February 3, 2011 G751:Game Theory Eric Rasmusen , [email protected]

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February 3, 2011

G751:Game Theory

Eric Rasmusen, [email protected]

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1. Not specifying the number of players. If you say that the the players are Advertisers, it isn't

clear whether you mean there are many advertisers, each acting independently, or just one. Both are possible models.

A related mistake is to be inconsistent about the number of of players, talking about the number of advertisers in one place and then having a game tree in which Advertisers is just one player who makes a single decision, or saying that the players are a User and an Advertiser and then saying that payoffs rise with the number of Users.

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2. Leaving out Searchers.

A good model must incorporate searchers, since their response to changes in advertisers is a key feature of the situation being modelled.

(Google's actions are not; if you left Google out as a player, that's fine.)

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3. Specifying an action Use Google if There Are No Ads.

That's a bit of a strategy, or maybe just something peculiar: it is an action contingent on another player's action.

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4. Ambiguity about whether payoff numbers are payoffs or components of payoffs,

e.g. Using Google get 10.

Does that mean that if a searcher uses Google his payoff is 10,

or that 10 is added to his payoff if he uses Google, but maybe he will have other costs and benefits depending on how the game proceeds?

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5. Having a player's payoff be independent of his own actions, e.g. the searcher's payoff is 5 minus the number of ads.

In this case, the player is completely indifferent about his action (e.g. how much he searches), so the model can't have any explanatory power.

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6. Leaving the order of play unclear,

e.g. saying that searchers learn about number of advertisers as they search, but not specifying whether a searcher decides his search intensity in advance or whether advertisers can change their advertising intensity as the game proceeds.

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7. Introducing variables without defining them,

e.g. writing $pi_i^p (S_1, \ldots S_k)$ without saying what $S_1$ denotes.

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8. Only specifying part of the payoff function,

e.g. saying what Google's best and worse possible payoffs are, but no others, or just saying what Google's equilibrium payoff is.

9. Giving two players control over the same action,

e.g., saying that Google chooses the number of ads and that the Advertiser also chooses the number of ads.

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10. Not even trying to specify payoffs.

This probably was an oversight. Some people need to learn to keep focussed on what question is being answered. For them, a good exercise is to read over the question after trying to answer it, or to write down the question as they answer it.

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11.Writing down assorted observations on the properties of the payoff functions without ever tying them together or making sure that a payoff is specified for each possible combination of actions.

12. Writing down a tautology instead of a payoff function,

e.g. saying that the advertiser's payoff is ``the increase in his sales as result of his advertising'' without saying how his sales increase with his advertising and the actions of the searchers.

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13. Saying a searcher's action is to Like or Dislike Google.

Ordinarily, a person can't choose what he likes, only what he does. His likes are given by his payoff function. I can't choose whether to like ice cream or not; I can only choose whether to eat it or not.

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To: PhD Students

From: Harry V. Roberts and Roman L. Weil

Graduate School of BusinessUniversity of Chicago

Re: Starting Research Early

Date: August 14, 1970

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The trouble is that the student uses his time in furthering his already high proficiency in taking courses and exams.

When we interview a faculty prospect here, we seldom ask him about what courses he took or what grades he received.

We always ask what research he has done and what he plans to do.

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The frame of mind with which you approach courses and exams has been with you for 16 years or so of formal schooling. During that time you have become wary about making mistakes or saying foolish things, because these tend to lower your grade.

In research, by contrast, you need a certain brashness and willingness to say and do things, even though you know that a certain fraction of the things you say and do will turn out in retrospect to have been foolish.

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For most people theoretical research is to empirical research as poetry is to prose, namely, much more difficult to carry off successfully.

An empirical study can focus on hypotheses to be tested, but most likely it won't. Descriptive research is not necessarily inappropriate nor useless: there is room, for example, even for case studies. Empirical work that reveals something worthwhile about the efficiency of measurement techniques is appropriate, either as a major or subsidiary purpose.

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Write down your tentative ideas and keep revising them as they develop. Keep a journal or at least a file. Until you have written down an idea clearly, you probably have not understood it clearly or seen its full implications.

Most of the students we have talked with have not learned this simple truth unless they have actually tried the suggestion.

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Set deadlines and stick to them. If you set and stick to a reasonable set of deadlines, or even if you fail to meet some of them by a few days, your tendency to procrastinate will be largely overcome.

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I begin with an example of good expository writing: This summer I raised a black swallowtail butterfly. It all started when we found a little caterpillar. We found it on a carrot top so I fed it carrot tops. Four days later it shed its skin and became a larger striped caterpillar. I kept on feeding it fresh carrot tops each day. It grew bigger and bigger. Two weeks later it stopped eating and got smaller. Then it spun a tread and hung itself on a stem. The next day it shed its skin and turned into a chrysalis, still attached to the carrot stem. Eight days later when we came to breakfast we found instead of a chrysalis a female black swallowtail butterfly.

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Why is this good writing? It employs all the simple Lorie rules. The sentences are short, simple, declarative sentences. Each sentence gets over a point. The point of one sentence leads to the point of the next sentence. There are no useless words. There are no vague, abstract words and only one ?big? word, ?chrysalis.? (?The pupa state of certain insects, especially of butterflies, from which the perfect insect emerges.?)

The big word is not there for show: it is the right word.

Words displace thought, and the weight of words makes it hard for the reader to see that no, or little, thought is present.

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You will find it helpful to study carefully academic writing of good style. Pick up anything written by Henry Simons, Dennis H. Robertson, or Paul Halmos, and study a haphazardly chosen paragraph. (My friends Lorie, Wallis, and Savage, mentioned in the first paragraph, will do just as well.)

Adam Smith, Robert Solow, George Stigler, Greg Mankiw, Richard Posner, Fischer Black.