Exam 5: Utility and Game Theory

A risk avoider will have a concave utility function.

Consider a two-person,zero-sum game where the payoffs listed below are the winnings for Player A.Identify the pure strategy solution.What is the value of the game? Player B Strategies Player A Strategies 5 5 4 1 6 2 7 2 3

A risk neutral decision maker will have a linear utility function.

A game has a saddle point when the maximin payoff value equals the minimax payoff value.

The decision alternative with the best expected monetary value will always be the most desirable decision.

Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.

For a game with an optimal pure strategy,which of the following statements is false?

Three decision makers have assessed utilities for the problem whose payoff table appears below. State of Nature Decision 500 100 -400 200 150 100 -100 200 300 Probability .2 .6 .2 Payoff A B C 300 .95 .68 .45 200 .94 .64 .32 150 .91 .62 .28 100 .89 .60 .22 -100 .75 .45 .10 a.Plot the utility function for each decision maker. b.Characterize each decision maker's attitude toward risk. c.Which decision will each person prefer?

Any 2 X 2 two-person,zero-sum,mixed-strategy game can be solved algebraically.

When consequences are measured on a scale that reflects a decision maker's attitude toward profit,loss,and risk,payoffs are replaced by

Consider the following two-person zero-sum game.Assume the two players have the same two strategy options.The payoff table shows the gains for Player A. Player B Plaver A Strategy Strategy Strategy 4 8 Strategy 11 5 Determine the optimal strategy for each player.What is the value of the game?

Consider the following two-person zero-sum game.Assume the two players have the same three strategy options.The payoff table shows the gains for Player A. Player B Plaver A Strategy Strategy Strategy Strategy 6 5 -2 Strategy 1 0 3 Strategy 3 4 -3 Is there an optimal pure strategy for this game? If so,what is it? If not,can the mixed-strategy probabilities be found algebraically?

A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(25000)+ (1  p)(5000).If the utility of 25,000 is 0 and of 5000 is 1,then the utility of 10,000 is

A decision maker whose utility function graphs as a straight line is

Draw the utility curves for three types of decision makers,label carefully,and explain the concepts of increasing and decreasing marginal returns for money.

Which of the following statements about a dominated strategy is false?

Game theory models extend beyond two-person,zero-sum games.Discuss two extensions (or variations).

The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.

A decision maker has the following utility function Payoff Indifference Probability 200 1.00 150 .95 50 .75 0 .60 -50 0 What is the risk premium for the payoff of 50?

Two banks (Franklin and Lincoln)compete for customers in the growing city of Logantown.Both banks are considering opening a branch office in one of three new neighborhoods: Hillsboro,Fremont,or Oakdale.The strategies,assumed to be the same for both banks,are: Strategy 1: Open a branch office in the Hillsboro neighborhood. Strategy 2: Open a branch office in the Fremont neighborhood. Strategy 3: Open a branch office in the Oakdale neighborhood. Values in the payoff table below indicate the gain (or loss)of customers (in thousands)for Franklin Bank based on the strategies selected by the two banks. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Lincoln Bank }$ Franklin Bank Hillsboro Fremont Oakdale Hillsboro 4 2 3 Fremont 6 -2 -3 Oakdale -1 0 5 Identify the neighborhood in which each bank should locate a new branch office.What is the value of the game?