Game Theory

[whatever]

I'm actually kind of surprized that nobody has mentioned the role of game theory in political strategies during the Cold War A lot of the games of brinksmanship and arms races and such was explained quite well by game theory!

I actually took a few game theory classes- I wasn't a big fan of the one in the Economics Department because they used too many mathematical models- the political science one was fun though

[bananatrombones]

Originally Posted by LostInNerSpace

... The real problem was systemic failure in the financial system...What happened was the investment banks were taking these subprime mortgages and packaging them with high grade mortgages in such a way that the credit rating agencies would rate the new CDO (collatoralized debt obligations) as AAA grade debt.

Very much so. Selling debt as an asset was never a very smart idea. You do not need game theory or advanced maths to work that one out. Although this is off-topic, technically.

Maybe the Nash Equilibrium of this topic is "off-topic"?

[bananatrombones]

Originally Posted by whatever

I'm actually kind of surprized that nobody has mentioned the role of game theory in political strategies during the Cold War A lot of the games of brinksmanship and arms races and such was explained quite well by game theory!

The documentary "The Trap: Whatever happened to our dreams of freedom?" by Adam Curtis, is on youtube, albeit in little sections. Curtis has a very interesting slant on why things are so f*cked up now directly relates to game theory developed (and implimented) by the US Military in the guise of the RAND Corp.

A friend's father worked for RAND Corp in the 60s and never mentioned any of the work he did up to his death, even after a few sherries...

RAND Corporation Provides Objective Research Services and Public Policy Analysis

[LostInNerSpace]

Originally Posted by typo

The financial markets are definitely not zero sum games, in that one trader's gain is not offset by another trader's loss. Viewing financial markets as a zero-sum game implies zero economic growth, with gains and losses determined only by changes in price. A more accurate view is that the gains in the market are driven by the assets involved creating more value than they were in the past. The economic pie tends to increase and the gains outweigh the losses.

The futures markets are definately a zero sum game. At the end of each day real cash is debited or credited from or to your account depending on whether your position was up or down for the day. That money is credited or debited to or from an account holding an opposing position. That is the definition of zero sum. One person's gain/loss is another person's loss/gain. The stock market is slightly different with this whole concept of settlement, but at the end of the day there are always buyers to meet sellers and sellers to meet buyers. Marketmakers make the market, they don't make whatever they are selling. If you want to buy or sell something but cannot due to lack of liquidity, the Marketmaker has to do the opposite, sell or buy, to make the market with you.

What you said seems to imply that economic growth depends entirely on the financial markets. This is completely untrue. In the US, around 70% of GDP comes from the consumer. The stock and futures markets have a much larger psychological effect on the heath of the economy than their relatively small slice of the pie warrants in reality. The pie shrinks when the US consumer stops borrrowing money to spend on useless imported crap, or when businesses become overly risk averse and reduce their debt leveraged capital expenditures and growth.

[LostInNerSpace]

Originally Posted by elfinchilde

but in the view of the entire portfolio: just because you lose one trade, doesn't mean the entire portfolio goes down the drain, if it's diversified. Plus, there's losing little, losing a fair sum, and losing a large sum. Same for winning. And so, it cannot be a simplistic binary situation of just win or lose. Years of winnings may be wiped out by one gigantic loss, or variables: Bear Sterns is the perfect example.

I agree.

Originally Posted by elfinchilde

edit: and one more thing: when you actually enter the markets, you can throw all your books out of the window. Preconceived notions are some of the best killers of new traders. Only one rule: follow the trend. Even experienced traders die, when they cling to concepts and refuse to acknowledge the reality of the trend in front of them.

I disagree somewhat. When it comes to making money trend following can't be beat. But I've learned to trade through books. I've read hundreds of books and just picked the best of each. I have no idea how you would have learned, but many sucessful traders learn through reading books.

Trend following can't be beat when it comes to making money in the markets, but I firmly believe that any strategy has to be backtested and verified statistcally. Trading is professional gambling. In a casino, the odds are stacked against you, in the markets the odds can be stacked in your favor. But the charts can play tricks on your eyes. A strategy that would appear to be solid often does not hold water when backtested on even in-sample data, let alone out of sample data.

Entries are easy. What is hard are the exits. My intuition in the markets is spot on. I consistently amaze myself at my ability to pick minor tops and bottoms in the mini sized futures contracts. I've built up this intuition through observation, losing a lot of money, and obsessively reading about the markets. The problem is that I frequently screw up my trades with poor judgement (P). That's why I prefer automated trading systems. You make the decisions ahead of time and let the system run. But I will always love some discretionary trading.

UPDATE: This brings me to the reason I was interested in this thread in the first place. I want to look into way to improve my trading systems with exotic techniques. This is the INTP in me speaking. My best trading system is actually quite simple. Simple is usually better because you are less likely to be restricting the degrees of freedom. That is the subject for another post.

[m a r r o k]

Here it is an interesting application of the game theory:

Some time back I thought of an example which shed light for me on some of the fail-to-disagree results. Imagine that two players, A and B, are going to play a coin-guessing game. A coin is flipped out of sight of the two of them and they have to guess what it is. Each is privately given a hint about what the coin is, either heads or tails; and they are also told the hint "quality", a number from 0 to 1. A hint of quality 1 is perfect, and always matches the real coin value. A hint of quality 0 is useless, and is completely random and uncorrelated with the coin value. Further, each knows that the hint qualities are drawn from a uniform distribution from 0 to 1 - on the average, the hint quality is 0.5. The goal of the two players is to communicate and come up with the best guess as to the coin value. Now, if they can communicate freely, clearly their best strategy is to exchange their hint qualities and just follow the hint with the higher quality. However we will constrain them so they can't do that. Instead all they can do is to describe their best guess at what the coin is, either heads or tails. And further, we will divide their communication into rounds, where in each round the players simultaneously announce their guesses to each other. Upon hearing the other player's guess, each updates his own guess for the next round.

Read on below the break for some sample games to see how the players can resolve their disagreement even with such stringent constraints.

Here's a straightforward example where we will suppose A gets a hint with quality 0.8 of Heads, and B gets a hint with quality 0.6 of Tails. Initially the two sides tell each other their best guess, which is the same as their hint:

• A:H B:T

Now they know they disagree. Their reasoning can be as follows:

A: B's hint quality is uniform in [0,1], averaging 0.5. My hint quality is higher than that at 0.8, so I will stay with Heads.
B: A's hint quality is uniform in [0,1], averaging 0.5. My hint quality is higher than that at 0.6, so I will stay with Tails.

• A:H B:T

So they remain unchanged. Now they reason:

A: B did not change, so his hint quality must be higher than 0.5. That is all I know, so it must be uniform in [0.5,1], averaging 0.75. My hint quality is higher than that at 0.8, so I will stay with Heads.
B: A did not change, so his hint quality must be higher than 0.5, so it must be uniform in [0.5,1], averaging 0.75. My hint quality is lower than that at 0.6, so I will switch to Heads.

• A:H B:H

And they have come to agreement. If both A and B had had higher hint qualities, they might have persisted in their disagreement for more rounds, but each refusal to switch tells the other party that their hint quality must be even higher, and eventually one side will give way. It's improbable that both sides will have high but opposite hint qualities. What happens in the more likely case where they have low but opposite hint qualities? Let's suppose that A gets a hint of Heads with quality 0.1, and B gets a hint of Tails with quality 0.15.

• A:H B:T

A: B's hint quality is uniform in [0,1], averaging 0.5, which is higher than my 0.1, so I will switch to Tails.
B: A's hint quality is uniform in [0,1], averaging 0.5, which is higher than my 0.15, so I will switch to Heads.

• A:T B:H

A: B switched, so his hint quality was lower than 0.5, making it uniform in [0,0.5] and averaging 0.25, which is higher than my 0.1, so I will stay with Tails (B's original guess).
B: A switched, so his hint quality was lower than 0.5, making it uniform in [0,0.5] and averaging 0.25, which is higher than my 0.1, so I will stay with Heads (A's original guess).

• A:T B:H

A: B stayed the same, so his hint quality was lower than 0.25, making it uniform in [0,0.25] and averaging 0.125, which is higher than my 0.1, so I will stay with Tails.
B: A stayed the same, so his hint quality was lower than 0.25, making it uniform in [0,0.25] and averaging 0.125, which is lower than my 0.15, so my original hint quality was higher, and I will switch back to my original Tails.

• A:T B:T

Once again agreement is reached. Note that when both sides have a low hint quality, they initially switch to the other side's original view, then they each stick with that new side. After enough rounds one of them decides that the other's hint must have been so poor that his hint was better, and he switches back to reach agreement. An interesting case arises if the hint qualities are near 1/3 or 2/3. In that case we can get sequences like this (I will skip the reasoning, you can work it out if you like):

• A:H B:T

• A:T B:H

• A:H B:T

• A:T B:H

• A:H B:H

Here we can have both sides changing back and forth potentially several times, each side taking the other's view, until they come to agreement.

A few interesting points about this game. It's a simple model that captures some of the flavor of the no-disagreement theorem. In the real world we have hints about reality in the form of our information; and there is something like a "hint quality" in terms of how good our information is. If we were Bayesians we could both report our hint qualities when we disagree, and go with the one that is higher. Even if we are limited merely to reporting our opinions as in this game, we should normally reach agreement pretty quickly. Another interesting aspect is that when you play the game, you can never anticipate your partner's guess. On each round you have an idea of the range of possible hint qualities he might have, based on his play so far, and it always turns out that given that range, he is equally likely to guess Heads or Tails on the next round. This is related to Robin's result that the course of opinions among Bayesians in resolving disagreement goes as a random walk.

As I noted, in the real world it should be uncommon for two people to have high quality but opposing hints, because high quality hints are supposed to be accurate. Hence it should be rare for people to stubbornly disagree and stick to their original viewpoints. Much more common should be the case where people have low quality hints which disagree. In that case, as we saw, people should switch position at least once, and then (depending on how low the hint quality was) either stick to their reversed position or else possibly alternate some more. This should be a common course of disputation between Bayesians, but it is strikingly rare among humans. Another point this game illustrates is that the Aumannian notion of "common knowledge" may not be as easy to use as it seems. Note in this game that even after announcing their positions, players' (current) views are not common knowledge. After each round, a player got new information that could have changed his view from when he stated it before. Once they reach agreement, then things seem to stabilize, but that may not be the case in general. I have constructed different games in which people can agree for two consecutive rounds and then disagree. It is an open question to me whether two people can agree for N rounds and then disagree, for arbitrary N.

Overcoming Bias: The Coin Guessing Game

[tblood]

Probability

The problem of probable inference — that is, of reaching a decision in the face of incomplete knowledge — is a broad one that cuts across many disciplines. However, the formal treatment of probability by the mathematicians has seduced many people into believing they know more than they really do. There are two totally distinct fields of probability, namely class and case probability. The former is applicable to the natural sciences and is governed by causality (i.e. mechanical laws of cause and effect), while the latter is applicable to the social sciences and is governed by teleology (i.e. subjective means/ends frameworks).

Class Probability

In class probability we know everything about the entire class of events or phenomena, but we know nothing particular about the individuals making up the class. For example, if we roll a fair die we know the entire class of possible outcomes, but we don’t know anything about the particular outcome of the next roll — save that it will be an element of the entire class. The formal symbols and operations of the calculus of probability allow the manipulation of this knowledge, but they do not enhance it. The difference between a gambler and an insurer is not that one uses mathematical techniques. Rather, an insurer must pool the risks by incorporating the entire class (or a reasonable approximation to it). If a life insurance company only sells policies to a handful of people, it is gambling, no matter how sophisticated its actuarial methods.

Case Probability

Case probability is applicable when we know some of the factors that will affect a particular event, but we are ignorant of other factors that will also influence the outcome. In case probability, the event in question is not an element of a larger class, of which we have very concrete knowledge. For example, when it comes to the outcome of a particular sporting event or political campaign, past outcomes are informative but do not as such make the situation one of class probability — these types of events form their own "classes." Other people's actions are examples of case probability. Therefore, even if natural events could be predicted with certainty, it would still be necessary for every actor to be a speculator.

Numerical Evaluation of Case Probability

It is purely metaphorical when people use the language of the calculus of probability in reference to events that fall under case probability. For example, someone can say "I believe there is a 70% probability that Hillary Clinton will be the next president." Yet upon reflection, this statement is simply meaningless. The election in question is a unique event, not a member of a larger class where such frequencies could be established.

Betting, Gambling, and Playing Games

When a man risks money on an outcome where he knows some of the factors involved, he is betting. When he risks money on an outcome where he knows only the frequencies of the various elements of the class, he is gambling. (The two activities roughly match up with the case/class probability distinction.) To play a game is a special type of action, though the reverse is not true; not all actions can be usefully described as part of a game. In particular, the attempt to model the market economy with "game theory" is very misleading, because in (most) games the participants try to beat their opponents, while in a market all participants benefit.

[FDG]

Originally Posted by m a r r o k

Here it is an interesting application of the game theory:

Some time back I thought of an example which shed light for me on some of the fail-to-disagree results. Imagine that two players, A and B, are going to play a coin-guessing game. A coin is flipped out of sight of the two of them and they have to guess what it is. Each is privately given a hint about what the coin is, either heads or tails; and they are also told the hint "quality", a number from 0 to 1. A hint of quality 1 is perfect, and always matches the real coin value. A hint of quality 0 is useless, and is completely random and uncorrelated with the coin value. Further, each knows that the hint qualities are drawn from a uniform distribution from 0 to 1 - on the average, the hint quality is 0.5. The goal of the two players is to communicate and come up with the best guess as to the coin value. Now, if they can communicate freely, clearly their best strategy is to exchange their hint qualities and just follow the hint with the higher quality. However we will constrain them so they can't do that. Instead all they can do is to describe their best guess at what the coin is, either heads or tails. And further, we will divide their communication into rounds, where in each round the players simultaneously announce their guesses to each other. Upon hearing the other player's guess, each updates his own guess for the next round.

Read on below the break for some sample games to see how the players can resolve their disagreement even with such stringent constraints.

Here's a straightforward example where we will suppose A gets a hint with quality 0.8 of Heads, and B gets a hint with quality 0.6 of Tails. Initially the two sides tell each other their best guess, which is the same as their hint:

• A:H B:T

Now they know they disagree. Their reasoning can be as follows:

A: B's hint quality is uniform in [0,1], averaging 0.5. My hint quality is higher than that at 0.8, so I will stay with Heads.
B: A's hint quality is uniform in [0,1], averaging 0.5. My hint quality is higher than that at 0.6, so I will stay with Tails.

• A:H B:T

So they remain unchanged. Now they reason:

A: B did not change, so his hint quality must be higher than 0.5. That is all I know, so it must be uniform in [0.5,1], averaging 0.75. My hint quality is higher than that at 0.8, so I will stay with Heads.
B: A did not change, so his hint quality must be higher than 0.5, so it must be uniform in [0.5,1], averaging 0.75. My hint quality is lower than that at 0.6, so I will switch to Heads.

• A:H B:H

And they have come to agreement. If both A and B had had higher hint qualities, they might have persisted in their disagreement for more rounds, but each refusal to switch tells the other party that their hint quality must be even higher, and eventually one side will give way. It's improbable that both sides will have high but opposite hint qualities. What happens in the more likely case where they have low but opposite hint qualities? Let's suppose that A gets a hint of Heads with quality 0.1, and B gets a hint of Tails with quality 0.15.

• A:H B:T

A: B's hint quality is uniform in [0,1], averaging 0.5, which is higher than my 0.1, so I will switch to Tails.
B: A's hint quality is uniform in [0,1], averaging 0.5, which is higher than my 0.15, so I will switch to Heads.

• A:T B:H

A: B switched, so his hint quality was lower than 0.5, making it uniform in [0,0.5] and averaging 0.25, which is higher than my 0.1, so I will stay with Tails (B's original guess).
B: A switched, so his hint quality was lower than 0.5, making it uniform in [0,0.5] and averaging 0.25, which is higher than my 0.1, so I will stay with Heads (A's original guess).

• A:T B:H

A: B stayed the same, so his hint quality was lower than 0.25, making it uniform in [0,0.25] and averaging 0.125, which is higher than my 0.1, so I will stay with Tails.
B: A stayed the same, so his hint quality was lower than 0.25, making it uniform in [0,0.25] and averaging 0.125, which is lower than my 0.15, so my original hint quality was higher, and I will switch back to my original Tails.

• A:T B:T

Once again agreement is reached. Note that when both sides have a low hint quality, they initially switch to the other side's original view, then they each stick with that new side. After enough rounds one of them decides that the other's hint must have been so poor that his hint was better, and he switches back to reach agreement. An interesting case arises if the hint qualities are near 1/3 or 2/3. In that case we can get sequences like this (I will skip the reasoning, you can work it out if you like):

• A:H B:T

• A:T B:H

• A:H B:T

• A:T B:H

• A:H B:H

Here we can have both sides changing back and forth potentially several times, each side taking the other's view, until they come to agreement.

A few interesting points about this game. It's a simple model that captures some of the flavor of the no-disagreement theorem. In the real world we have hints about reality in the form of our information; and there is something like a "hint quality" in terms of how good our information is. If we were Bayesians we could both report our hint qualities when we disagree, and go with the one that is higher. Even if we are limited merely to reporting our opinions as in this game, we should normally reach agreement pretty quickly. Another interesting aspect is that when you play the game, you can never anticipate your partner's guess. On each round you have an idea of the range of possible hint qualities he might have, based on his play so far, and it always turns out that given that range, he is equally likely to guess Heads or Tails on the next round. This is related to Robin's result that the course of opinions among Bayesians in resolving disagreement goes as a random walk.

As I noted, in the real world it should be uncommon for two people to have high quality but opposing hints, because high quality hints are supposed to be accurate. Hence it should be rare for people to stubbornly disagree and stick to their original viewpoints. Much more common should be the case where people have low quality hints which disagree. In that case, as we saw, people should switch position at least once, and then (depending on how low the hint quality was) either stick to their reversed position or else possibly alternate some more. This should be a common course of disputation between Bayesians, but it is strikingly rare among humans. Another point this game illustrates is that the Aumannian notion of "common knowledge" may not be as easy to use as it seems. Note in this game that even after announcing their positions, players' (current) views are not common knowledge. After each round, a player got new information that could have changed his view from when he stated it before. Once they reach agreement, then things seem to stabilize, but that may not be the case in general. I have constructed different games in which people can agree for two consecutive rounds and then disagree. It is an open question to me whether two people can agree for N rounds and then disagree, for arbitrary N.

Overcoming Bias: The Coin Guessing Game

That's extremely interesting. I took two game theory courses so far, and they have been those I have enjoyed the most, especially the more mathematically-oriented ones. It's an awesome branch of applied mathematics.