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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What makes some people more likely to shiver than others?
Some people just aren't bothered by the cold, no matter how low the temperature dips. And the reason for this may be in a person's genes.
Eating veggies is good for you. Now we can stop debating how much we should eat.
- A massive new study confirms that five servings of fruit and veggies a day can lower the risk of death.
- The maximum benefit is found at two servings of fruit and three of veggies—anything more offers no extra benefit according to the researchers.
- Not all fruits and veggies are equal. Leafy greens are better for you than starchy corn and potatoes.
An open letter predicts that a massive wall of rock is about to plunge into Barry Arm Fjord in Alaska.
- A remote area visited by tourists and cruises, and home to fishing villages, is about to be visited by a devastating tsunami.
- A wall of rock exposed by a receding glacier is about crash into the waters below.
- Glaciers hold such areas together — and when they're gone, bad stuff can be left behind.
The Barry Glacier gives its name to Alaska's Barry Arm Fjord, and a new open letter forecasts trouble ahead.
Thanks to global warming, the glacier has been retreating, so far removing two-thirds of its support for a steep mile-long slope, or scarp, containing perhaps 500 million cubic meters of material. (Think the Hoover Dam times several hundred.) The slope has been moving slowly since 1957, but scientists say it's become an avalanche waiting to happen, maybe within the next year, and likely within 20. When it does come crashing down into the fjord, it could set in motion a frightening tsunami overwhelming the fjord's normally peaceful waters .
The Barry Arm Fjord
Camping on the fjord's Black Sand Beach
Image source: Matt Zimmerman
The Barry Arm Fjord is a stretch of water between the Harriman Fjord and the Port Wills Fjord, located at the northwest corner of the well-known Prince William Sound. It's a beautiful area, home to a few hundred people supporting the local fishing industry, and it's also a popular destination for tourists — its Black Sand Beach is one of Alaska's most scenic — and cruise ships.
Not Alaska’s first watery rodeo, but likely the biggest
Image source: whrc.org
There have been at least two similar events in the state's recent history, though not on such a massive scale. On July 9, 1958, an earthquake nearby caused 40 million cubic yards of rock to suddenly slide 2,000 feet down into Lituya Bay, producing a tsunami whose peak waves reportedly reached 1,720 feet in height. By the time the wall of water reached the mouth of the bay, it was still 75 feet high. At Taan Fjord in 2015, a landslide caused a tsunami that crested at 600 feet. Both of these events thankfully occurred in sparsely populated areas, so few fatalities occurred.
The Barry Arm event will be larger than either of these by far.
"This is an enormous slope — the mass that could fail weighs over a billion tonnes," said geologist Dave Petley, speaking to Earther. "The internal structure of that rock mass, which will determine whether it collapses, is very complex. At the moment we don't know enough about it to be able to forecast its future behavior."
Outside of Alaska, on the west coast of Greenland, a landslide-produced tsunami towered 300 feet high, obliterating a fishing village in its path.
What the letter predicts for Barry Arm Fjord
Moving slowly at first...
Image source: whrc.org
"The effects would be especially severe near where the landslide enters the water at the head of Barry Arm. Additionally, areas of shallow water, or low-lying land near the shore, would be in danger even further from the source. A minor failure may not produce significant impacts beyond the inner parts of the fiord, while a complete failure could be destructive throughout Barry Arm, Harriman Fiord, and parts of Port Wells. Our initial results show complex impacts further from the landslide than Barry Arm, with over 30 foot waves in some distant bays, including Whittier."
The discovery of the impeding landslide began with an observation by the sister of geologist Hig Higman of Ground Truth, an organization in Seldovia, Alaska. Artist Valisa Higman was vacationing in the area and sent her brother some photos of worrying fractures she noticed in the slope, taken while she was on a boat cruising the fjord.
Higman confirmed his sister's hunch via available satellite imagery and, digging deeper, found that between 2009 and 2015 the slope had moved 600 feet downhill, leaving a prominent scar.
Ohio State's Chunli Dai unearthed a connection between the movement and the receding of the Barry Glacier. Comparison of the Barry Arm slope with other similar areas, combined with computer modeling of the possible resulting tsunamis, led to the publication of the group's letter.
While the full group of signatories from 14 organizations and institutions has only been working on the situation for a month, the implications were immediately clear. The signers include experts from Ohio State University, the University of Southern California, and the Anchorage and Fairbanks campuses of the University of Alaska.
Once informed of the open letter's contents, the Alaska's Department of Natural Resources immediately released a warning that "an increasingly likely landslide could generate a wave with devastating effects on fishermen and recreationalists."
How do you prepare for something like this?
Image source: whrc.org
The obvious question is what can be done to prepare for the landslide and tsunami? For one thing, there's more to understand about the upcoming event, and the researchers lay out their plan in the letter:
"To inform and refine hazard mitigation efforts, we would like to pursue several lines of investigation: Detect changes in the slope that might forewarn of a landslide, better understand what could trigger a landslide, and refine tsunami model projections. By mapping the landslide and nearby terrain, both above and below sea level, we can more accurately determine the basic physical dimensions of the landslide. This can be paired with GPS and seismic measurements made over time to see how the slope responds to changes in the glacier and to events like rainstorms and earthquakes. Field and satellite data can support near-real time hazard monitoring, while computer models of landslide and tsunami scenarios can help identify specific places that are most at risk."
In the letter, the authors reached out to those living in and visiting the area, asking, "What specific questions are most important to you?" and "What could be done to reduce the danger to people who want to visit or work in Barry Arm?" They also invited locals to let them know about any changes, including even small rock-falls and landslides.
The famous cognition test was reworked for cuttlefish. They did better than expected.
- Scientists recently ran the Stanford marshmallow experiment on cuttlefish and found they were pretty good at it.
- The test subjects could wait up to two minutes for a better tasting treat.
- The study suggests cuttlefish are smarter than you think but isn't the final word on how bright they are.
Proof that some people are less patient than invertebrates<iframe width="730" height="430" src="https://www.youtube.com/embed/H1yhGClUJ0U" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe><p> The common cuttlefish is a small cephalopod notable for producing sepia ink and relative intelligence for an invertebrate. Studies have shown them to be capable of remembering important details from previous foraging experiences, and to adjust their foraging strategies in response to changing circumstances. </p><p>In a new study, published in <a href="https://royalsocietypublishing.org/doi/10.1098/rspb.2020.3161" target="_blank" rel="noopener noreferrer">The Proceedings of the Royal Society B</a>, researchers demonstrated that the critters have mental capacities previously thought limited to vertebrates.</p><p>After determining that cuttlefish are willing to eat raw king prawns but prefer a live grass shrimp, the researchers trained them to associate certain symbols on see-through containers with a different level of accessibility. One symbol meant the cuttlefish could get into the box and eat the food inside right away, another meant there would be a delay before it opened, and the last indicated the container could not be opened.</p><p>The cephalopods were then trained to understand that upon entering one container, the food in the other would be removed. This training also introduced them to the idea of varying delay times for the boxes with the second <a href="https://www.sciencealert.com/cuttlefish-can-pass-a-cognitive-test-designed-for-children" target="_blank" rel="noopener noreferrer">symbol</a>. </p><p>Two of the cuttlefish recruited for the study "dropped out," at this point, but the remaining six—named Mica, Pinto, Demi, Franklin, Jebidiah, and Rogelio—all caught on to how things worked pretty quickly.</p><p>It was then that the actual experiment could begin. The cuttlefish were presented with two containers: one that could be opened immediately with a raw king prawn, and one that held a live grass shrimp that would only open after a delay. The subjects could always see both containers and had the ability to go to the immediate access option if they grew tired of waiting for the other. The poor control group was faced with a box that never opened and one they could get into right away.</p><p>In the end, the cuttlefish demonstrated that they would wait anywhere between 50 and 130 seconds for the better treat. This is the same length of time that some primates and birds have shown themselves to be able to wait for.</p><p>Further tests of the subject's cognitive abilities—they were tested to see how long it took them to associate a symbol with a prize and then on how long it took them to catch on when the symbols were switched—showed a relationship between how long a cuttlefish was willing to wait and how quickly it learned the associations. </p>
All of this is interesting, but what use could it possibly have?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNTcxNzY2MS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY2MTM0MzYyMH0.lKFLPfutlflkzr_NM6WmnosKM1rU6UEIHWlyzWhYQNM/img.jpg?width=1245&coordinates=0%2C10%2C0%2C88&height=700" id="77c04" class="rm-shortcode" data-rm-shortcode-id="7eb9d5b2d890496756a69fb45ceac87c" data-rm-shortcode-name="rebelmouse-image" data-width="1245" data-height="700" />
A diagram showing the experimental set up. On the left is the control condition, on the right is the experimental condition.
Credit: Alexandra K. Schnell et al., 2021<p> As you can probably guess, the ability to delay gratification as part of a plan is not the most common thing in the animal kingdom. While humans, apes, some birds, and dogs can do it, less intelligent animals can't. </p><p>While it is reasonably simple to devise a hypothesis for why social humans, tool-making chimps, or hunting birds are able to delay gratification, the cuttlefish is neither social, a toolmaker, or is it hunting anything particularly <a href="https://gizmodo.com/cuttlefish-are-able-to-wait-for-a-reward-1846392756" target="_blank" rel="noopener noreferrer">intelligent</a>. Why they evolved this capacity is up for debate. </p><p>Lead author Alexandra Schnell of the University of Cambridge discussed their speculations on the evolutionary advantage cuttlefish might get out of this skill with <a href="https://www.eurekalert.org/pub_releases/2021-03/mbl-qc022621.php" target="_blank" rel="noopener noreferrer">Eurekalert:</a> </p><p style="margin-left: 20px;"> "Cuttlefish spend most of their time camouflaging, sitting and waiting, punctuated by brief periods of foraging. They break camouflage when they forage, so they are exposed to every predator in the ocean that wants to eat them. We speculate that delayed gratification may have evolved as a byproduct of this, so the cuttlefish can optimize foraging by waiting to choose better quality food."</p><p>Given the unique evolutionary tree of the cuttlefish, its cognitive abilities are an example of convergent evolution, in which two unrelated animals, in this case primates and cuttlefish, evolve the same trait to solve similar problems. These findings could help shed light on the evolution of the cuttlefish and its relatives. </p><p> It should be noted that this study isn't definitive; at the moment, we can't make a useful comparison between the overall intelligence of the cuttlefish and the other animals that can or cannot pass some variation of the marshmallow test.</p><p>Despite this, the results are quite exciting and will likely influence future research into animal intelligence. If the common cuttlefish can pass the marshmallow test, what else can?</p>