Results for “solve for equilibrium” 219 found
These days there are so many sentences to ponder
If you’re running an insolvent bank, and you get a slug of equity from
Treasury, your shareholders will thank you if you use that equity to
take some very large risks. If they pay off and you make lots of money,
then their shares are really worth something; if they fail and you lose
even more money, well, there was never really any money for them to
begin with anyway.
That’s Felix Salmon: read the whole thing. Read this too. Here is Megan McArdle on the pooling equilibrium. Here is a good article on how Paulson "sold" his plan to the bankers. And here are yet some more sentences to ponder:
So it in the end, we have what is basically an economic loan, but structured
in a way to game bank capital adequacy requirements. What strange times we live
in when Treasury and the Fed have to engineer a deal to circumvent their own
regulations.
Hypergamy is the word of the day.
Yes, men are also, to their own detriment, continually surrounded with images of exceptionally attractive women. But this has less practical import, because–to say it once more–women choose.
Or:
The decline of matrimony is often attributed to men now being able to “get what they want” from women without marrying them. But what if a woman is able to get everything she wants from a man without marriage? Might she not also be less inclined to “commit” under such circumstances?
This essay is not politically correct and at times it is misogynous and yes I believe the author is evil (seriously). The main behavioral assumption is that women are fickle. So they are monogamous at points of time but not over time; Devlin then solves for the resulting equilibrium, so to speak. The birth rate falls, for one thing. The piece also claims that the modern "abolition" of marriage strengthens the attractive at the expense of the unattractive. Some of you will hate the piece. I disagree with the central conclusion, and also the motivation, but it does seem to count as a new idea. If you’re tempted, read it.
I thank Robin Hanson for the pointer.
Logic of Life – Chapter 2: Game Theory isn’t Always about the Games We Play
This review is cross posted on orgtheory.net, the management & social science blog.
It’s a pleasure to be back at the Marginal Revolution. Let me start out by agreeing with Tyler and Bryan. Tim Harford is one of the leading popular social science writers and we’re lucky to have him.
Today, I’ll focus on Chapter Two of Tim’s book, "Las Vegas: The Edge of Reason." In this chapter, Harford describes game theory. In a nutshell, game theory studies any situation where (a) you have multiple people striving to achieve a goal and (b) your actions depend on the actions of the other people in the game. By most accounts, game theory is one of the great accomplishments of modern social science. Once you realize that people’s actions are both utility maximizing and interdependent, then game theory can help you model just about any form of cooperation or conflict.
Harford discusses the basic concepts of game theory with vivid examples ranging from poker, to nuclear war, to quitting smoking. And, as expected, game theory usually provides a great deal of insight. Harford shows how game theory can also be enormously useful, even life saving. Harford recounts how economist Thomas Schelling realized that some situations might encourage participants to jump the gun and initiate devastating conflict. What Schelling realized is that these dangerous games had low information, such as the US misunderstanding a Soviet action, and starting nuclear war. Schelling advocated increased communication between the US and Soviet leadership, including the creation of the hotline between Moscow and the US, which helped defuse tensions in later Cold War disputes.
I’ll finish this post with my one big criticism of game theory, at least the basic version described by Harford and taught in intro courses. In game theory 101, you assume that people develop optimal strategies in response to other rational actors. One huge problem with a lot of these models is that the games are very complicated. It’s hard to imagine most people perform the mental acrobatics of game theory actors.
One response is that game theory is empirically well supported, which suggests that some process drives people to the strategies described by game theory. For example, Harford describes how economists and mathematicians used game theory to sort through the insanely complex game of poker and that the optimal game theory strategy was actually fairly similar to what world class poker players do.
So game theory is supported, right? Not so fast. Game theory has two parts (a) a description of optimal strategies, and (b) a prediction that people will actually solve the game and find these strategies. In my view, game theory 101 is well supported, in poker at least, on point (a), but not (b). In other words, world class poker players rarely sit around and do backwards induction, or any other flavor of equilibrium analysis, but they still obtain strong strategies through trial and error.
What I suspect is that world class poker emerged from an evolutionary process. Very smart people can figure out certain strategies, but nobody can figure out the whole game by themselves, lest they become full time mathematicians. The typical world class poker player probably inherits a bunch of rules that were tested by earlier generations, and adds a few new twists. Competition weeds out bad rules. Even Steve Levitt, star economist, Harvard & MIT grad, developed his own idiosyncratic strategy, rather than solve the game himself.*
In the end, game theory is really a first step in understanding complex interactions. The next step is developing an evolutionary theory of games where actors inherit a tool box of strategies from previous generations of players. Already, there is a fairly well developed genre of game theory taking this approach, but I welcome the day when it becomes refined enough so that it can account not just the strategies of leading poker players, but how these strategies emerged from generations of competition.
*According to the news reports, he developed his own "weird style" rather than completely solve the poker game. But it works for him! What would Johnny von Neumann say?
Another way to limit draws in chess
A compromise is that a draw offer should remain valid for some fixed period,
say ten moves. This will allow the person who has been offered a draw to test
whether the offer was truly justified, e.g. by trying a daring line which may
or may not be refuted by the opponent. If it is he can claim the draw on his tenth move, even if his position is losing. The limitation to ten moves avoids the potential problem of people playing on interminably after a draw offer, waiting for their opponents to blunder or overstep the time.
That is John Nunn, here is more. A draw, of course, is a form of trade, albeit one with some negative social externalities (a quick draw makes chess more boring for the spectators). If you want to limit trades in some markets, a similar rule could be contemplated. If you offer to buy a currency at a particular price, you have to keep a similar offer open for one week to some number of other market participants. Solve for the resulting equilibrium, and see how it matters.
Make pennies into nickels
Mr. Velde, in a Chicago Fed Letter
issued in February, has come up with a solution that would abolish the
penny, solve the excess costs of making nickels, help the poor, keep
the Lincoln buffs happy and save hundreds of millions of dollars for
taxpayers.As Mr. Velde explained in an interview, “We face a
very medieval problem so I took inspiration from the medieval practice
of rebasing.”He would rebase the penny by having the government declare it to be worth 5 cents.
We would then stop coining nickels at a loss. Here is more, from Austan Goolsbee. I am reminded of Neil Wallace’s work from the 1980s on the indeterminacy of equilibrium exchange rates in the absence of legal restrictions. If we take away government acceptance at par for taxes and the like, is there not an equilibrium where each penny is worth a million dollars? More ambitiously, if the U.S. government declared that each $20 bill is now worth $100, or each $100 worth $500, would the real exchange rate adjust immediately?
It is also Gerard Debreu’s birthday
Remember Theory of Value, that elegant 128 pp. book which summed up general equilibrium theory? Here is a brief bio of Debreu, courtesy of Liberty Fund. Here is Debreu’s own autobiography. Here is Wikipedia.
I recall Debreu once saying he took his inspiration from Proust. To what extent is time a dimension just like space in its effects on human organization? Debreu solved for those conditions, with of course assistance from Arrow, Hurwicz, Wald, and others.
And by the way, Yana just got her bag, so I feel Debreu’s model is just a little less unrealistic than it was appearing last night.
A Humean thought experiment
Let us say, just for fun, that you woke up one morning to a world where everyone else’s demand curve — except yours — slopes upward. But it is not common knowledge that this is the case. What is the first oddity you would notice?
1. The most expensive radio stations would be filled with the most ads. The music would never come.
2. Your house would have no electricity, due to grid overload. (Is this true? An upward-sloping curve does not mean you will demand more at the current price. Think of twisting the demand curve around the current point of intersection.)
3. The most transparent agents would be found wandering the streets, bereft of all wealth, the victims of corporate price hikes.
4. You would wonder why so few people were reading your blog.
5. You would check ebay and find very high prices for items with active bidding. (Hmm…what kind of auction markets are behind the scenes for our power supply?) (Addendum: What is the Nash equilibrium here? Will people hold off bidding, hoping that tomorrow’s price will be higher?)
6. You would be puzzled why the Nordstrom’s sale was so empty.
7. It would take you days to notice any significant difference at all. After a few weeks, they would call in the econometricians to solve the identification problem in the data.
How long would it take you to figure out that other peoples’ demand curves were sloping upwards? How long would it take for society to fall apart?
Comments are open.
Why we feel overloaded, and can it be fixed?
The real source of our frustration is signaling with "face time."
People — and not only at work — get insulted if they are dealt with in peremptory fashion, even when the issue at hand can be resolved quickly. Imagine a visiting professor comes to give a seminar, but you can’t find time for lunch. Lunch would have been chit-chat anyway, but now the professor feels you don’t value his research — or him — very much. Can you imagine such vanity? And if others perceive your time as important, they want it all the more.
What are some possible solutions to this problem? After all, a day has only twenty-four hours and your face has (one hopes) only one side.
1. Pretend that some other privilege you offer (hand kisses? birthday cards?) is extremely costly to you. Offer this other privilege in lieu of large amounts of time.
2. Pretend to be busier than you are. Let people believe — perhaps truthfully — that everyone else receives even less time.
3. Pretend your time is unimportant. (NB: This may involve dressing down.) The hope is that no one will feel slighted if they don’t get much time. Who feels slighted not to be given free thumb tacks? But there exists another equilibrium, in which the neglected person feels all the more insulted. After all, you are not giving away even your crummy low-value time.
4. Tell people you are autistic, or that you have Asperger’s syndrome.
I await your suggestions in the comments.
Abuses at mutual funds
Mutual funds control some $7 trillion for about 95 million investors.
But to this economist, much about the industry is a puzzle. Why, for instance, do so many investors seek out funds other than minimum commission, “buy and hold” funds? This could be a significant market failure, since managed funds do not in general outperform the market and generally charge higher fees. Alternatively, we might think that investors enjoy trying to beat the market, and that they are consuming a kind of gambling service. Investment clubs, for instance, are almost certainly a bad financial idea, especially if you do them with your friends. But maybe they improve your social life.
The current abuses include the `unholy trinity’ of illegal late trading, abusive market timing and related self-dealing practices. In other words, the mutual fund keeps the good trades for itself, or offers them to favored investors. The practice now appears to be widespread, read the above link or here.
This reminds me of the equilibrium we often observe in the car dealership market. When you buy a new car, most dealers put you through hell. You have to fill out all sorts of paperwork, taking up half your day and locking you in psychologically to sticking around through protracted negotiations, based on deceit and lies. Most buyers don’t leave and go elsewhere, in part because they know they can only expect to start all over again with the same. And as long as it is not too visible, you don’t feel too bad about your initial investment decision.
I suspect we see the same kind of stickiness with mutual funds. Many investors will not be shocked by the recent revelations. But why bother switching to another fund? Once you get there, you can expect more of the same.
I’ve never seen a good analysis of which market features lend themselves to this kind of outcome. Could it be the occasional allocation of large sums of cash that lies at the root of the problem? But why can’t firms make credible commitments to honesty up front? Clearly fraud is not the norm for all industries, the restaurant sector does not work this way. I suspect legal penalties alone will never solve the problem, our best hope is that technology, and monitoring, somehow change to make mutual funds, and buying a car, more like the experience of going to a nice restaurant.