Game-theory

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How to Use Game Theory to Change Your Fortune

Imagine this: you drop on the couch, turn on your favorite game show, with your iPad, Android or other tablet in hand, being the modern “two-screen” TV viewer that you are. Let’s say it’s Jeopardy!, which celebrated its 50th anniversary (30th with host Alex Trebek) in Mar 2014. As part of your two-screen experience, you like to check Facebook and Twitter while you watch the game show, looking for mentions of the players on today’s episode. Wait, what’s this? One of today’s contestants, Arthur Chu, is not only exhibiting unorthodox game-play, but he’s live-tweeting his appearance. What’s going on here?

A Game Theorist Games Jeopardy!?

Of course, Chu is not really live-tweeting, since Jeopardy! episodes are recorded ahead of time, sometimes by months, but it’s still an unusual experience — especially since he’s offering what amounts to a play-by-play via Twitter of what he is thinking for each clue played. He’s also using Twitter hash tags like “#chuphoria” (play on “euphoria”) and “#ChuChuTrain” (his wife’s creation). His wife is in on the act as well. What really irked some viewers was Chu’s seeming non-strategy of jumping all over the Jeopardy! board and yet somehow coming out ahead each game. He wasn’t a good little contestant like most, going down an entire category column on the board before switching to another category. That annoyed them, making them uncomfortable at home because they couldn’t play along as easily. Another thing about Chu that irked viewers was his seemingly incessant jamming on his game buzzer — which there’s an explanation for, but is actually part of his overall game theory strategy. Chu angered enough tweeting viewers of the show that some of the tweets got shockingly racist.

Jeopardy Non-Strategy as Strategy

Chu’s reaction to the hate-o-sphere? Not to sweat it. He just kept up his “live” tweeting each day that he appeared on Jeopardy! In a strategy that social media marketers might applaud, his wife actually re-tweeted the most obnoxious comments using the Chu-specific hash tags, leveraging the haters to gain more supporters, stirring up further retweets. Brilliant. Of course, any long-time Jeopardy! fan (or anyone who bothered to search online) would know that Chu’s seeming non-strategy was in fact a strategy, and nothing particularly new — aside from the social media marketing aspect, which he and his wife milked. He professed to using “game theory,” which derives from mathematics and statistics, and is often applied to economics and other disciplines. Game theory is essentially the study of making strategic decisions based on the probabilities of different outcomes due to a sequence of actions or “plays.” It can be applied to every day life, to a degree, not just on game shows and to economics.
• The category-hopping move that Arthur Chu used is known as the “Forrest Bounce,” named after the 1985 Jeopardy! champion, Chuck Forrest, who is credited with first using the technique.
• Other Jeopardy! champions who’ve used the Forrest Bounce include Ken Jennings, who played for 74 episodes (73 wins).
• To someone unfamiliar with the technique, it appears to be a non-strategy and entirely random.
• The idea is to find all the Daily Doubles, which game theorists will say is essentially one of the few points of control for contestants on Jeopardy!
• Even if the seeker gets a Daily Double question wrong (without dropping into last place), she/he eliminates it as a control point for opponents.
• So the earlier you find all the Daily Doubles, the better, and hence the need for hopping categories.
• Statistically speaking, most Daily Double questions appear in the bottom two rows. This can be verified by scanning the fan-run J! Archive (j-archive.com) Web site, which has an online database of all the clues and questions for every episode of the modern version of Jeopardy! (Jeopardy! aired in the 1960s and 70s with host Art Fleming. The Alex Trebek run started in 1984.)

Other game theory-based objectives that Chu and other former champions have collectively used include what we might think of as common sense as well as strategy:
• Maximize advantage.
• Minimize risk.
• Be first to buzz, when appropriate. The buzzer is activated by a crew member of the show. If a contestant buzzes too soon (before host Alex Trebek finishes his clue), the buzzer deactivates briefly. Chu has  said that Jeopardy! is a game of reflexes and psychology, not just a test of knowledge. He admits that it took him a bit of getting used to, to not press the buzzer too early. (His initial awkwardness with the buzzer annoyed some viewers.)
• Never play for 2nd place. According to blogger Keith Williams, the goal of Jeopardy! is to return the next day, else you don’t get the money you earned in a given episode, only a consolation prize. (Arthur Chu was googling for “Jeopardy strategies” and ended up on Keith William’s blog, studying his strategies and memorizing them)
◦ That is, if you’re in 3rd place, you leave with $1K. For 2nd place, the prize is $2K.
◦ So for Final Jeopardy, anyone who is behind is likely to bet everything.
◦ The leader, on the other hand, should only bet to tie the most that the 2nd place contestant could win in Final Jeopardy.
◦ Chu did this twice, when the 2nd place contestant had relatively high earnings compared to his lead amount. The first time he did it, both he and the 2nd place contestant tied, so both returned for the next episode.

At least, so go some of the game theory strategies. Ultimately, game theory is only useful on Jeopardy! if you know a sufficient number of answers (or in this case, the questions that went with the clues. What ended Arthur Chu’s 12-game run was that he got a lot of the questions wrong — even early in his run, not just on his final appearance. On the other hand, 73-time winner Ken Jennings, on the other hand, knew the questions to many different categories, and supposedly diligently prepared himself for every batch of games. (An entire week’s worth of episodes are filmed in one day.)

Some Notes on Game Theory

While game theory has been applied to economics for over five decades, typically, game theory works best on closed systems with fixed rules and at least some expected outcomes regardless of the participant.
• Game theory works best in a closed system, with well-defined rules and outcomes per action.
• Game theory is good for describing rational actions and their outcomes.
• If the system is not closed (i.e., the stock market, your own investments), game theory is not likely to be as useful or reliable. However, that does not mean it’s entirely useless. The more variables we know to a system, the easier it is to model game theory approaches.
• The more assumptions there are, the less likely game theory is reliable in predicting outcomes.

Game Theory in the Real World

Board Games

Of course, game theory works well on strategic board games because they can be model as a relatively closed system.
• Chessmasters and Go players, in particular, are master game theorists, whether they realize it consciously or not.
• The person who typically wins in any particular type of strategic board game is the one who most effectively applies strategic thinking.
• They think ahead the most steps, weighing out the outcomes of any particular play by themselves, as well as their opponent’s most likely reaction — and then pick a move that they feel is most likely to either lead them to a win or at least gain an advantage over the opponent until the next move.
• The most difficult part about this for games, besides gaining the game knowledge and skills in the first place, is applying the strategic thinking — being able to mentally imagine what opponent reaction a specific move might trigger, then weighing if there is any better move — all in a limited amount of time.
The more you know about the outcome of a move in the complex games of chess or Go, the easier it becomes to apply game theory strategy. If you’re playing chess games for *ahem* money at a park table, it’s worth the effort to learn action and reaction.

Card Games
Card games are another good candidate for applying game theory. However, when money enters the picture, it becomes “gambling” instead of just a friendly game of cards. Which is why any serious card player — whether in a competition poker game or a game of Hearts amongst friends or colleagues — tries to learn each game’s rules. It’s gambling because card games are deceptive. Consider this:
• There are 52 cards in a deck.
• Shuffle any brand new pack a few times and you have a sequence of 52 cards.
• That sequence is unlikely to be repeated for a very long time.
• That’s because a deck of 52 cards can form 52! (52 factorial) different, unique sequences.
• 1!= 1; 2!= 2×1; 3! = 3x2x1 =6; 4! = 4x3x2x1 =24.
• So 52! = some huge number that’s larger than 8 with 67 zeros after it.
• If we had a machine that could create each unique sequence of 52 cards once per second, it would take more than 2 followed 60 zeros years to cover them all — many billions and billions of years.

Despite the complexity of a card deck, people still win at card games. That’s because each game sets down some rules, and within that framework, you can apply game theory to the cards you get and the cards you think an opponent might have. Of course, the more opponents, the more complex your strategic thinking becomes. When it comes to games like poker, what also helps your strategy is psychology — similar to what Arthur Chu did in Jeopardy!, whether he meant to or not. For example, bluffing helps if you don’t do it all the time in any particular set of games where you’re facing the same opponents. You still have to play your optimal strategy as far as the cards go, but you often have the edge if you can make people think a bad hand is good. It just will not work every time.

Sports Betting
Sports is a slightly different story. A particular sports game is less of a closed system than, say, a game of cards or a board game. There are so many variables which athletes and coaches may not have control over:
• The skill and experience of each player,
• Weather in an uncovered stadium,
• The impact of fan behavior on a (new) player,
• An injury during the game,
• A simple mistake made by one or more players in a play,
• A player is secretly sick and it’s affecting performance,
• Etc.

Fortunately, an athlete’s skill can be quantified to a degree. Several sports have a long history of tracking statistics of players, teams, starting lineups, coaches, etc. That’s closer to a “closed system,” having those stats. At least for as long as the team’s roster does not change. One sport in which game theory is more relevant is baseball.
• There’s an entire field of study, Sabermetrics, which is essentially analytics applied to baseball.
• The term is derived from SABR (Society for American Baseball Research).
• Any use of this analytics methods to predict player and team outcomes by, say, a coach, becomes an application of game theory.
• Fans can also use the analytics for betting.
• Baseball also tends to have a lower rate of serious athlete injury than other team sports — maybe with the exception of basketball. This reduces injuries as an unknown factor that affects game outcomes.

Of course, any professional team sport can have analytics similar to Sabermetrics applied. By understanding the analytics of a sport, you can devise game plays if you’re a coach, or betting strategies if you’re a fan. Fantasy sports pools are more complex, but there are game theory strategies for fantasy sports, using something called a minimax solution, aka a Nash equilibrium. The latter is named after John Nash, an Nobel prize-winning American mathematician, whom actor Russell Crowe portrayed in the movie “A Beautiful Mind.”

Car Buying
Looking for a new car? What if you could save money on your purchase with a simple strategy? Would you try? The only setback is that you may have to step past your social comfort level. Here’s the general approach:
• Decide on the car make and model you want.
• Make a list of all the dealerships within a comfortable driving range that sell that car.
• Call each of them and say that you will buy the car from the dealer who has the lowest price, but you will not discuss one dealer’s price with another dealer.
• If they tell you that you can’t buy a car over the phone, politely say that that’s not true, that other’s have done so. Promise that you’ll come check in hand if that dealer has the lowest price.
• If they refuse to give you a price, thank them and tell them they obviously don’t have the lowest price, then move on.
• If they agree, record info about the price and salesperson — they do typically work for commissions.
• Once you have the lowest price, take your checkbook and go to that dealer with that price.
• If they don’t honor the quote, bid them goodbye and go to the dealer with the second-lowest quote, etc.

A few caveats:
• The strategy assumes at least one dealer will honor their quote.
• Most people are going to get discourage by the reaction of the salesperson. However, those who persist are likely going to end up with a better price on a car.
• This is not going to work the same way for leases, but it’s possible to devise a similar strategy, if you factor in different finance company terms.

Home Buying
You’re trying to buy a new home. You’ve made a bid and the real estate agents tells you there are multiple offers. Of course, you don’t usually get details of the other bids. So here are your options at this point:
1. Walk away.
2. Maintain your offer.
3. Increase your offer.

If you want the house, your only option really is #3, since the multi-bid situation means what you’re already offering isn’t enough. The question is, how much more do you offer? Answer: the amount that you think will win the bid, based on what you know about the place, based on similar properties nearby, based on what you can afford, etc. Whatever that amount is, it actually is the correct amount in your situation. At this point, you can do nothing more than possibly overbid. No one wants buyer’s remorse on a house.

Auctions
If you’re auctioning off something and have a choice at the type of auction, something called the second-prize auction will often maximize your profit — assuming you’re auctioning not just something of value, but something that more than one person wants. It works like this:
• The item for auction is put on display so that potential bidders can assess it.
• Knowing this is a second-prize auction, they make their sealed bid at an amount they are comfortable with.
• When the item’s bid period is over, the person with the highest bid wins, but only has to pay the second-highest bid price.

The strategy of the seller here is that bidders are all more likely to overbid what they might have otherwise bid in a different type of auction. So even the second-highest bid price could be more than you were expecting.

Games People Play: Relationships, Marriage

Someone once joked that compromise is getting what neither party wants. However, when it comes to marriage and relationships, sometimes compromise is actually the best outcome for both parties. Marriage and other relationships are more like playing a game than most of us realize or will admit to — meaning that game theory applies here as well. Paula Szuchman and Jenny Anderson published a whole book on game theory applied to marriage, “It’s Not You, It’s the Dishes — formerly titled “Spousonomics.” Szuchman, editor of thedailybeast.com, distilled some of her book in an article called “Marriage and the Art of Game Theory.” The gist is as follows. Game theory applies because there are a number of suitable factors:
• Two players (more if children or other family are involved).
• Each has a personal agenda limited by the other person.
• They could choose to cooperate (“cooperative strategy”) or not (“non-cooperative strategy”).

The non-cooperative strategy is often the easiest reaction, but usually has the most consequences. So what do you do? Answer: according to Szuchman, you go after the “best results possible” — which really often boils down to compromising, but in a way that gives a deferred reward. Here is Szuchman’s general strategy for achieving the best results possible with a spouse or significant other:
• Think ahead to what your mate’s reaction will be to your planned action. Should that potential reaction influence what action you actually take?
• Consider previous similar situations. How did your mate react then? If it wasn’t positive, what can you do differently now.
• Change your perspective. Try to be your spouse; what would they do in the current situation.

The example she gives is one where a couple are fighting over the fact that neither wants to go grocery shopping, and have ended up eating pizza everyday. A cooperative strategy could mean a nice, romantic meal. An non-cooperative strategy could mean forever eating take out. To that we add: possibly gaining weight, getting sick, breaking up, or even dying.

Other Applications
It’s not possible here to cover all possible applications of game theory, but they include salary negotiations, kidney donation chains, government gridlock, stock market investing and more. Game theory strategies are more successful for some of these applications than others. It all boils down to having as much information as possible, and understanding what reactions there could be to any given action.

Game-theory

References

Information for this article was collected from the following pages and web sites:
1. http://ed.ted.com/lessons/how-many-ways-can-you-arrange-a-deck-of-cards-yannay-khaikin
2. http://www.thedailybeast.com/articles/2012/06/13/marriage-and-the-art-of-game-theory.html
3. http://thefinalwager.co/tutorial/
4. http://www.theguardian.com/tv-and-radio/2014/feb/24/arthur-chu-jeopardy-misunderstood-mastermind-game-theory
5. http://www.wired.com/techbiz/media/news/2002/07/54131
6. http://www.businessinsider.com/how-to-use-game-theory-to-your-benefit-2012-4?op=1
7. http://thoughtstreak.wordpress.com/major-old-posts/applying-game-theory-into-everyday-life/