Test 2 Review

Test 2 in Decision Theory/Game Theory will focus on Chapters 4, 5 in Peterson, and Lessons 1.5 and 1.6 in Spaniel. Here is a partial list of topics, concepts, arguments, and techniques that you will be responsible for:

Finding and calculating MSNE for a two person/two move game.

Presenting and explaining the Long Term/Aggregation Argument for the Expected Utility Theorem.

The Expected Utility Theorem.

The Gambler's Ruin Objection to the Long Term/Aggregation Argument for Exp(U)

You do not need to reconstruct the Indirect Axiomatic or Direct Axiomatic Proofs for Exp(U), but you should understand them and be able to explain their purpose and place in Decision Theory.

What is the Allais Paradox argument against Exp(U)?

The definitions and examples of PSNE, MSNE.

Calculating payouts for PSNE, and calculating payouts for MSNE.

You should also understand and be able to explain how Morgenstern and von Neumann use preferences and lotteries to derive an interval scale for utilities from an agent's preferences.

Be prepared to solve a problem like this using VnM's Lotteries as preferences method:

Give an ordinal ranking of the utilities of these: X, Y, Z. Assign interval values to the top and bottom choices. Devise a VnM lottery that captures where the middle choice fits in that range. Solve and find the utility of the middle choice. Suppose you rank W between the best and second best choice. What it it’s utility?

What are the axioms of Utility Theory from Chapter 5? Completeness, Asymmetry, Transitivity, Negative Transitivity, ...

What is the Money Pump Argument for the Transitivity Axiom?