Vincent Conitzer conitzer@cs.duke.edu Utility theory Vincent Conitzer conitzer@cs.duke.edu.

Slides:

Advertisements

Similar presentations

CPS Utility theory Vincent Conitzer

Advertisements

Utility theory U: O-> R (utility maps from outcomes to a real number) represents preferences over outcomes ~ means indifference We need a way to talk about.

Paradoxes in Decision Making With a Solution. Lottery 1 $3000 S1 $4000 $0 80% 20% R1 80%20%

Strongly based on Slides by Vincent Conitzer of Duke

Decision-Making under Uncertainty – Part I Topic 4.

Economics 202: Intermediate Microeconomic Theory 1.HW #5 on website. Due Tuesday.

1 Utility Theory. 2 Option 1: bet that pays $5,000,000 if a coin flipped comes up tails you get $0 if the coin comes up heads. Option 2: get $2,000,000.

Risk a situation in which there is a probability that an event will occur. People tend to prefer greater certainty and less risk.

Intro to Game Theory Revisiting the territory we have covered.

1 Modeling risk attitudes Objective: Develop tools to compare alternative courses of action with uncertain outcomes (lotteries or deals) A B $30 -$15 $100.

1 Utility Examples Scott Matthews Courses: /

Attitude toward risk Problem: Costello likes to ride his bike to school. If it is raining when he gets up, he can take the bus. If it isn’t, he can ride,

Risk attitudes, normal-form games, dominance, iterated dominance Vincent Conitzer

Decision Analysis (cont)

CPS 270: Artificial Intelligence Decision theory Instructor: Vincent Conitzer.

Reminder Midterm Mar 7 Project 2 deadline Mar 18 midnight in-class

CPS Utility theory, normal-form games

Utility An economic term referring to the total satisfaction received from consuming a good or service. A consumer's utility is hard to measure. However,

Experiments and “Rational” Behavior, 5/1/07. Beauty Contest Game Each person choose a number from 0 to 100. We will average these numbers. The person.

Risk and Uncertainty When we represent outcomes as possibilities rather than a deterministic outcome, we must address feelings about risk. Why would risk.

1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews Courses: / / Lecture 12.

L12 Uncertainty. Model with real endowments 1. Labor Supply (Labor-Leisure Choice) 2. Intertemporal Choice (Consumption-Savings Choice) 3. Uncertainty.

Independence and Conditional Probability

Bayesian games and mechanism design

Consumer Behavior: Utility Maximization

Bayesian games and their use in auctions

C H A P T E R C H E C K L I S T When you have completed your study of this chapter, you will be able to Calculate and graph a budget line that shows.

Vincent Conitzer CPS Utility theory Vincent Conitzer

CPS Mechanism design Michael Albert and Vincent Conitzer

Utilities and Decision Theory

L11 Uncertainty.

Prospect Theory - complement

The Economics of Information and Choice Under Uncertainty

6a – Consumer Decisions This web quiz may appear as two pages on tablets and laptops. I recommend that you view it as one page by clicking on the open.

Decisions under risk Sri Hermawati.

Games of pure conflict two person constant sum

CPS 570: Artificial Intelligence Decision theory

12 Uncertainty.

Theory of Consumer Behavior

Lecture 2 Hastie & Dawes: Changing Our Minds: Bayes’ Theorem. In Rational Choice in an UncertainWorld, 2nd ed., 2010, pp

HOLT: Economics Chapter 3

L11 Uncertainty.

Unit 8. Day 5..

Rational Decisions and

Buying and Selling: Uncertainty

Consumer Behavior Ch. 7.

Chapter Twelve Uncertainty.

Utility Theory Decision Theory.

Behavioral Finance Economics 437.

Vincent Conitzer Mechanism design Vincent Conitzer

Vincent Conitzer CPS 173 Utility theory Vincent Conitzer

Instructor: Vincent Conitzer

Vincent Conitzer CPS 173 Mechanism design Vincent Conitzer

Buying and Selling: Uncertainty

Chapter 12 Uncertainty.

Behavioral Finance Economics 437.

Walter Nicholson Christopher Snyder

Vincent Conitzer Utility theory Vincent Conitzer

Behavioral Finance Economics 437.

Behavioral Finance Economics 437.

Artificial Intelligence Decision theory

Utilities and Decision Theory

Utilities and Decision Theory

Are the outcomes equally likely?

Buying and Selling: Uncertainty

Making Simple Decisions

Is all about sharing and being fair

Vincent Conitzer CPS Mechanism design Vincent Conitzer

CPS Bayesian games and their use in auctions

Presentation transcript:

Vincent Conitzer conitzer@cs.duke.edu Utility theory Vincent Conitzer conitzer@cs.duke.edu

Risk attitudes Which would you prefer? How about: A lottery ticket that pays out $10 with probability .5 and $0 otherwise, or A lottery ticket that pays out $3 with probability 1 How about: A lottery ticket that pays out $100,000,000 with probability .5 and $0 otherwise, or A lottery ticket that pays out $30,000,000 with probability 1 Usually, people do not simply go by expected value An agent is risk-neutral if she only cares about the expected value of the lottery ticket An agent is risk-averse if she always prefers the expected value of the lottery ticket to the lottery ticket Most people are like this An agent is risk-seeking if she always prefers the lottery ticket to the expected value of the lottery ticket

Decreasing marginal utility Typically, at some point, having an extra dollar does not make people much happier (decreasing marginal utility) utility buy a nicer car (utility = 3) buy a car (utility = 2) buy a bike (utility = 1) money $200 $1500 $5000

Maximizing expected utility buy a nicer car (utility = 3) buy a car (utility = 2) buy a bike (utility = 1) money $200 $1500 $5000 Lottery 1: get $1500 with probability 1 gives expected utility 2 Lottery 2: get $5000 with probability .4, $200 otherwise gives expected utility .4*3 + .6*1 = 1.8 (expected amount of money = .4*$5000 + .6*$200 = $2120 > $1500) So: maximizing expected utility is consistent with risk aversion

Different possible risk attitudes under expected utility maximization money Green has decreasing marginal utility → risk-averse Blue has constant marginal utility → risk-neutral Red has increasing marginal utility → risk-seeking Grey’s marginal utility is sometimes increasing, sometimes decreasing → neither risk-averse (everywhere) nor risk-seeking (everywhere)

What is utility, anyway? Function u: O →  (O is the set of “outcomes” that lotteries randomize over) What are its units? It doesn’t really matter If you replace your utility function by u’(o) = a + bu(o), your behavior will be unchanged Why would you want to maximize expected utility? This is a question about preferences over lotteries