Reputation, Cooperation, Evolution, Repeated Games, Optimal Play etc.

I shall find time to write something on this topic. I might also take time to investigate into the “the meek/submissive mindset” of people (I am right now thinking of it as a form of risk-aversion).

For starters, read this article:

In Games, an Insight Into the Rules of Evolution

Self-control depletion

After receiving a number of (friendly) criticisms on my unnecessary self-awareness, I sought for help. I borrowed a book from the library on this subject. I skimmed it in one hour and found most of the text dry, boring and rather academic (read useless), except for one chapter on self-control, another favorite subject of mine precisely because I have problems with it. There is a notion called “ego depletion”, whose essense is that you just have that much of psychological power to force yourself to do things that are right but unpleasant, and although this power is replenishable usually on a daily basis, its depletion simply means you are out of power on yourself, like it or not.

Honestly this would not be the first time I saw this phrase, however a systematic examination of the subject was still informative and enlightening. I promptly linked this to my lack of motivation to study after I completed a long run that was beyond my comfort zone (for example, I slacked off for almost two days after I ran from U of C to the river on Wednesday under the scorching sun, something I never did before). The will power was used up as I forcing myself to keep running. It is then not surprising that excessive self-training on will power would always backfire, in the same fashion that you only get injuries if you overtrain your muscles. To rest your nerves and be easy with yourself when you have to, is as important as to push yourself when needed. Do NOT waste on your will power - spend them economically. Additionally, just as you do not get your iron pecs and abs overnight, you will not get your formidable will power in short term. Everything should follow a schedule. A firm success should override any self-pride. When your reserve is low, try ways that require less consciousness involvement, such as staying away from the pleasure stimuli, which I in the past would always resist doing, because I regarded it as an acknowledgement of lack of self-control, which hurts my ego. For instance, I would deliberately put a shortcut to my favorite game on the desktop when I was trying to stop playing it. Sounds silly isn't it. That was the way I perceived it. As the book points out, pride often leads us the wrong way.

Lastly: focusing on such matters once again reveals my excessive interest in “self”. Hopefully it is not restricted to “myself” this time.

The Yen Carry Trade

So the other day it crossed me the idea of making easy money by exploiting the difference in interest rates of yen and US dollar, as the latter is always higher. One simply borrows yen, exchanges and deposits the money in a USD account to generate risk-free income - or the yen has to go up. However the arbitrageur should hedge against the risk in movements of exchange rate - say by a forward contract of exchange rate. Then I did google a bit, and read the interest rate parity (which correlates the two interest rates and spot & forward exchange rates), whose “intention” is to prevent such opportunities of arbitrage. However, I also read that, in practice it is not working. In fact, there has been a term coined for such practices, called “The Yen Carry Trade”, where investors borrow yen and invest them in securities of other currencies. It could even be linked with the recent crisis of global financial markets. As subprimal markets turn sour, investors with investment backed by borrowed yen, a lot of which are with high leverage but without proper hedging, are forced to sell them off quickly and pay back their debts in yen, therefore putting a stress on the demand of yen, effectively drives yen up - and an expensive yen is bad news for anyone whose investment is backed by borrowed yen, and they are going in panic to do the same thing - sell the investment, get USD, exchange for yen, and pay off their debts, forming a vicious circle. The central bank of Japan can provide more supply of yen to break the chain, which they just tried (BoJ injected 400b yen into the banking system as it observes the interbank rate increasing). Oh - do not forget that strong yen hurts Japanese economy (Nikkei received heavier loss at least yesterday - did not keep track of it though).

I admit that I speculated most of the above - however who has the data of historical exchange rates can prove or disprove it easily: we all read yen went up against USD on the news. What about yen against other currencies? My suspicion is that yen would be generally driven up in such a global crisis. BoJ served for too long a period as the “generous lender of capital” and only Holy Moly would know how much yen is still out there.

Edit: Actually I got the data: Exchange rates for JPN Yen. See for yourself. USD rose (not as much as JPY did) against most currencies too - because of the difficulty now to get dollars. Well there is always the exception and mystery about RMB and China stock market. Leave them alone.

Edit²: An article titled Currency ‘Carry Trade’ Becomes Harder Play Amid Aversion to Risk appeared on WSJ front page just now. Also read Minsky's Theory.

Heads up strategy (tournament)

Assuming the following winning opportunity P(x) as a function of your stack proportion x:


Figure 1. P(x) vs. x

One would expect the deviation from P₀(x)=x grows larger as the BB size, R, grows larger.

Situation: after you placed BB of size R, your opponent pushes all-in. Should you call it, or fold?


Figure 2. When you should call the all-in (R=0.05)

One interesting finding is that one should be most cautious when he is 70-30 dominating the table, folding even when the odds are 3:2.

Voluntary all-in is different because your gain of winning is lowered by your opponent folding his inferior hands, in other words, you win small and lose big (somehow reminds me of winner's curse).

Linear P(x)?
If players are only exchanging blinds, i.e. the winning/losing is a complete random walk, one can show rigorously that P₀(x)=x. In other words, the chance for W(t) to reach +B before -A is exactly A/(A+B), if W(t) is a Brownian motion. Obviously the leading player would have a higher winning chance than this, that is why we would have the S-shape for P(x).

Quantum scar references

Three papers regarding "quantum scar and phase space" (Ref 72-74 in Rice' review)

E.J. Heller Phys. Rev. Lett. 53, 1515 (1984)
M.V. Berry Proc. R. Soc. Lond. A 423, 219 (1989)
E.B. Bogomolny Physica D 31, 169 (1988)