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Logic of Life – Chapter 2: Game Theory isn’t Always about the Games We Play

Fabio

This review is cross posted from the Marginal Revolution blog, which is having a book forum on The Logic of Life by Tim Harford.

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 basics 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, consulted a more experienced player during his run at the World Series of Poker, 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?

Written by fabiorojas

January 28, 2008 at 1:41 pm

Posted in books, economics, fabio

8 Responses

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  1. I had been meaning to write something or other about this , but perhaps I’ll just leave it here as a comment. I thought the paper was interesting and the video was great in the fascinated-by-human-nature-slash-social-norms kinda way.

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    Peter

    January 28, 2008 at 3:42 pm

  2. 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.

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    Tim Harford

    January 28, 2008 at 4:09 pm

  3. The one thing I’d like to add about game theory is that I think optimal strategies are discovered unconsciously. It is not necessarily through a process of thinking and rationalization.

    John Maynard Smith came up with the concept of evolutionarily stale strategy (ESS) along with his concept of evolutionary games. An ESS is the most optimal strategy that an organism in an ecology has found for gathering and managing resources. If a population of individuals is utilizing an ESS then it is essentially impossible for any other strategy to invade since it simply can’t out-compete.

    I think this translates very well to a social setting. Through trial-and-error, playing a particular game over many repitions, a player may discover a strategy that wins. It’s possible that others in the environment notice this strategy and copy it. Eventually we’d expect everyone (almost) to adopt this strategy and alternative strategies to become almost impossible to maintain.

    Game theory does not require rational actors. It just requires actors that depend on game payoffs for their continued existence.

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    Jesse

    January 28, 2008 at 5:47 pm

  4. Can we use game theory to play gambling?

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    Michael Poker

    March 2, 2008 at 9:54 pm

  5. Can we use game theory to play stock?

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    Books

    March 11, 2008 at 4:08 pm

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