Posts Tagged ‘game theory’
Review of The Chessboard and the Web
Title: The Chessboard and the Web
Author: Anne-Marie Slaughter
Publisher: Yale University Press
Copyright: 2017
ISBN13: 978-0-300-21564-9
Length: 296
Price: $26.00
Rating: 92%
I purchased a copy of this book for personal use.
The first step to winning a debate is to define the terms used to discuss the issue. In The Chessboard and the Web, Anne-Marie Slaughter, the former director of policy planning for the U.S. Department of State, characterizes international relations as a series of interconnecting relationships. Rather than pursue a statist realpolitik strategy, she argues in favor of a cooperative, supportive approach.
Games in Theory and Practice
Dr. Slaughter starts her argument by comparing the traditional view of competition described by Thomas Schelling’s classic text on game theory, The Strategy of Conflict, with operations on a chess board. Of the classic two-by-two matrix games that Schelling describes in his book, the game of Chicken comes closest to emulating the risk of nuclear war that lurks in the background of many international conflicts. If you’re not familiar with the game of Chicken, you might have seen it in 1950s teen movies, when two boys drive at each other at high speed. The first one to swerve is the “chicken” and takes a small loss, but if neither swerves there’s a head-on collision and both players suffer a huge loss.
The Prisoner’s Dilemma, perhaps the best known of the classic games, demonstrates how a game’s payouts can be constructed to convince individuals to violate their best interests. The idea is that two criminals have been apprehended, separated, and offered a choice. If a criminal testifies against the other (defects) and the other refuses to testify against them (cooperates), the one who testified will go free and the other will go to prison for ten years. If both testify, they will go to jail for five years. If neither testifies, each will go to jail for one year. Even though the best choice for both criminals is to refuse to testify and serve a little time in jail, the fact they can’t communicate with each other means they can’t trust the other’s intentions. The penalty for unmatched cooperation is a long jail term while the other goes free, so the logical choice is for both to defect and accept a suboptimal outcome.
The third game Slaughter mentions, the Stag Hunt (also called the coordination game) allows for scenarios where two players can achieve better outcomes by cooperating than by competing. In the Stag Hunt, two hunters can choose to go after a hare or a stag. If a player goes after a hare, they will always get it and win one point. If both players go after a stag, they will each get three points. If one player chooses hare and the other chooses stag, the player choosing hare gets one point and the player choosing stag gets zero. Even with repeated play, it’s easy for players to fall into the trap of getting a steady payoff of one point per round without discovering that cooperation yields better results. As with all of the classic two-by-two games, the main limitation is the lack of communication between the players.
Networks and Connections
After introducing game theory, Slaughter describes networks and basics of network analysis in the context of international relations. For example, she mentions different measures of connectedness, such as the number of connections leading to and from a network node (its degree), the node’s place in the network (its centrality), and the number of times it serves as a connection between two other nodes (its betweenness). She then explores the strengths and weaknesses of the standard network topologies: star, hub-and-spoke, and mesh. Networks appear throughout international relations, whether among states (such as the European Union) or in non-governmental organizations and terrorist groups. Some networks are tightly interconnected (have a high density), while others are more sparse.
Slaughter describes several major types of international networks, starting with resilience networks. Resilience networks can serve as defense, recovery, and stabilization tools. Doctors Without Borders is one example of a networked organization that provides health care in recovery and stabilization roles. Task networks are similar to resilience networks in some respects, but one distinction is that they are temporary groupings assembled to complete work through cooperation, collaboration, or innovation. Cooperation comes with significant risks. If a partner defects, such as when an OPEC member nation produces more oil than its quota allows, then the strength of the network depends in large part on the effectiveness of punishments administered by other group members.
The final category of networks, scale networks, describe how solutions that work well in microcosm can grow. In a replication network, a solution can be repeated with little or no modification at a new location. One such network is the Global Alliance for Vaccination and Immunization (GAVI). GAVI coordinates transport and delivery of vaccines to vulnerable populations to help restrict the spread of disease. Finally, cumulation networks bring knowledge and expertise into a single entity. One example is GitHub, the online source code repository that programmers around the world rely on.
Network Power
As you might expect, Slaughter argues strongly in favor of a networked approach instead of following the realist’s emphasis on states with interests rather than allies. She cites former Secretary of State Hillary Clinton’s adoption of Joseph Nye and Suzanne Nossel’s concept of “Smart Power”, where states use all means at their disposal, from military power to trade, diplomacy, and foreign aid, to influence allies, institutions, and international norms. At some point the distinction between “smart power” and the traditional realist view becomes moot; realists use all of those tools as well, they just do so with different intentions.
Near the end of The Chessboard and the Web, Slaughter compares her liberal internationalist (she would say humanist) approach to Joshua Ramo’s “Hard Gatekeeping” (statist) approach. As she notes, the discussion has raged between proponents of a power-based foreign policy versus those advocating a values-based foreign policy for centuries. Her ideal scenario is an Open Order where states remain important and powerful but operate within an international network charged with “acknowledging and validating individuals, groups, businesses, and institutions not simply as state subjects but as actors in their own right through global networks.”
Conclusion
Foreign policy, diplomacy, and statecraft require careful planning and execution to advance one’s interests. As with all such debates, it’s a matter of striking a balance between a state’s interests and those of its allies, competitors, and neutrals. Advocates of the Hard Gatekeeping approach would argue that the “Smart Power” approach isn’t so smart because it would leave the U.S. exposed to defectors. Even so, I find Slaughter’s arguments in The Chessboard and the Web to be convincing if not quite compelling. States can benefit from well-applied connections, but deciding on the extent of that connectivity and exposure is a devilishly tricky prospect. Highly recommended.
Curtis Frye is the editor of Technology and Society Book Reviews. He is the author of more than 30 books, including Improspectives, his look at applying the principles of improv comedy to business and life. His list includes more than 20 books for Microsoft Press and O’Reilly Media; he has also created more than 50 online training courses for lynda.com. In addition to his writing, Curt is a keynote speaker and entertainer. You can find more information about him at http://www.curtisfrye.com and follow him as @curtisfrye on Twitter.
Reasons for Playing Chess
Chess is a rewarding but maddening game. You can build up an overwhelming position for the first 40 moves and then make a simple tactical error that lets your opponent back into the game or, in extreme and highly embarrassing cases, even win on the next move.
Interviewer: So, tell me…does throwing away a win hurt?
Curt: Yes. Yes it does.
You see golfers going crazy over their rounds, alternating between self-loathing over the short putts they missed and self-praise for the 150-yard shot that ended up a foot from the hole. I played golf occasionally for a few years and can testify to that effect. Some of my friends play 18 holes just so they can feel the satisfaction of hitting one good shot.
Some days they have to play 36 holes.
A golfer having a bad day still gets in some physical exercise. What about chess players? As with many endeavors, it depends on why you’re playing in the first place. You always get to exercise your brain and look over the consequences of your moves, which keeps you sharp and might fight off the effects of aging, but what else?
If you’re playing with someone who’s about your own strength, you get the benefit of an equal competition and, very likely, enough wins to keep things interesting. Playing someone stronger than you helps you learn and winning every so often helps keep you going. Playing a weaker player lets you win more often and teach the game, even if only indirectly.
What’s often overlooked is that chess can be a social game. If you play blitz chess, where players have to make all of their moves within three or five minutes, you can get in a lot of games and try many different types of positions. Playing a longer game lets you think more deeply, and playing without a clock lets you approach the game more casually.
You can also take time to analyze your game with your opponent. Serious players often try to identify the move where the winner got an advantage and what the loser missed. When done with a spirit of exploration and sharing, post-game analysis can be fun and helpful.
Chess as metaphor
Games have long played a part in literature, representing a competition between humans or supernatural beings. Chess features prominently in many stories. The game’s intellectual nature lends itself to such depictions, with the idea being that if you can beat someone else at chess, you are the better man.
Other games, both real and invented, serve similar roles. For me, the best example is the game Azad from Iain M. Banks’ book The Player of Games. The game of Azad is a vast undertaking, with high-level matches often taking a month to play. There are several boards, a combination of team and individual play, and so many pieces as to nearly defy description.
In the story, the game was developed as a metaphor for the structure and values of the Empire of Azad. It was part pastime and part civil service exam. The Azadian home world held a tournament every so often, with the winner crowned emperor. The better you did in the tournament, the higher your position in the government.
The premise of the story is that another civilization, the Culture, sends its best game player to compete in the tournament. Banks was known for a political bent to his stories; The Player of Games is no exception. On its surface a simple diplomatic exchange, our player’s participation and continued success brings the conflict between the two civilizations and their values into sharper relief.
It’s telling that the Culture’s hero only starts to play at a high level when he takes on aspects of the Empire’s philosophy in his own play. Banks manages that conflict magnificently.
Chess is an abstract game with arbitrary but well-balanced rules that allow for a wide range of successful strategies and tactics. Though it doesn’t approach the (admittedly fictional) resolution of a game like Azad, it has long played a role as a metaphor for accomplishment and brilliance. As such, it provides a terrific instructional base.
Chess as a game (among many)
Chess is often called “the queen of games”, at least in Western culture. The game’s austere appearance, when combined with its tactical and strategic depth, provides an air of challenge and mystery.
In many ways, chess is the prototypical Western game. Strategies and tactics are direct, with little progress to be made unless you directly confront your opponent. Chess is also a perfect information game, meaning there is no element of chance. You might not know your opponent’s next move, but there’s nothing hiding it from you. If you didn’t see what was coming, you can only blame yourself.
Although chess has increased in popularity in Asia, the traditional strategy game of Japan, China, and South Korea is go. Unlike chess, where the goal is to create a position where your opponent’s king is under attack and cannot move to a safe square, go players place their stones in an attempt to surround territory on the board. Chess boards are 8 x 8, with 64 squares, and the pieces stand on the squares. In go, the board has 19 x 19 lines, with 361 intersections, and players may place a stone on any unoccupied intersection (with a few exceptions).
The complexity of go far outstrips that of chess, at least in terms of the computation required to analyze and evaluate a position. Computers have conquered humans at chess…their calculating speed and positional evaluation let them beat even the strongest carbon-based players regularly. The most advanced go programs can only beat top professionals if they are given a substantial head start. That said, the gap is closing.
I said that chess is the prototypical Western game, but it’s mostly thought of as a European (and even more specifically, Russian) game. In America, the game of choice is poker. Poker is a gambling game, with a significant element of chance involved. You can do everything right but still lose if your opponent decides to fight the odds and draws the cards they need. Ironically, the better you play, the more of these “bad beat” stories you’ll have to tell. If you’re always in the lead, the luck of the draw means you will get chased down on occasion.
I hope I don’t sound bitter. But I am.
Do the Russians play chess, the Chinese play go, and the Americans play poker? If you look at our cultures and practices, you’ll see there’s a fair amount of truth to that statement. How well that metaphor translates to actionable intelligence is debatable, but it’s an interesting way to start a conversation.
Chess and Motivation
To paraphrase the Great Oz, “I’m a good man, but a very bad chess player.” I can beat almost any non-serious player in a casual game, but I’m in the lower half of those of us who pay to play on the Internet Chess Server.
And yet, even though I lose a lot more than I’d like to, I enjoy the game immensely. In some sense, I like the idea of being a chess player…there’s a certain nerdy caché to the game that fits my personality. I also enjoy my occasional successes (I wouldn’t call them brilliancies) where I’ve seen just a bit farther or evaluated a position more accurately than my opponent.
My rating, the number that indicates my relative strength as compared to my fellow competitors, swings up and down within a range that runs from kind of impressive to “maybe I should go back to Candyland.” Sometimes I feel strong, like I’m concentrating well and see the outcomes of move sequences, while at other times I make the first move I see and hope I get lucky. I’m not sure why my concentration varies so much, but it’s an interesting phenomenon.
So why, if I’m not a very good serious (or even semi-serious) player, do I keep playing? What are the psychic benefits I get from banging my head against 32 pieces and 64 squares? Sure, the game’s fun in and of itself, but what specifically keeps me coming back?
I’ll address these questions in more detail in my forthcoming series of posts, but I’ll start out with a note on what my motivation is not. A friend once said, when I was furious at myself for a series of embarrassing losses, “It would be a shame for you to give up the game after you’ve put so much into it.”
She was right in a way, but her statement is an example of the sunk cost fallacy. The sunk cost fallacy says that the investment (of money, or time, or whatever) you’ve made in an endeavor should affect future decisions. In fact, if you have no way of reclaiming the money or time you’ve invested in something, those “expenses” should in no way affect your future decisions. All you should care about is whether future investments are worth the cost.
I keep playing, so I obviously must think it’s worth my effort to continue. Chess is a rich game, after all, one that rewards its players for their efforts beyond rating points or games won. I look forward to examining it more closely.
Law and Magic: Revealing the Links
I had the very good fortune to speak at the Law and Magic: Revealing the Links conference, co-hosted by the Law and Humanities Institute and the Thomas Jefferson School of Law last Friday in beautiful San Diego. The conference was organized by Professors Christine Corcos of the LSU Law Center and Julie Cromer Young of the Thomas Jefferson School of Law. Licensed attendees could earn up to 6.5 hours of CLE credit.
As the conference’s name implies, the day’s presentations were about how the art and practice of the law intersects and interacts with the art and practice of magic and what Professor Corcos called the “crafty sciences.” I had the good fortune to perform a 30-minute show over lunch. Later in the afternoon, my presentation Rhetorical Mathematics examined how performers and lawyers can use and abuse math to further their arguments. Practitioners of both arts have a wide range of confusion-inducing techniques from which to choose: misstating probabilities, relying on unspoken assumptions, pulling numbers out of thin air, and many others.
I think my paper went over pretty well. I covered probability calculations that went beyond simple liability calculations such as the Hand Rule articulated in United States vs. Carroll Towing, so there was some head scratching at times. The most fun for me was when I presented the Monty Hall Paradox, which describes the math behind the game played at the end of Monty’s show Let’s Make a Deal. The idea of the game is that Monty displays three doors, two of which hide a losing choice, such as a goat, and the third a prize such as a new car. You start the game by choosing one of the doors. Once you do, Monty (who knows where the car is) opens a losing door. You can then either stay with your original choice or switch.
The question for you: does it matter whether you switch or stay? If so, what are your chances of winning for either strategy?
The National Coin Flip Lottery
On January 23, 2014, the International Monetary Fund (IMF) released a paper citing income inequality as a threat to economic security in developed and developing countries. In part, they found that:
- Income inequality has increased in both advanced and developing economies in recent decades.
- There is growing evidence that high income inequality can be detrimental to achieving macroeconomic stability and growth.
- Fiscal policy is the primary tool for governments to affect income distribution.
Unfortunately, the IMF declined to offer a solution, stating that “[t]his paper does not advocate any particular redistributive goal or policy instrument for fiscal redistribution.”
That’s where I come in.
Gettin’ Rich Ain’t Easy
Warren Buffett once remarked that if a person won $1 million flipping coins, he could sell a book entitled How to Make One Million Dollars Flipping Coins. His point is that some investors, regardless of how unskilled they are, will get lucky every now and then. We should not attribute everyone’s gains to great skill.
That said, there is a general pattern we can follow. People get rich by combining two abilities: making money and keeping money. The problem is that when you keep money it doesn’t flow through the system. Trickle-down economics in an age of hyper efficiency doesn’t work as well as it might. What we need is a low-impact system for wealth redistribution.
In the interest of creating up to 334 new millionaires every day, I propose a National Coin Flip Lottery. All 350 million Americans, regardless of age or income, must contribute one dollar per day to the lottery. We all need car insurance if we want to drive and we all need health insurance if we want to live, so this slight imposition is little more than an annoyance. If you have a Social Security number, you have to pony up.
Every morning at 5 AM Eastern time, a computer divides the database of American citizens into two groups: Heads and Tails. A representative flips a coin, probably a virtual coin because quarters come up heads slightly more often than tails, and eliminates the losers. The computer then randomly re-divides the population into halves and continues until we have 334 winners. That’s correct: after just 20 flips we will have 334 lucky millionaires.
The system collects $350 million every day, but the excess can fund lottery operations, reduce the national debt, and support a special lottery held every February 29. Let’s say we hold back $1 million of the $16 million excess from each drawing. There are 1,460 days between leap days, so we could give away enough money to create 1,460 new millionaires on that day alone.
Supporting the Public Interest
Just think about the positive social impact that creating 334 new millionaires every day could have on society. Yes, the less socially responsible winners would just blow their newfound riches and hope to win again, but quite a few of the lucky individuals will redistribute the wealth among their family and community. That level of liquidity would free up small-scale investments, provide competitive pressure for traditional lending institutions, and relieve poverty for a small percentage of the population every day.
It would be cruel for citizens to win 19 straight coin tosses and lose when they are on the cusp of being a millionaire. Therefore, I propose that individuals may enter a preference to split their prize at the $32,768 level or higher. If two individuals who are willing to split meet at a given level, they both automatically get the prize.
Given the raging expansion of gambling across the United States, with the quaint exceptions of Hawaii and Utah, this modest proposal fits comfortably into the American zeitgeist. Next February 29, join me in celebrating our new national holiday: Millionaires Day!
When You’re “Due” — The Gambler’s Fallacy
I travel to Las Vegas once or twice a year, both to play poker (where I convince myself I have an advantage) and to dabble in other games (where I definitely don’t). Since 1993, when I started playing while on the East Coast, I’ve seen thousands of players succumb to the insidious gambler’s fallacy.
Let’s say you’re playing roulette and notice, as posted on the so very helpful display by the wheel, that five red numbers have come up in a row. Is black due? What about green (0/00)? The answer is neither. Roulette wheels are well-balanced and the little obstacles spread around the wheel, called canoes in casino parlance, make outcomes random enough to be considered independent trials. If red numbers come up five times in a row, the next number will be red 18/38 of the time, black 18/38 of the time, and green 2/38 of the time. Ironically, it’s our human urge to discover patterns that makes the gambler’s fallacy work. The wheel has no memory, but we do.
The bottom line is that when you play roulette, the proportion of red, black, and green numbers will tend toward the target ratios over millions of spins and the weighted payoffs will ensure the house earns its profit over the long run. But what about games like poker? Poker is a skill game with a healthy dose of luck thrown in, so trials aren’t truly independent. Inferior players beat better players over the short term, but only because of luck. But what happens when equal players face off?
It’s hard to find players of the same skill level at a poker table, but I tested the theory by replicating an experiment described by poker author Lou Krieger. Like Lou, I set up ten identical players in Wilson Software’s Turbo Texas Hold’em simulation mode and let them play hundreds of millions of hands against each other. Six of the ten players were just above or below breaking even, but there were two big winners and two big losers. Remember that each player followed an identical strategy — the only factor controlling their fate was the luck of the draw.
As human beings trying to extract a living from an indifferent universe, we must realize that the odds are not always in our favor and that we will go through bad streaks we can’t seem to reverse. At these times it pays to strengthen your base by learning new skills or practicing old ones, reinforcing friendships, reaching out to others for help, and offering assistance where you can. Doing these things doesn’t constitute “good karma” or “putting things out into the universe”, both dubious concepts. What you are doing is improving the chances you’ll be ready to take advantage of opportunities that you and your contacts discover.
Clustering and Streaks — Real or Imagined?
The folk wisdom that “bad things come in threes” is still popular in the U.S. Whenever two celebrities die on the same day, for example, even the most hardened critical thinker feels the urge to look for the third.
Is clustering real? Do events happen in streaks, or are they just a product of our pattern-seeking brains? George Carlin made fun of the “bad things happen in threes” adage by stating that bad things actually happen in 27’s, noting that “it just takes longer to see the pattern.” You can always find instances of “bad things” in the world to fill out your sets of three, but what does the research say? There have been a lot of studies on the subject, including Koehler and Conley’s “The “Hot Hand” Myth In Professional Basketball”, published in 2003 in the Journal of Sport and Exercise Psychology. The authors examined the National Basketball Association’s long distance shooting contest and looked for statistical aberrations in the sequences of made and missed shots. As in all but a few other studies, they found no significant deviation from chance. When they took each player’s base shooting accuracy into account, the effect disappeared.
Sports are physical contests and even little variations in physical conditions can affect performance, but what about chess? Chess is a mental game played with perfect information. That is, you know everything there is to know about a position and there’s no hidden information, such as a player’s hole cards in poker. As of this writing, I have played 19,738 games of blitz chess (each player has 3 or 5 minutes to make all moves in a game) at the Internet Chess Club since June 27, 2001. As I watch my online chess rating fluctuate from embarrassing to “not bad for me”, I wonder how much the streaks of wins, losses, and draws reflect my abilities and how much is the “luck” of an opponent making some horrible mistake.
The three-year graph of my rating shows huge swings, but the average is right about where I perceive myself as a player. Perhaps my streaks are due to luck. After all, I don’t seriously study the game and play to take a break from other work. The big changes make a strong visual impression, but there are a lot of small shifts in there, too.
Improvisers can make a fun game out of looking for apparent patterns and justifying reasons for believing streaks exist. The lesson for analysts? Carefully examine whether a sequence of events is due to some underlying cause or is just a sequence of events that might be due to chance. That said, given the strength of our innate need to discover patterns, is there any way to dispel what appears to be the myth of the hot hand? In a 2006 review of the literature, Michael Bar-Elia, Simcha Avugosa, and Markus Raab summarized the situation in this way:
As Amos Tversky, who initiated the hot hand research, used to say (cited by Gilovich in an online chat, September, 2002), ‘‘I’ve been in a thousand arguments over this topic, won them all, but convinced no one’’.
Improspectives 
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