# slides2 - 14.12 Game Theory Lecture 2: Decision Theory...

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14.12 Game Theory Lecture 2: Decision Theory Muhamet Yildiz Road Map 1. Basic Concepts (Alternatives, preferences,…) 2. Ordinal representation of preferences 3. Cardinal representation – Expected utility theory 4. Applications: Risk sharing and Insurance 5. Quiz 1

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Basic Concepts: Alternatives • Agent chooses between the alternatives X = The set of all alternatives • Alternatives are – Mutually exclusive, and – Exhaustive Example • Options = {Tea, Coffee} X = { • T= Tea, • C = Coffee, • TC = Tea and Coffee, • NT = Neither Tea nor Coffee} 2
Basic Concepts: Preferences A relation (on X) is any subset of X×X. • e.g., ={(T,C),(T,CT),(T,NT),(C,CT),(C,NT),(NT,CT)} T C (T,C) . is complete iff x,y X, x yor ±y x. is transitive iff x,y,z X, [x yand ±y z] x z. Preference Relation Definition: A relation is a preference relation iff it is complete and transitive

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Examples Define a relation among the students in this class by • x T y iff x is at least as tall as y; • x M y iff x’s final grade in 14.04 is at least as high as y’s final grade; • x H y iff x and y went to the same high school ; • x Y y iff x is strictly younger than y; •x S y i f f x i s as old as y; More relations Strict preference: • Indifference:
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## This note was uploaded on 11/28/2011 for the course ECONOMICS - taught by Professor Muhammadyildiz during the Spring '05 term at University of Massachusetts Boston.

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slides2 - 14.12 Game Theory Lecture 2: Decision Theory...

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