How game theory solves tough negotiations
Want to tax corporations without scaring them off, outsmart a calculating kid, or get rid of the world's nuclear warheads? Think like a game theorist.
Kevin Zollman is an associate professor in the Department of Philosophy at Carnegie Mellon University. He is also an associate fellow at the Center for Philosophy of Science at the University of Pittsburgh, visiting professor at the Munich Center for Mathematical Philosophy (part of Ludwig-Maximilians Universität), and an associate editor of the journal Philosophy of Science. His research focuses on game theory, agent based modeling, and the philosophy of science. Zollman is the co-author of The Game Theorist's Guide to Parenting: How the Science of Strategic Thinking Can Help You Deal with the Toughest Negotiators You Know--Your Kids, with Paul Raeburn.
Kevin Zollman: So game theory is the science of strategic thinking. The idea here is that any time that you’re interacting with another person who has their own interests and is trying to achieve their own ends, they are trying to do the best they can given what they want, you’re trying to do the best you can given what you want, and so you’re interacting in a strategic situation. One of you is trying to achieve what you want, the other is trying to achieve what they want.
Game theory is a mathematical theory that attempts to make sense of how it is that people interact in these strategic situations. It was originally developed in economics in order to try to understand economic behavior like why people buy certain things or why they’re willing to work for certain wages, but later on it was expanded and applied to a variety of different situations including biology, international relations, and even interpersonal relations like friendships and parenting and family relations.
So one of the big problems that parents constantly confront when they’re raising two kids is that the kids will sometimes compete with one another in order to get out of doing family chores, leaving them to the siblings. But the problem is, of course, the other kid, the sibling or friend, is going to figure that out too and so will try and shirk as well. In the end the parents are left for a messy room, the kids are upset with one another, and nobody is happy.
One of the things that game theory has tried to deal with are these types of situations—they’re sometimes called social dilemmas or prisoner’s dilemmas. These are situations where each individual has a private incentive to do something, but when both of them follow their private incentives the group or the two siblings are worse off than if they had ignored their private incentives and just worked together.
One of the seminal discoveries in this area is that by teaching kids or countries, or anyone for that matter, that you can break up that interaction into a bunch of little, small interactions where you can cooperate with the other one—but just on condition that the other one cooperated with you before. You can change a bad social dilemma into a positive interaction.
This was put to its biggest use during the Cold War. Reagan and Gorbachev negotiated the START treaty with one another, and one of the big problems that they had is: how can you be sure that while you’re eliminating nuclear weapons your adversary is also eliminating nuclear weapons?
So rather than saying, “We’re just going to get rid of some large percentage of our nuclear weapons and hope that the USSR would do so as well,” they broke up the interaction into a bunch of little, tiny ones.
So the USSR would eliminate just a few nuclear weapons, then the U.S. would eliminate just a few nuclear weapons. They would check, and then they would go onto the next stage, and then each would eliminate a few more, and they would go onto the next stage.
This process of taking a big interaction and breaking it down into little, small parts is one that we can use all over our lives, including in parenting. So rather than Mom or Dad coming into the room and saying to the kids, “Clean up the room,” and then leaving, Mom and Dad can come up and say, “Here’s the deal: each of you take turns putting away one toy, and you make a deal with one another: ‘If you put away your toy I’ll put away mine.’”
And by taking the big interaction, cleaning up the room, and breaking it into a series of small interactions you make it feasible for the kids to cooperate with one another in a way that wasn’t really possible before when you just left them with one big chore where they had to decide whether they wanted to do it or not.
One popular proposal that’s often occurred in tax debates is that we ought to lower our corporate tax rate in order to encourage companies that have located their assets offshore to bring them back into the United States. The idea here is that if we lower our corporate tax rate to be competitive with other countries then corporations don’t have a reason to move their money offshore.
The danger here is that if we lower our corporate tax rate then another country might lower their corporate tax rate, and as a result we end up in a race to the bottom, each country lowering their rate to compete with the other one until eventually we end up with a corporate tax rate of zero or near zero, or at least so low that we barely make any money.
If only we could get together with all the other countries and agree to fix our corporate tax rate at a kind of uniform number and not to compete with one another, all countries would be better off. No company would have an incentive to move their assets off shore, but countries wouldn’t lose out on the income from the higher corporate tax rate.
The difficulty here, of course, is that international cooperation is a hard thing to do. The Nobel Prize-winning economist Elinor Ostrom did a history of social dilemmas and prisoner’s dilemmas, and found that there are lots of different strategies that people have used over time in order to prevent races to the bottom and competitions of this form.
The traditional economic story about social dilemmas and prisoner’s dilemmas has been, there are kind of two solutions. One solution is the completely libertarian solution where you just privatize everything and you make everyone own everything. The other is to have a single government that controls everything. The problem in international relations is neither of these are really feasible. There’s no way that we can privatize individual corporations and give their ownership to individual countries, but nor can we have a world government that specifies what the corporate tax rate in every single country would be.
What Elinor Ostrom found in her historic study of these types of social dilemmas was that over history, people have found very sophisticated strategies that involve complicated checks and balances, agreements and structures that allow them to solve these problems without going to either extreme.
We suggest that there might be ways of modifying these individual small institutional arrangements in order to try to develop a series of international agreements where individual countries could have mechanisms to punish those countries who lower their corporate tax rate so we don’t have to just trust that other countries are going to follow through on their promises.
I want something from you. You want something from me. How will we act out those agendas in a strategic situation? Unravelling and understanding this scenario is how game theorists make a living. Economist Roger Myerson, who co-won the Nobel Prize for his foundational work on game theory, defines it as "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers," and while the theory was born in the field of economics, it by no means stayed there. Today, game theory can be applied to everything from biology and international relations, to interpersonal relations like friendship and parenting. Here, philosopher and game theorist Kevin Zollman applies the science of strategic thinking to three questions: how can a parent get a kid to clean their room, how can we reduce the number of nuclear warheads in the world, and most pertinently in America at this moment: how would a game theorist respond to the Trump administration's corporate tax cuts? Kevin Zollman and Paul Raeburn are the authors of
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The images and our best computer models don't agree.
A trio of intriguing galaxy clusters<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQzNDA0OS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxNTkzNzUyOH0.0IRzkzvKsmPEHV-v1dqM1JIPhgE2W-UHx0COuB0qQnA/img.jpg?width=980" id="d69be" class="rm-shortcode" data-rm-shortcode-id="2d2664d9174369e0a06540cb3a3a9079" data-rm-shortcode-name="rebelmouse-image" />
The three galaxy clusters imaged for the study
Mapping dark matter<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="d904b585c806752f261e1215014691a6"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/fO0jO_a9uLA?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>The assumption has been that the greater the lensing effect, the higher the concentration of dark matter.</p><p>As scientists analyzed the clusters' large-scale lensing — the massive arc and elongation visual effects produced by dark matter — they noticed areas of smaller-scale lensing within that larger distortion. The scientists interpret these as concentrations of dark matter within individual galaxies inside the clusters.</p><p>The researchers used spectrographic data from the VLT to determine the mass of these smaller lenses. <a href="https://www.oas.inaf.it/en/user/pietro.bergamini/" target="_blank" rel="noopener noreferrer">Pietro Bergamini</a> of the INAF-Observatory of Astrophysics and Space Science in Bologna, Italy explains, "The speed of the stars gave us an estimate of each individual galaxy's mass, including the amount of dark matter." The leader of the spectrographic aspect of the study was <a href="http://docente.unife.it/docenti-en/piero.rosati1/curriculum?set_language=en" target="_blank">Piero Rosati</a> of the Università degli Studi di Ferrara, Italy who recalls, "the data from Hubble and the VLT provided excellent synergy. We were able to associate the galaxies with each cluster and estimate their distances." </p><p>This work allowed the team to develop a thoroughly calibrated, high-resolution map of dark matter concentrations throughout the three clusters.</p>
But the models say...<p>However, when the researchers compared their map to the concentrations of dark matter computer models predicted for galaxies bearing the same general characteristics, something was <em>way</em> off. Some small-scale areas of the map had 10 times the amount of lensing — and presumably 10 times the amount of dark matter — than the model predicted.</p><p>"The results of these analyses further demonstrate how observations and numerical simulations go hand in hand," notes one team member, <a href="https://nena12276.wixsite.com/elenarasia" target="_blank">Elena Rasia</a> of the INAF-Astronomical Observatory of Trieste, Italy. Another, <a href="http://adlibitum.oats.inaf.it/borgani/" target="_blank" rel="noopener noreferrer">Stefano Borgani</a> of the Università degli Studi di Trieste, Italy, adds that "with advanced cosmological simulations, we can match the quality of observations analyzed in our paper, permitting detailed comparisons like never before."</p><p>"We have done a lot of testing of the data in this study," Meneghetti says, "and we are sure that this mismatch indicates that some physical ingredient is missing either from the simulations or from our understanding of the nature of dark matter." <a href="https://physics.yale.edu/people/priyamvada-natarajan" target="_blank">Priyamvada Natarajan</a> of Yale University in Connecticut agrees: "There's a feature of the real Universe that we are simply not capturing in our current theoretical models."</p><p>Given that any theory in science lasts only until a better one comes along, Natarajan views the discrepancy as an opportunity, saying, "this could signal a gap in our current understanding of the nature of dark matter and its properties, as these exquisite data have permitted us to probe the detailed distribution of dark matter on the smallest scales."</p><p>At this point, it's unclear exactly what the conflict signifies. Do these smaller areas have unexpectedly high concentrations of dark matter? Or can dark matter, under certain currently unknown conditions, produce a tenfold increase in lensing beyond what we've been expecting, breaking the assumption that more lensing means more dark matter?</p><p>Obviously, the scientific community has barely begun to understand this mystery.</p>
Astronomers spot an object heading into Earth orbit.
Minimoons<p>Scientists have confirmed just two prior minimoons. One was <a href="https://en.wikipedia.org/wiki/2006_RH120" target="_blank">2006 RH120</a>, which orbited us from September 2006 to June 2007. The other was <a href="https://en.wikipedia.org/wiki/2020_CD3" target="_blank">2020 CD3</a>, which got stuck in the 2015–2016 timeframe, and is believed to gotten away in May 2020.</p><p>2020 SO, the new kid on the block, is expected to arrive in October 2020 and pop out of orbit in May 2021.</p><div id="37962" class="rm-shortcode" data-rm-shortcode-id="f4c0fc8a2cba6536ea4cd960ebed3e6e"><blockquote class="twitter-tweet twitter-custom-tweet" data-twitter-tweet-id="1307729521869611008" data-partner="rebelmouse"><div style="margin:1em 0">Asteroid 2020 SO may get captured by Earth from Oct 2020 - May 2021. Current nominal trajectory shows shows capture… https://t.co/F5utxRvN6Z</div> — Tony Dunn (@Tony Dunn)<a href="https://twitter.com/tony873004/statuses/1307729521869611008">1600621989.0</a></blockquote></div>
Identifying 2020 SO<p>The first clue 2020 SO isn't your ordinary asteroid is its exceptionally low velocity. It's traveling much more slowly that a typical asteroid — their <a href="https://www.lpi.usra.edu/exploration/training/illustrations/craterMechanics/" target="_blank">average rate of travel</a> <a href="https://www.lpi.usra.edu/exploration/training/illustrations/craterMechanics/" target="_blank" rel="noopener noreferrer"></a>is 18 kilometers (58,000 feet) per second. Even <a href="https://en.wikipedia.org/wiki/Moon_rock" target="_blank">moon rocks</a> sent careening into Earth orbit by impacts on the lunar surface outpace pokey 2020 SO.</p><p>For another thing, 2020 SO has an orbital path very similar to Earth's, lasting about one Earth year. It's also just slightly less circular than our own orbit, from which it's barely tilted off-axis.</p><p>So, what is it? <a href="https://cneos.jpl.nasa.gov/ca/" target="_blank">NASA estimates</a> that the object has dimensions very reminiscent of a discarded Centaur rocket stage from the <a href="https://en.wikipedia.org/wiki/Surveyor_2" target="_blank" rel="noopener noreferrer">Surveyor 2 mission</a> that landed an unmanned craft on the moon. Back in the day, rocket stages were jettisoned as craft were aimed toward their desired position. This stuff, if released high enough, remains in space. It appears that this Centaur rocket, launched in September 1966, is now making its way back homeward, at least for a little bit.</p><p>When 2020 SO arrives at its closest point in December, the rocket is expected to be about 50,000 kilometers from Earth. Its next closest approach is much further: 220,000 kilometers, in February 2010.</p><img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQzMDk3NC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYyODg1MTQ1MX0.HGknDwqp0GmeuczKY_AS7vrPG7KMFUc_XO95tNoI2xo/img.jpg?width=980" id="e5cda" class="rm-shortcode" data-rm-shortcode-id="85eb1f790d8c3ee5b261f7ba13eaa5e1" data-rm-shortcode-name="rebelmouse-image" alt="Centaur rocket stage" />
Centaur rocket stage
What we may be able to learn<p>Earthly space programs being as young as they are, scientists would love to know what's happened to our rocket during a half century in space.</p><p>While 2020 SO won't get close enough to drop into our atmosphere, its slow progress has scientists hopeful that they'll still get some kind of a decent look at it.</p><p>Spectroscopy may be able to reveal what the rocket's surface is like now — has any of its paint survived, for example? Of course, being out in space, it's likely to have been hit by lots of dust and micrometeorites, so the current state of its surfaces is also of interest. Experts are curious to know how reflective the rocket is at this point, valuable information that can help planners of future long-term missions anticipate how well a craft out in space for extended periods will remain able to reflect sunlight.</p>
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