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MattG comments on [Link] Game Theory YouTube Videos - Less Wrong Discussion
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Hey James,
In the Game Theory book I'm currently going through, Introduction to Game Theory, it says that the assumptions behind game theory are that the numbers are ordinal - That is, the numbers used to represent utility don't say that you value "1,000,000" a million times as much as you value "1", only that you'd rather have the "1,000,000" over the 1. However, many of the examples you use for numbers seem to contradict this.
Did I misread Introduction to Game Theory, or are there two different version of game theory, or am I misunderstanding something else?
You are right that the usual assumption in game theory is that payoffs are ordinal. When I teach game theory I find it useful to mostly ignore this fact because some of my students (those who took Intermediate micro) have spent a lot of time on ordinal utility while most of the class has never encounter the concept before. In my video lectures I ignore the ordinal assumption except for assuming that players seek to maximize their expected payoff. (This follows from ordinal utility.) But all of the solutions I give would still be correct if you interpret the payoffs as ordinal.
Maybe you could just mention this briefly, as a sidenote, without theory. Something like: "Note that if we'd replace the numbers 1, 2, 3 with 1001, 1002, 1003, or 1000, 2000, 3000, nothing changes. (Show three versions of the same simple decision tree.)"