midterm answers 2005

Econ 223 Midterm Examination: August 15, 2005 with comments by JF after grading

This is a closed book exam: no notes, no books, no cell-phones, no calculators just you. Your script will be taken from you and you will receive a zero grade for this paper should you be found with any of these items – so please deposit them at the front of the room.

Attached is a 1 page answer sheet for question 4 to be handed in with your personalized exam booklet. Make sure your name and student ID are clearly written on this answer sheet and place it inside your answer book before leaving. Please leave your answer book at your assigned desk space (to preserve alphabetic arranging of scripts).

BEFORE YOU START MAKE SURE: your answers are written in the answer book that has your name on the label. There are 4 questions for a grand total of 100. Answer all questions in the answer booklet provided.

Question 1 18 marks Dixit and Skeath’s classifications of games

Question 2 32 marks trust game

Question 3 20 marks Multi-choice

Question 4 30 marks 2x2 simultaneous games (Multi choice matching)

Q1 pure types of games (18 Marks)

Dixit and Skeath (DS) classify games into a number of various "pure types" by asking and answering some interesting questions. Identify these types and briefly explain the key concepts/distinctions used to interpret and understand each type. (By "briefly" I mean in no more than 1-2 sentences; you do not have to provide example games in your explanations.)

2005 For a preset question , with suggested answers on the web, (see web page week 6) some of you still managed to do quite poorly on this one.

Q4 2 Trust (32 marks, 3 parts) s.a on your answer booklet means "see answers"

Going to the doctor has a number of strategic aspects to it. Suppose for example that the doctor is a salaried employee of a hospital or an owner/partner in a medical clinic, and that everyone knows that the hospital/clinic has a reputation for trying to cut costs. Patients then get concerned (rightly) that the doctor may give advice/treatment that isn’t in their best health interests. Simplifying, suppose patients can either offer trust (OT) or not, ie don’t trust, (DT); doctors can honour trust (HT) or act opportunistically, ie don’t honour trust (DHT). If the Patient (column player) and Doctor (row player) were playing a simultaneous game the payoffs for the various strategy combinations would look like those in the following table. The numbers refer to preference ranks, so higher numbers indicate more preferred outcomes.

Q2a [7 marks] Use game theory to predict the outcomes (strategies and payoffs) of this simple simultaneous game of doctor patient interaction.

The doctor has a weakly dominant strategy to act opportunistically. Anticipating this the patient won't trust, leading to payoffs (1,2). [you may have made the same statement by identifying best resonses in the table and identifying (DHT,DT) as the nash equilibrium predicition.

Q2b [13 marks] Suppose the real game being played here is sequential not simultaneous, with the Doctor moving first, and the Patient moving second. Using the same payoffs as in the Table, Draw and clearly label the game tree for this sequential game and analyse the game clearly pruning relevant branches to show the rollback path of play and outcomes. See Graph

Q2c [12 marks] Take the sequential game in 2b and analyse that game as a simultaneous game. Briefly explain the relationship between your answers to part 2b and part 2c. See Graph There are still many peole, maybe 1/4 of the class, who interpreted this question to mean redoing question 3a and comparing answers to question 3a and question 3b . You are to AnALYZE this suequential game of part 3b as a simultaneous game -not change it back into a simultaneaous game. This analysis involves identifying all the strategies for each player (2 for docs, 4 for patients) and constructing the relevant payoff matrix. To receive a full 12 points here you need to recognize and work with the ideas of multiple equilibria and at least the concepts of sub game perfection (ie the element of beliefs about rational/irrational play in subgames off the equilibrium path - in less jargon, the "what-if beliefs underlying each equilibrium may have an element of irrationality built into them)

Q3 Multi Choice [4 marks each, 20 in total]Answers in red

Q3.a Two stores, one a Dairy, the other a Supermarket, are the only two firms active in a particular market. Each (independently and simultanaeously) must choose between opening early (7 am) or opening late (9am). The payoffs (in thousands of dollars per day) of the stores are shown (in the standard way) in the accompanying table.

Choose one of the following answers that correctly fills in the blanks in the following statement: “The game illustrated here _____a prisoners’ dilemma because _____.”

(a)is; it has all the characteristics of a prisoners’ dilemma

(b) is not; neither Firm A nor Firm B has a dominant strategy

(d)is not; using their dominant strategies gives the firms a mutually beneficial outcome

(e) is not; it is an assurance game

(f) is; it is a simultaneous version of the entry deterrence game

Q3.b Consider a game in which Player A and Player B each choose one out of two possible actions, so that the game has four possible outcomes. Suppose that we can rank (with no ties) each of those four so that we know A’s favorite outcome, second-favorite, and so on, and also B’s favorite outcome, second-favorite, and so on. Suppose the game has the following characteristics: the outcome that A likes best is the same one that B likes second best, and the outcome that B likes best is the same one that A likes second best. What sort of game has these features? [Choose one of the following answers]

(a) A prisoners’ dilemma

(b) A battle-of-the-sexes game

(d) An assurance game

(e) A pure coordination game

(f) None of the above are correct.

I accepted b or c

Q3.c Consider the following (old) quote from Rugby News magazine. “Professional rugby players playing forward positions will never adopt helmets, hard or soft. The use of helmets in rugby will spread only through fear caused by serious injuries or through a rule making them mandatory”. NZ star hooker James McGraw, alias “Shrek”, cites the simplest factor: “Vanity. You don’t want to look like a donkey out there on the field…”. One player, whose head told a sad tale of many injuries, summed up most players’ feelings: “It’s foolish not to wear a helmet. But I don’t—because the other guys don’t. I know that’s silly, but most of the players feel the same way. If the league made us do it, though, we’d all wear them and all be better off.”

Viewing the wear helmet–don’t wear helmet choice as though it were a 2 player game, it most closely resembles (Choose one of the following answers):

(a) a prisoners’ dilemma

(b) a battle-of-the-sexes game

(d) an assurance game

(e) A pure coordination game

(f) All of the above are correct.

I accepted a or d

Q3.d. Robert Gibbons described the situation of two firms that produce products that consumers may use together (for instance, a computer and software). The most important concern for these two firms is that they coordinate their product designs and agree on one set of technical standards (either both pick standard A or both pick standard B) that will make their products compatible with each other. Such coordination will leave both firms better off than they would be with no coordination. As a secondary concern, each firm has its own favorite standard that it would most like to see both firms adopt. The game between these two firms (in which each chooses its standard) can be best described by saying that is it most like a (Choose one of the following answers):

(a) a prisoners’ dilemma game.

(b) a chicken game.

(d) an assurance game.

(e) a game with no nash equilibrium in pure strategies

Q3.e Consider the following two situations. (i) Two governments choose between imposing health and safety restrictions on international trade and not imposing such restrictions. Regardless of what other governments are doing, imposing such restrictions always increases the payoff earned by the home country by 5 but also always decreases the payoff earned by the other country by 10. (ii) Fans at a sporting event choose between cheering for the home team and not cheering. Regardless of what other fans are doing, cheering increases a fan’s enjoyment and thus always increases his or her payoff by 5, and also adds to the enjoyment of other fans and thus always increases their payoff by 1. Which of these situations has the characteristics of a prisoners’ dilemma?

(a) Only situation (i)

(b) Only situation (ii)

(d) Neither situation (i) nor situation (ii)

(e) there isn’t enough information to answer the question using Game theory

Q4 Simultaneous games Multiple Choice (Answer template provided; 3 marks per question 30 marks in total).

The 10 payoff matrices on the answer template describe various types of 2x2 simultaneous games. Payoffs to players are the numbers with higher numbers indicating more preferred alternatives, and negative numbers indicating losses. On the answer sheet provided write down the option, or set of options, from the following list (“a” through “i”) that most accurately describes the game AND identify all pure strategy equilibrium strategies for each game (in some cases more than one option may be appropriate). Use the answer sheet provided and the codes for the options below. Write your code in the box underneath the number of the game and circle the cell(s) to indicate the equilibrium startegies. You do NOT have to rewrite the payoff matrix in your answer booklet nor on your multi choice answer sheet. Make sure your name and student ID’s are clearly written on the answer sheet.

a) A prisoner’s dilemma game

b) A constant sum game

c) A game with no Nash Equilibrium in pure strategies

d) A game of chicken

e) An assurance game

f) A pure coordination game

g) A dominance solvable game

h) A game of battle of the sexes

i) A game with a (strict) dominant strategy equilibrium

Example of how to answer Q4 on your answer template [eg only –not a correct answer]

To get full marks for each question you need to circle the relevant cell AND specify the correct answer(s) completely. Typically you might receive 1 mark for correctly identifying the game but not answering the second part about circling the equilibrium strategies. Correctl answering the type of game but incorrectly specifying the equilibrium strategies was graded as zero - you can't have the "right" answer for the "wrong" reasons. Zero also occurred if there is a complete mismatch - eg in 4.4 writing "c" and circling some cell, or writing "b" in 4.1 and circling the two equilibrium strategies.