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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?
Posted by Fabio Rojas on January 28, 2008 at 07:04 AM in Books | Permalink
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Comments
Harford also mentioned a drawback of game theory (especially the branch he attributed to von Neumann) being that the player basically assumes the opponent is as smart as him.
On TV the announcers for poker tourneys often mention that the pros sometimes have trouble with newbies, because they are so unpredictable and erratic. I recall the ESPN "Sports Guy" columnist, Bill Simmons, went to play in the WSOP, quite confident he could, at the least, fleece some of the fish (how's that for a mixed metaphor?) but busted out so quickly he did not have enough material for a column-- and blamed it on the poor play of the same newbies he planned to take down.
Adanthar, a pro at the 2+2 poker forum that exposed the Absolute Poker scandal discussed on Levitt's blog: http://freakonomics.blogs.nytimes.com/2007/10/17/the-absolute-poker-cheating-scandal-blown-wide-open/
actually developed a "robotic system" algorithm to take advantage of poor, low-stakes, on line play. This was something he wrote up back-of-the-envelope style and threw up on a message board for fun. Supposedly the refined version offered approximately a 20% return before play adapted to it:
http://www.pokersourceonline.com/forum/viewtopic.php?t=17417
Posted by: burger flipper at Jan 28, 2008 8:33:42 AM
Burger flipper, here's an old joke - two cops see a man commit a crime. Instead of chasing the crook, cop #1 starts working through some equations. Cop #2 is shocked - he asks, why are you not chasing the bad guy? Cop #1: "Don't worry, he has to work throug the equilibrium as well."
Posted by: Fabio Rojas at Jan 28, 2008 8:46:54 AM
The evolutionary assumption is what political scientists appeal to also: whoever arrives at positions of leadership must have mastered the kinds of calculations game theory assumes. Although it's pretty critical in, say, nuclear standoff scenarios, it's not so well supported by evidence (e.g., what if Curtis LeMay had been advising Nixon instead of JFK).
Posted by: Jim M at Jan 28, 2008 9:18:49 AM
Given the time constraints imposed by poker games isn't there a certain amount of Gladwellian "Blinking" going on? So all these game theory strategies have to be whittled down to the most useful cues and lines of action--perhaps like music you have the technically perfect players and ones able to recognize and react to emotions.
Something along the lines of what the following player suggests:
www.pocketfives.com/CFDA036B-6850-4003-B845-42FBF58B2093.aspx
Posted by: Pitt at Jan 28, 2008 11:03:14 AM
Fabio - Many thanks for these thoughts. I tend to agree with your criticism of game theory both here and in chapter two.
When it comes to poker - where Von Neumann's highly-mathematical, zero-sum approach applies in principles - I argue that no player until Chris Ferguson ever solved the game in the way that Von Neumann sketched out. Even the best players triumph in part by taking advantage of poor play by opponents - an idea which immediately throws a spanner in the work of Von Neumann's equillibrium, which is defined in terms of optimal strategies. Several players did make steps forward - for instance, Doyle Brunson realised that certain types of low cards ("suited connectors") were attractive because they would occasionally form unexpected straights or flushes just when everyone else's cards were proving useless. It took a while for other players to catch up with this insight. I agree that an evolutionary approach might be very helpful in understanding how strategies in play have become stronger - although this is not the approach that Chris Ferguson actually used on the way to his World Championship.
As for game theory outside poker, I argue that it is deeply problematic: the games are not well defined and the outcomes aren't robust. In many situations in the book, I argue that "nearly rational" is close enough. But not in a game theory situation, where your calculations involved figuring out what the other player will do. That's why when Tom Schelling is introduced I start with his faked invasion of Berlin, trying to get Henry Kissinger, McGeorge Bundy and the rest to think about their human responses to an uncertain situation, rather than getting out the slide rule.
Posted by: Tim Harford at Jan 28, 2008 11:08:08 AM
I think the real value to game theory will be realized not in modeling human interactions but in modeling/designing machine intelligences which operate in interactive settings.
For instance, my field of expertise - cognitive radio - software processes define how radios "intelligently" use radio resources (e.g., what spectrum to use, how much power to transmit, when to transmit...). However, each radio's choice of radio resources impacts the performance (and thus the choices) of other radios which spawns an interactive decision process. Unlike with humans, we know exactly how we coded the radios to behave so the mathematical formalism can be directly applied.
Further, since we're coding the behavior, we're not restricted to merely modeling, but can introduce notions of design. This means we can code the radios' algorithms to conform to whatever game model we think would yield the most desirable behavior given the interactions. For examples - see my dissertation or this recent conference paper where I altered radio processes to induce a utility-function symmetry condition which yield social (network) optimums from non-cooperative behavior.
As we approach the Singularity and we put increasingly more intelligence into machines (and the number of "intelligent" devices outnumber the number of intelligent humans), I think that there's going to be an increasing premium placed on how we design machines which act intelligently, not just in isolation, but in interactive settings. I think this is a natural fit for the existing economics/game theoretic tools - in fact a far better fit than the human interactions typically modeled. But for economics/game theorists to maximize their contribution to this burgeoning field, I think economics/game theory needs to move beyond viewing itself a social science and consider applications beyond the interactions of human intelligences.
Posted by: Jody at Jan 28, 2008 11:47:45 AM
I would like to see more literature on a sort of "institutional game theory" that gives emphasis on focal points, conventions (ala David Lewis), and differential risk preferences as in the Stag Hunt (Hare: low risk low payoff; Stag: high risk, high payoff). A good mix of rational choice micro-sociology can possibly add in group strategies & ethnographies or history for empirical evidence. I think there is too much emphasis in the conflictual free-rider PD and not on the spontaneous cooperative orders that are primal. Micro-foundations and evolutionary game theory are great scientific foundations (low risk, low payoff). Is there room in the economic profession for the higher risk "Social" Game Theory? Can "ESS" social orders that maximizes social cooperation under the division of labor solve the wealth of nations dilemma better than the "Macro-" social sciences? Risky, but I'd like to see more.
Posted by: R M Daza at Jan 28, 2008 11:52:35 AM
I would have liked additional clarification on Chris “Jesus” Ferguson’s minimal attention to his opponents at the Las Vegas tables. Now I’ve seen plenty of poker and I would have loved a more comprehensive coverage of how antics from the likes of Phil Helmuth factor into Ferguson’s decision-making. Are these calculations part of the overall game theory he employs? How can such actions be accounted for using game theory?
P.S. Tim, I enjoyed your talk in Chicago last week. Let us hope we have no virtual 15th Street situations arise in this forum.
Posted by: Chicagoan at Jan 28, 2008 12:00:11 PM
Computer scientists have studied this question and have said some rigorously provable things. For example, finding Nash equilibria (even approximately) for general games (even 2-player games) is provably as hard as a much more general search problem. Formally, this problem is "PPAD-complete," which is close to saying that it is NP-complete, for which a large amount of evidence suggests it cannot be solved in a reasonable amount of time, except on small instances or in special cases (such as zero-sum games).
On the other hand, correlated equilibria are much easier to find.
The field is new and doesn't tell us much about how equilibria *do* emerge, but already it can tell us a lot about what we shouldn't expect to see.
Posted by: aram at Jan 28, 2008 12:30:07 PM
Jim M
I think you are missing the strength of evolutionary models - they work well for large populations. Any specific individual can fall outside the norm for the population, and provide a seeming counter-example, but that doesn't disprove the model.
I'm struck by how the different methods have different strengths. Pure game theory is precise, handles the equilibrium situation, and can model perfect behavior. Evolutionary game theory or an evolutionary simulation can handle imprecise information, and lack of equilibrium, but it can be hard to understand and explain the results produced. I see the gut-level understanding from role-playing a nuclear standoff as similar to explaining the results of evolutionary simulation - you are trying to provide the best story for a complex, fantastically interdependent interaction. The advantage of a simulation is that you can restart it to test your explanation.
Posted by: Aron at Jan 28, 2008 12:50:31 PM
For evolutionary game theory, poker seems some distance from an ideal example for study. Games with a longer history and more stable rules seem a better bet. A great deal of compurtised analysis has gone into both chess and backgammon over the last generation or so. Are they not better "lab animals"? Chess has little room for bluff and psycholgical strategies, backgammon much more (though probably less than the common forms of poker). How does the evolution of strategies over the centuries in chess map or not map to their evolution in backgammon?
As a meta question about equilbria, what can we learn from the evolution of the generally accepted rules in these long-lived games? are there general lessons that map to the evolution of the rules in, say, poker or bridge?
Posted by: Diversity at Jan 28, 2008 1:06:15 PM
Game Theoretic models are not supposed to be perfectly accurate representations of how people operate. They are models, and as such necessarily simplifications. The quote about statistical models applies here: No model is correct, but some are less wrong than others.
Posted by: TWM at Jan 28, 2008 1:35:02 PM
As a meta question about equilbria, what can we learn from the evolution of the generally accepted rules in these long-lived games? are there general lessons that map to the evolution of the rules in, say, poker or bridge?
Isn't it reasonable to think that rules evolve to make games more interesting? That is, a strategy is discovered that is so powerful that it reduces the game's interest, perhaps even making it trivial. So rules are designed to eliminate that strategy. Putting it too strongly, the original game is solved, so a variation is created.
Suppose castling did not exist in chess. I'd guess that the king's vulnerability would make games somewhat repetitive. So maybe castling is an example of such a rule. As for bridge, there have been modifications to the scoring even recently (most notably the penalties for going down doubled not vulnerable were increased) designed to alter strategies.
Posted by: Bernard Yomtov at Jan 28, 2008 1:48:36 PM
Suppose that the Poker Playing project at the University of Alberta pays off and generates computer programs that routinely beat the best human poker players.
See: http://poker.cs.ualberta.ca/
What do people here think about how, if at all, the rules of poker will change?
Posted by: michael webster at Jan 28, 2008 6:05:48 PM
Ken Binmore has a very interesting compilation of his papers out, with additional material added, called Does Game Theory Work? It focuses on his work with bargaining experiments and his explorations of evolutionary models to explain the data. It's a useful corrective to some of the more naive "behavioral" game theory one sometimes sees.
Posted by: srp at Jan 28, 2008 8:55:12 PM
I really enjoyed Harford's chapter on poker and the contrast he makes between von Neumann and Schelling's approaches to game theory. I teach law and consider poker playing a neat metaphor for the kind of strategic decisions lawyers have to make about when to settle a case or go to trial, but I am hard-pressed to say that such decisions are "rational" in the strict sense. Also, I really like "evolutionary game theory" as developed by biologists such as John Maynard Smith precisely because there is no ex ante assumption of rationality -- all strategies are allowed to compete with one another
Posted by: enrique at Jan 28, 2008 11:11:31 PM
This is an interesting topic for someone who plays poker and who likes economic / game theory.
I think you under-estimate the amount of mental acrobatics good poker players do, especially on line players. Just like good chess players, there are people take time to calculate out profitability of different courses of action they can take in common situations against a range of possible opponent holdings and counter moves. The internet speeds up this "group-learning" process because people can share their views and their calculations.
Also, the speed of the online poker game puts a lot of evolutionary pressure on people who play suboptimal strategies. Avid players can literally play hundreds of thousands of hands in a year, so bad strategies and players are weeded out quickly. In fact, you can see strategies evolve over time, as one strategy dominates, gets replicated by internet forum discussions, and then counter strategies arise to pick them off.
But whether poker players act as predicted by game theory doesn't really say that much about the population at large -- real world interactions are more one-off compared with the controlled repetition of poker. And even if real world interaction repeats, its subtly different the next time, so it can almost be classified as a new game.
One observation I have from applying game theory to poker is that its very easy to misapply theory. Most theory include simplifying assumptions, and its getting the assumptions that is the difficult part.
IMO the human gut works pretty well in a complicated, partial information environment. Game theory is almost better used as an after-the-fact way of improving gut decisions rather than as a playing guide. In poker, if you don't know how to play and think theory will make you unbeatable, you're most dangerous to yourself.
So I'm leery of people taking theory results (whether poker or economics or social science) and instantly concluding that the solution is better than the evolved solution over time. Most of the time, evolved solutions are taking into account factors omitted in the theoretical model, which can dominate the explicit factors of the model. But I think theory is useful as an explanatory tool and as a way to look for improvements that can be easily missed when thinking in purely traditional terms.
Posted by: pokerfan at Jan 29, 2008 12:58:20 AM
lest
1. for fear that; so that (one) should not (used negatively to introduce a clause expressive of an action or occurrence requiring caution): He kept his notes by his side lest faulty memory lead him astray.
2. that (used after words expressing fear, danger, etc.): There was danger lest the plan become known.
I'm sure it was meant to be "unless" in the original post. Не надо выпендриваться.
Posted by: A Tykhyy at Jan 29, 2008 2:21:18 AM
On poker and trial lawyers, Steven Lubet has nice book entitled What Trial Lawyers can learn from Poker.
It is worth reading.
Posted by: Michael Webster at Jan 29, 2008 8:59:33 AM
I agree with the earlier blog that stated Hartford's drawback theory of game modeling (that we assume everyone in the game is of equal intelligence). For poker, this could carry over into the fact that everyone is equally invested on playing, and winning, the game. Newbies at the WSOP are looking more for that defining moment where some announcer says "oh look at the play this guy just made!" For them it may be less about the actual game and more about being noticed. That makes it very hard to interject game theory. For example: I used to play poker with a friend who would play absolutely any cards. She didn't care if she won the hand or lost - she just enjoyed the social interaction. That pretty much keeps anyone at the table from being able to apply game theory while she was still in the game.
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