just about differences in income.

Over the past year, in many parts of the world -- from Bosnia to Brazil to Burma -- the effects of political inequality between rulers and the ruled are being felt and tested with a new intensity.

In Bosnia, citizens have attacked the buildings of a nepotistic government that wastes $1 billion in graft per year and is grounded in ethnic identity and patronage. The current Bosnian political system was set up as a temporary, reconciliatory measure after the Yugoslav Wars in the 1990s, but has remained in place for two decades. In Brazil, a 2013 hike in public transit fares set off historic protests by a million people nationwide because top-level decisions to host extravagant sporting spectacles (the 2014 World Cup and 2016 Olympics) triggered public dissatisfaction with poor government services. Even highly respected traditional elites are not immune to this trend. In Burma, more than 100 civil society groups have taken the unprecedented step of labeling the previously venerated Buddhist clergy as "crony monks" for allegedly colluding with a government suspected of promoting religious radicalism.

Corruption and extremism are no longer stopping citizens from demanding their voices be heard, calling for economic opportunity, public services, and accountable government. In short, citizens are demanding dignity and equality, the central values enshrined in the Universal Declaration of Human Rights. Technological empowerment is helping individuals expose violence against women, discrimination, poor labor conditions, and other injustices for which officials can be held to account. Meanwhile, the number of people registered on social media has climbed from 1 million ten years ago to 2 billion today. Out of the world's 7 billion people, 6 billion have access to mobile phones -- more than the number of people who have access to working toilets. The world is connected online.

This phenomenon of fortified "people power" is one of the most important developments in international affairs today, and it is a principle theme of two multi-year projects launched by Carnegie Council for Ethics in International Affairs on the occasion of its centennial year 2014: interviews with 55 global influencers, called the Thought Leaders Forum, and conversations with hundreds of community representatives in several countries, called Global Ethical Dialogues. I manage both projects at Carnegie Council and have had the opportunity to witness this growing people power firsthand in more than 12 countries, including the three countries mentioned above. What is behind this citizen movement?

Inequality doesn't result only from differences in income or wealth (the focus of French economist Thomas Piketty). It also has a political dimension, fueled by unequal access to power and the norm that all citizens deserve an equal voice.

Harvard professor Michael Ignatieff, who chairs our Global Ethical Dialogues, writes: "Two features distinguish the modern situation: new technologies are accelerating the interaction and new ethical principles are structuring the dialogue. New technologies allow for real-time, interactive dialogue as never before. These dialogues are occurring under a new normative dispensation: the idea that every person, every faith, every race and creed come to the table as equals, with the same right to be heard and the same right to shape both the conversation and the outcome."

Ignatieff concludes, "These citizens live -- or want to live -- in a morally flat world, one based on equality of respect, meaning a world where everyone has a right to speak and be heard. The new social media technologies have enormously empowered and enabled this idea of equality of voice."

With the presumption of at least an aspiration to equal voice, citizens are no longer settling for subpar performance or abuse from their officials. "The biggest single problem in societies aspiring to be democratic has been their failure to provide the substance of what people want from government: personal security, shared economic growth and the basic public services (especially education, health care and infrastructure) that are needed to achieve individual opportunity," Francis Fukuyama recently wrote. The issue is not just a concern for democracies, either. A major force behind Xi Jinping's anti-corruption campaign is the maintenance of social stability and public credibility, a central preoccupation of the Chinese Communist Party.

As part of Carnegie Council's interviews with thought leaders, former Irish President Mary Robinson told me, "What strikes me about the world today is that it's a world of 7 billion people who are more connected than ever before, and yet the divides are huge." We see growing inequality both within countries and between countries, she warned, pointing to the public angst behind the Occupy movement and Arab Spring. Robinson said that, in her travels around the world, she notices a growing awareness of the rest of the world via smart phones and satellite dishes, which is fueling public scrutiny of local officials.

When this schism between peoples' expectations and their immediate lives reaches a breaking point, newly empowered, educated, connected, and globally aware citizens rise up against their rulers, making their voices heard. AsNew York Times columnist Thomas Friedman recently observed, a "new global force" is emerging, thanks to the democratization and diffusion of the IT revolution and globalization, that he calls "the Square People" in reference to their use of smart phones (squares) as well as demonstrations in the public squares of "Tunis, Cairo, Istanbul, New Delhi, Damascus, Tripoli, Beirut, Sana, Tehran, Moscow, Rio, Tel Aviv and Kiev, as well as in the virtual squares of Saudi Arabia, China and Vietnam."

Even in Japan, a country that is often considered stagnant and stable to a fault, a group of activist changemakers is on the rise, as I describe in a recent article in Foreign Affairs titled "Japan's Change Generation." Several factors in Japan, including a widely held belief that the government response to the devastating 2011 Tohoku earthquake was inadequate and a feeling that the status quo is unsustainable, have helped to create a cohort of elite professionals that are changing society from outside politics, though it is likely that they will have a long-term impact on the political culture. The younger tech-savvy crowd calls this group "the ‘76 Generation" (nana roku sedai in Japanese), since many of them were born around 1976. Their emergence has an echo of the normative shifts represented by the political influence of the 88 Generation in Burma or even Generation X in the United States.

Elsewhere in Asia, citizens have similarly displayed their disappointment with incompetent officials and demanded accountability. President Obama's trip to Asia in spring 2014 coincided with a public outcry in Philippines over poor government response to Typhoon Haiyan, in South Korea over failure by its coast guard to respond effectively to the sinking of a ferry packed with school children, and in Malaysia over the embarrassment of the disappearance of Malaysia Airlines Flight 370.

Worldwide, citizens are saying in effect: "Our voices need to be heard on an equal basis with those in power. We demand accountable government. We refuse to be distracted by cynical political tactics. Enough is enough." As one protester told me in Brazil, "We have a message for our government: Stop treating us like clowns!" While today's movements have much in common with predecessors such as the Czech Velvet Revolution in 1989 and the Philippine People Power movement in 1986, they are drawing enormous energy from technological innovation and social change.

The normative shift toward an equality of voice is being augmented by the positive developments of globalization, the IT revolution, economic growth and poverty reduction, and public awareness and education. The fastest change in demands for government accountability is taking place in the emerging markets, where, as political scientist Ian Bremmer has observed, politics has made a comeback after the seemingly utopian 1990s when the free market and economic globalization seemed destined to dominate world affairs. Once basic needs are fulfilled -- like food, shelter, and health -- citizens in these countries start to demand a voice as well. World economic output has quadrupled since the 1970s. The Millennium Development Goal of halving global poverty (the percentage of those living on less than $1.25 a day) between 1990 and 2015 was achieved five years ahead of schedule. In other words, when the "swamp" is drained and basic human needs are met, political needs emerge and new policies must reflect that.

But the less positive development in this call for change is the ubiquity of politicians who have learned to game the system and cling to the status quo, often on the questionable grounds of national interest. When the new norm of equal voice crashes into the incumbent political powers, there are casualties. When traditional forces prevail, the change-makers are imprisoned and sometimes killed. But when the equality of voice prevails, a fairer, more just, and usually more liberal society emerges. History is not linear, and as even Fukuyama has conceded, there will be setbacks. But over the long run the more progressive of these two forces will win the day as they represent a brighter, more inclusive future.