Freeriding+Game Theory=Disproves Adam Smith???

Economics Economics Questions
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21

I’m sorry to nitpick. It is not that I want to play the bully when it comes to Game Theory, but as a result of my sequence of replies on this matter I’m afraid I will come off as one.

With that said, there are a couple of points in your post that doesn’t rest well with me.

One, he is not determining values, he asserts the presence of a group of individuals who agree to maximize a value, i.e. the total value. Think of a scenario of owners of a company, Neighbors Inc, increasing its total value. There is nothing to suggest he denies subjective value. Also, I disagree about your assertion that he is setting “the relative value of each option”. Well, obviously I cannot know if that is what the professor thinks he is doing; however, I cannot see why it is necessarily wrong. The game setup allows for subjective valuation of each option, otherwise game theory would be void, i.e. if every player where supposed to always choose the most profitable option, “to desert”. This is primarily why Nash got it wrong the first time. The main idea about giving each option a nominal value is to discern a trend, ex post. Nevertheless, just arbitrarily setting each nominel value, ex ante, seems silly. Obviously, for a game to give any robust results you would need to simulate many games using many different values, but for explanatory purposes, in the professor’s case, one set of nominal values is fine. At this point I am well aware that my discussion so far is prone to invoke misunderstanding. When von Neumann and Morgenstern originally laid the groundwork to Game Theory they did it as a “revolt” against conventional mathematical marginal utility theory, who can blame them?, but unfortunately, probably owing to von Neumann, they “just” gave the world another constrained set of mathematical tools. Now, I might be wrong, but I think this is what Austrian economists normally revolt against; and seen in this light, I would probably agree with them if I knew more about it. But the moment you realize you aren’t modeling reality, per se, and you do not use game theory to guide law making (thus causing injustice) but use the results to guide your own actions (as an individual, collective, firm, “nation” etc.) what is wrong with it? I know it comes close to positivism, á la Milton Friedman, but that is far from my position. I know the brevity of this reply is already in jeopardy, so I’ll stop short here, and go on to my next point.

Two, I believe you are confusing changes in circumstances and changes in outcomes, or perhaps forgetting one. If you have spotted a “real life” situation where you know for certain that the set of possible outcomes cannot change over time (e.g. cooperate, not cooperate) it becomes possible to loop the game thus simulating changes in time, i.e. finding trends.

22

Ah, yes, I see, where I went wrong in my reply because of my unfamiliarity with game theoy. But the professor is still wrong and he has still made a value judgement. The game matrix correctly identifies a free rider issue, but his conclusion that cooperating is more efficient than free market is still untouched. That’s because he’s still had to define “more efficient”. In this case, his only criteria is home value. That is his fallacy.

Say you have 4 houses in this neighborhood, essentially the same.

Possibility 1: All spend 200 hours improving the house and gain $20,000 in value.

Possibility 2: Three spend 200 hours improving, their houses gain in value $15,000. One person does no work but house still gains $5000.

Now I mix in some praxeology and stir. In possibility 1, does everybody value 200 hours of free time as being worth $100 an hour? If so, great. But what if one of the owners has a side business making $200 an hour (lucky stiff). He would gain $20,000 on his house, but lose $40,000 in opportunity costs. So the tally is 4x$20,000= $80,000 net gain for the neighborhood.

Obviously the dude making $200 an hour isn’t going to play that game. That would be stupid. So he sits out and we get Possibility 2…the greedy selfish option. Here, we get 3*$15,000 +1*$5000 = $50000. So at first, the neighborhood seems to have lost out. But since the free rider was off making $40,000 that he didn’t earn in possibility 1, we can add that to the total. Here then the neighborhood has really net $90,000. Better than possibility 1 by $10,000!

So, some individual neighbors did not do as well, but in aggregate, the neighborhood is richer in possibility 2. So for this specific case I would argue that possibility 2 is actually more efficient from a market standpoint. Especially if the first three still value $15000 more than 200 hours of free time. Everybody is satisfied. In my Possibility 1, the fourth guys house is $20,000 more valuable, but he had to give up $40,000 to get it…he is very unsatisfied. Even though the first three houses are MORE satisfied, it is impossible to measure their satisfaction against the 4th guys dissatisfaction.

Again the professor could come back and say that maximizing home values was the goal. Ok, fine, then only possibility 1 exists on the matrix. Because in order for possibility 2-4 to exist someone has to value their freetime more than maximum house value. If someone values their freetime more than the maximum house value then you have the possibility to get into my, more efficient possibility 2. If you limit the case to possibility 1, then you HAVE no game theory, so his arguement simply doesn’t exist.

Which means that either the professor has to agree that he has no argument because game theory is not applicable, or that sometimes his argument is wrong…in which case he has proven nothing.

23

Nice one Greg [:D]

Essentially you are bringing in the broken window fallacy to the mix.

This is in fact what I fear about Game Theory. I still maintain, it can have great explanatory power, but your point is exactly why it must never be allowed to direct law making.

EDIT: Your reply also enforces macsnafu’s reply, i.e. you cannot assign a real world evaluation to each option, since your are, in fact, in total disregard as to what else each homeowner could otherwise be doing if not trapped inside the professor’s collectivist mind game.

24

Morgernstern was an Austrian, incidentally. Be that as it may, the problem with game theory is when it is used to establish the non sequitur that a state is needed to ameliorate some perceived “problem”. The doctrine of demonstrated preferences also comes to mind when discussing whether the route chosen by the individuals is preferred or not by them, more so than any hypotheticals as to what they value most.

-Jon

25

Better? For who? Not for the blonde.

Of course, if you wait until your friends have picked up brunettes you can still score the blonde. So really cheating is the “best” outcome.

The benefit of conspiracy is not a new idea. But obviously these collisions never last because of the obvious advantage to cheating. Look at opec. They conspire to keep prices high, but each individual memeber stands to gain even more by cheating on their quotas.

It doesn’t prove anything that he claims it does.

26

Greg, I know this post is quite old but it seems like no one addressed the enormous logical mistep here and that makes me a little concerned. I appreciate the discussion here but I feel like some of you may want to try playing a little devil’s advocate for the left or you’ll end up being satisfied where you shouldn’t be.

  1. First, the prisoner’s dilemma requires that a) it’s better for each person to defect as long as the other’s continue to do the work; and b.) it is worse for each individual if no one does the work than if everyone does the work. Your set up that has violated a and b (I know that’s your point, but I’ll get to that issue in a sec…).

You violate a) by changing the payoff for one person such that it is still better for that person to not do house work EVEN IF no one else does housework ($40 000 if all defect, $20 000 is none defect). So there’s no game here. I’d love it if my neighbor mowed his lawn more but if the incentive not there (even if I stop mowing my lawn), oh well, but no one is claiming it’s a prisoner’s dilemma or tragedy of the commons.

You violate b) b/c the prisoner’s dilemma would require that the 3 left you don’t have defecting will still defect in a prisoner’s dilemma. In fact, if 1 of the 4 defects, they have even more incentive to defect. You calculate payoffs w/o this possibility (indeed, necessity).

OK, so I think the point you were trying to make is that these neighbor’s may have hidden utility not considered in the game. And maybe you are trying to suggest that this will always be the case, such that a prisoner’s dilemma is too simple to ever be the case in the real world. Well if this was your point, then you can’t say of the prof “that sometimes his argument is wrong…in which case he has proven nothing.” I doubt the professor was trying to say that everything is a prisoner’s dilemma. You don’t even need to get into made up scenarios to say that, just change the payoffs the professor provided and you can accomplish that. That’s like someone pointing to an orange and saying “That’s an orange” and me disproving them by pointing to an apple and saying “Yeah, but that’s an apple.”.

If you should take anything away from the prisoner’s dilemma think this way: 1. Is it THEORETICALLY possible? The answer is yes and there’s simply no refuting that; 2. WIll it ever happen in real life? Of course it will. As a kid, I tattled on my friend b/c I was told it was the only way I wouldn’t get in trouble. He did the same being told the same. Now we’re both in trouble. Not as bad for me if I was the only one blamed, but worse than if neither of us had said anything (too bad I was such a rational kid). And yes this does mean a total free market system is imperfect (though at this point, there’s so many other reasons that we know we don’t need to go here anymore) 3. Is it frequent and important enough to consider in terms of legislation or to even dismiss a free market as the BEST possible system? That’s more complex and I have my own opinions, but if you want to try and make the case by inventing billions of non-prisoner dilemma’s in an attempt to limit the number of possible ones, good luck.

By the way, there’s a much better way to limit the prisoner’s dilemma effect, and the Objectivist approach to shrugging it off (pun intended I guess) and saying it’s just a game, or limited to a one-shot deal (not true) won’t cut it. Just trying to be preemptive here.

KerrioBrown

27

competing firms are necessarily more efficient than cooperating firms

Your professor is correct. Competing firms are not necessarily more efficient than cooperating firms, unless we are to understand “cooperating firms” as government sanctioned monopolies. The free market is neither entirely absent of cooperation amongst firms or always in competition with other firms. The potential of competition simply need exist to ensure efficiency, even when firms cooperate. This cannot be when government sanctioned monopolies and/or cartels are created on the argument of Natural Monopoly. So to answer your professor, it is necessary to determine what is meant by “cooperating firms” and whether it is the result of government mandate or not.

28

Others seem to be answering the general case pretty well. I’ll just comment that his second example disproves what he wants to do. Nash and his buddies came to this agreement and acted on it. They did not form a government to do it. They were able to make an agreement to cooperate. Case closed.

29

The other thing about the prisoner’s dilemma is that, in real life, we’re just about always dealing with the iterative prisoner’s dilemma, rather than the one-shot version. In the iterative version, cooperating is the best strategy for each as well.

For example, suppose we live in a state where it is illegal to sell raw milk, and you’re a farmer and you want to sell me raw milk. We make an agreement: each week I’ll drop a paper bag of money in spot A, and you’ll drop a paper bag with milk in at at spot B. We can see A from B and vice-versa, so we each watch the other drop their bag. I can put in money or leave it empty, and it won’t affect what you do. You can put milk or leave it empty, and it won’t affect what I do. That is, this is just the prisoner’s dilemma with positive payoffs. So we’re each incentivized to defect and leave an empty bag, right? Wrong. By assumption, we both want to trade, and if either of us leave an empty bag, we know that in the future, the other will always leave an empty bag (or, what amounts to the same thing, will tit-for-tat and leave an empty bag the next week.) So, since we want to trade, and we therefore want trades in the future, we leave the item in the bag.

30

I am sure the Law of Association could be applied in some way here.

31

To be technical, the Prisoner’s Dilemma (PD) is actually a last-shot deal since in a finite multi-round game, if you know the other person will defect in the last round, you will defect in the round before it and so on until the defection occurs immediately. Still, in many cases cooperation is possible. Say there’s a bunch of farmers and consumers and if one farmer doesn’t care what we think because he has calculated that bad reviews alone will not be spread amongst consumers fast enough to not be worth screwing each customer. Other farmers realize the same thing and now it’s basically just a 50/50 shot that you’re going to get a raw deal. Consumers are only willing to pay half price for a 50/50 deal and the good farmers can’t make a living off of that so no one buys milk. The bad guy farmers now have a choice to make, which is whether or not it is better to really give the milk. Well, this depends on the number of other farmers willing to do the same. Perhaps good farmers can make a living off of 90% product price (that is, when 10% of the farmers are going to be bad). I believe what you’ll get with perfect rationality and complete information is an oscillating equilibrium depending on profit margins for true farmers. Every time it goes above the profit margin, all farmer’s should be bad (according to self-interest, though not Objectivist self-interest, unless we change this to a non-illegal game which is easy enough). With perfect rationality, then, ALL farmers will go bad when all are being good and all will go good when all are being bad. Sounds like on Day 1 we consumers get our milk, Day 2 we know we won’t and so won’t buy, and so on. But remember that the farmers have complete rationality. So all farmers will make sure to actually be bad on Day 1 and good on Day 2. You get a situation much like the carrot dangling in the face of the horse cliche. But if the farmers are truly rational there is often a way out which is based on using mixed strategies (randomizing being good and bad), and often it can work such that it can only hurt you to be irrational.

Unfortunately, there are also cases where the cooperation variables can become really complex and it becomes massively inefficient to try and satisfy everyone’s freedom of choice (inefficiency of course depending on how much you value free choice), but complex scenarios are really annoying to write up (no less read).

32

Prisoner’s dillema is a huge fallacy itself. It implies and completely ignores third, judging, party. It is “dillema” between at least three people. Not two.

33

What if the third party is a computer?

34

Who designed the computer?

35

I think another point is, granting what the professor is saying, what follows? The OP doesn’t continue with what comes next, but so far, it looks like argument by magic: here’s the problem, and invoke government to fix it. How? Basically, the invocation of government is always in the form of a black box, allowing them to not even consider that whatever problem they talked about applies to government officials too. Why on earth should we presume, even granting his analysis, that the government would simply enforce the useful cooperative agreement? Why can’t players bribe government officials to exempt them while binding the rest?

36

You can have prisoner’s dilemmas without third parties. Example: democracy

37

You mean modern day applied democracy or just a theoretical concept, where 2 people decide to kill the third?