Wednesday, July 29, 2009

Game Theory Lectures

I've been watching some Game Theory video lectures out of Yale University ( ). It's a subject area I've been intrigued by for a while, so I was happy to see their availability online. Professor Ben Polak is an energetic and compelling presenter.

However, I keep being reminded that this is a course being given in Yale's Economics department. And I've long held a few very key critiques about the foundations of standard economic theory, that I feel make the entire enterprise miserably inaccurate. What I didn't expect is for these Game Theory lectures to feature a high-intensity spotlight directly on those shortcomings, in practically every single session.

Critique #1 is that economics deals only with money, and wipes out our capacity to deal with other values. Critique #2, probably more important, is that economics fatally depends on a “rational actor” assumption for all involved, which is simply not true. Let's consider them in order:

Critique #1: Economic theory is all about money, and the widespread use of the theory destroys our other values like family, community, craftsmanship, healthy living, emotional satisfaction, and good samaritanhood. As one wise man said, “They don't take these things down at the bank,” and therefore, they get obliterated when economic theory is put in play.

Now, Professor Polak makes a good, painstaking show in Session #1 of trying to fend off this criticism. “You need to know what you want,” he says, and runs an extended example wherein, if one player really was interested in the well-being of his partner in a game, well, that could be accounted for by assessing the value of those feelings, and adding/subtracting to the payoff-matrix appropriately, and then running the same Game Theory analysis on the new matrix, finally arriving in a different result. (Of course, along the way he also snidely refers to this caring player as an “indignant angel"). See? Game Theory can handle all kinds of different values, not just money.

But lets look later in the same lecture, where he has the students play the “two-thirds the average game” (more on that later). He holds up a $5 bill and says that the winner will receive this as a prize. Now – does he do the analysis of “what people want” (payoffs), which he just said was so keenly important? No, he does not. Only 15 minutes after this front-line defense, it goes forward without comment, that obviously the only value for anyone in the game is the money. So, even though we just lectured on how economic theory can handle different values, we immediately thereafter turn around and act out exactly the opposite assumption. Maybe some people want the $5... maybe some want to corrupt the results for their snotty know-it-all classmates... But no, we get it played out right before our eyes, immediately following the defense that “all values can be handled”, that as soon as money comes in the picture, in practice, we dispense of all other values and speak of nothing except for the cash money.

Critique #2: Economic theory presumes “rational players”, where all the people involved knowingly work to their own best interests all the time. Frankly, that's just downright absurd. People are routinely (1) uneducated or uninformed about what's best for themselves, (2) barred from receiving key information by more powerful institutions or interests, (3) obviously non-rational in instances of emotional stress, drug use, mental failures, and modern Christmas purchasing behavior, and (4) proven by cognitive brain science to be unable to correctly gauge simple probabilities and risk-versus-reward.

Now, consider lecture #1, where Professor Polak introduces game payoff matrices, and the idea of avoiding dominated strategies (that is, a strategy where some other available choice always works out better). With exceeding care, he transcribes each “Lesson” along the way onto the board, including this one: “Lesson #1: Do not play a strictly dominated strategy”. Okay, that's a reasonable recommendation.

But about 10 minutes later, he pulls a devious sleight-of-hand. Analyzing another game, he asks what strategy we should play. “Ah,” he says, “Notice that for our opponent strategy A is dominated, so you know they won't play that, they must instead play strategy B, and thus we can respond with strategy C.” Well, no, that reasoning about our opponent (the 2nd logical step here) is completely spurious; it only make sense if our opponent is actually following our lesson #1. But, have they taken a Game Theory class? Do they know about “dominated strategy” theory? Do they actually follow received lessons? None of those things are necessarily (or even likely, I'd argue) true.

In other words, he assumes that all players are equally well-informed and “rational”, which isn't supportable. And, this assumption is kept secret and hidden. It would even be one thing if Professor Polak came out and said “For the rest of our lectures, let's also assume that our opponents are following the same lessons we are,” but no, he quite scrupulously avoids calling attention to the key logical gap.

And he does is it again, even more outrageously, in Session #2, when analyzing the class' play of the “two-thirds the average game” (a group of people all guess a number from 1-100; take the average; the winner is whoever guessed 2/3 of that average). He has a spreadsheet of everyone's guesses in front of him. Speaking of guesses above 67 (2/3 of 100), he says, "These strategies are dominated – We know, from the very first lesson of the class last time, that no one should choose these strategies." Except that, as he points out mere seconds later, several people did play them! (4 people in the class had guesses over 67; this occurs 46 minutes into lecture #2.) Nontheless, he continues: "We've eliminated the possibility that anyone in the room is going to choose a strategy bigger than 67...". But how can you possibly contend that you've “eliminated the possibility” when you have hard data literally in your hand that that's simply not true? Answer: It's the “rational player” requirement of all economic theory, which demonstrably collapses into sand if the logical gap is recognized and/or refuted. This infected logic continues throughout the class; in sessions #3 and #4 he repeats the same goose-step in regard to "best response" (1:10 into lecture #4: "Player 1 has no incentive to play anything different... therefore he will not play anything different."), and so on and so forth.

1 comment:

  1. if a player is not rational then they may or may not get their desired outcome; but if the player does not know what they desire, it doesn't matter which outcome they get. the assumption of players (people) being rational is that they know what they desire and desiring it requires that they act to reach that outcome.

    certainly, as you point out, not all players are informed and they don't always act rationally, but however these players act they can be considered to not be playing the strategy that gets the highest payoff.