Econ 223 Midterm Examination:  March 28 2008
2 hours max: 6:30 pm to 8:30 pm

with suggested answers

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. On the desk space in front of you you should have

• ONE set of exam questions
• ONE A4 answer sheet, double sided, for recording your multi choice answers and for recording your answers to Question 1 of Part B. Please print your name and student ID number clearly on the double sided A4 sheet right now!.
• ONE answer booklet with your name printed on it for answering the remainder of questions in Part B and for other working.
  
  

Before you leave the exam room tonight:

• Make sure your name and student ID are clearly written on the A4 answer sheet and place it inside your answer book.
• Please leave your answer book at your assigned desk space when you leave (to preserve alphabetic arranging of scripts). ie DON'T bring it down to the front as you leave.
• No one will be admitted after 6:50 and you may leave any time after 6:50

There are 9 multi choice questions worth 6 marks each, 54 in total, in section A.
There are 3 "written answer" type questions for a total of 46 marks, in section B.

Multiple choice Section A (answers here)

A1 ( 6 marks) The game tree below represents a stylised 3 player (A, B, C) sequential game (no payoffs are shown at the terminal nodes).

Count the number of strategies for each player and write your answer on your multi-choice answer sheet for this question in the three blank spaces provided, selecting from the following list : 2, 3, 4, 5, 6, 8, 11, 12, 16, 24, "none of these"

 

A2 ( 6 marks) Some workers like leaving early to beat the rush hour (5 pm) traffic, but if everyone leaves early it just shifts the congestion problem in time. Of course, people are different and some abhor congestion less than others...if they can get home early! Suppose preferences for Row (red) and Column (Blue) for leaving early or at 5pm and for the associated congestion are as indicated in the following payoff table. Red's preferences ranks are in letter grades (A is better than B is better than C is better than D, for her), while Blue's preferences are in numbers (higher number indicating more preferred outcomes). .

Choose one of the following answers that correctly fills in the blanks : “The game illustrated here _____a prisoners’ dilemma because _____.”(Choose an answer from below and enter it on your multi-choice answer sheet) 

• (a) is; it has all the characteristics of a prisoners’ dilemma
• (b) is not; neither Row (red) nor Column (blue) has a dominant strategy
• (c) is not; the game has no Nash equilibrium (in pure strategies)
• (d)is not; using their dominant strategies gives the firms a mutually beneficial outcome
• (e) is not; it is a battle of the sexes game with each producer prefer differring equilibria
• (f) is; because both players want to avoid rush hour traffic no matter what.
• (g) is not, but for none of the above reasons.

A3 ( 6 marks) Bend it Like Beckham: The penalty shoot in soccer is a dramatic game of strategic interaction. If we simplify we can think of three basic strategies for each player. The Goalie can decide to move to the left , stay in the middle, or move right. . The Kicker can shoot to the (goalie's ) left or the (goalie's) right or down the middle. Even if the goalie moves to the same side the Kicker kicks to, he doesn't always prevent the goal, and even if a kicker kicks to the opposite side to where the goalie has moved a goal isn't always scored. The following payoff matrix describes the moves and payoffs in a simple simultaneous game version of the penalty shootout. The payoffs for the goalie are success percentages in stopping goals: the chance (in %) that the ball doesn't go in the net and so there is no score score (higher such probs being better for the goalie) . Payoffs for the Kicker are preference ranks, higher numbers are better. The kicker's name is Beckham and while he likes scoring goals, he really likes outfoxing the goalie with his does his famous "bend it like beckham" kick...Shots down the middle are more or less boring for him, depending on how the goalie defends.

Complete the following sentence: The strategic issues in this game are closest to those ______: .......(Choose one answers from the list below and enter it on your multi-choice answer sheet ) 

• (a) in a game of chicken
• (b) in a coordination game because the physical speed and coordination of the players will ultimately determine the outcome
• (c) in the textbook's tennis shot game (down-the-line or crosscourt)
• (d) in the battle of the sexes game
• (e) in the stag hunt game
• (f) in a game where iterated elimination of dominated strategies can be used
• (g) none of the above accurately describe the strategic issues .

A4 ( 6 marks) Examine following 2 player 4x4 payoff matrix. The first two steps of the method of iterated elimination of dominated alternatives can eliminate which two rows and colums? On your multi choice answer sheet for this question write down the identifying letters of the rows and/or columns that are your answer to this question.

A5 (6 marks) Millions of people in LDCs have died prematurely of AIDs and its' opportunistic infections in spite of the fact that there are combinations of modern drugs which, if taken regularly, can extend both the quality and length of life for HIV+ infected people. Technically the drugs are "available" to infected people in LDCs - but only at the same high prices that they are available in wealthier western countries. But how can someone in an LDC with income of $25 a year afford a drug that is priced at $10,000 a year? Multinational pharmaceutical companies (BigPharma) say they would gladly lower prices for AIDS drugs in LDCs if those countries would impose and enforce restrictions on the resale of those drugs back in wealthy countries like Amercia or Europe. But if BigPharma did actually price AIDS drug low enough to make them affodable to the LDCs, people in the LDCs would benefit by NOT enforcing restrictions on resale of these drugs (why not buy enough for your own medical uses and then buy some more to sell back in Amercia or Europe at high prices there?).  This question asks you to use basic game theory to analyze the strategic interaction between the multinational pharmaceutical companies (BigPharma) and the LDCs.

Suppose  Big Pharma and the LDC's are engaged in a one-shot simultaneous game. Big Pharma has only two prices they can offer to LDCs, PH, price high , or PL, price low, and that LDCs have only two actions, ER, enforce restrictions on resale back to America/Europe, or not,  NER. Let payoffs be described by the numbers in the following payoff matrix (higher numbers indicate more preferred outcomes for that player):

The dominance solveable prediction for the payoffs in this game is______: (write your answer on your multi-choice answer sheet for this question by selecting the letter a,b,c,d from one of the above cells , or write "Not dominance solveable " )

A6 (6 marks) Suppose the game between Big Pharma and the LDCs in the previous question (A5) could be changed to a one-shot sequential game , with the LDC's moving first, committing to either enforcing restrictions or to not enforcing restrictions in an observable way, everything else remaining constant. The rollback prediction for the payoffs in this game is______: (write your answer on your multi-choice answer sheet for this question by selecting the letter a,b,c,d from one of the above cells in A5 , or write "Not solveable by rollback ")

A7 (6 marks) Recall the Stop-Go alternating offer game from class, where two players take turns making offers about how to divide up a fixed, but shrinking, pie. In class we had the pie shrinking from 10 to 6 to 4 to 0 chocolate bars, where the shrinking occurs after one player refuses to accept a proposal made by the other, until eventually there was no pie to share out. Imagine that Apple Farmers (AF) and the pickers that work for them (W) are playing a similar alternating offer bargaining game at the start of the harvest season (ie basically the same rules about who can offer and counter offer, and when) . The apple harvest looks profitable this year, but the crop goes bad fast: the available pie shrinks very quickly, from $200K to $60K to $30K to $0 (imagine a week between each bargaining interval). Assume offers and counter offers are made in units of $1K , that each player values only their own $ incomes , and that either party has to be offered a strictly positive amount to induce them to accept as compared to what they can get by rejecting and possibly taking the bargaining to the next round. Choose the answer from the list below that is closest to the prediction that game theory would make about the outcome of this bargaining game, and write the answer in the space provided on your multi-choice answer sheet.

1. a) the Apple Farmers will will hold out till week 3 and exploit the workers, dividing the $30K to keep $29K for themselves and offer the bare minimum $1K for the workers, which the workers will grudgingly accept.
2. b) The Apple Farmers will offer to split the first week catch evenly $100, $100 each and the workers will accept rather than delay and run the risk of get a lower share of a smaller pie later.
3. c) The Apple Farmers will keep $198K for themselves in the first week and offer the worker’s $1K more than the minimum $1K they will work for in the last round, and the workers will accept, grudgingly.
4. d) Same as above (c) except that workers reject this initial 198/2 split and hold out till week 2 where they propose a $30K, $30K split of the $60K proceeds , and the Apple Farmer's will accept rather than run the risk of either not getting an agreement before the season runs out or of having to divide the small $30K crop.
5. e) The Apple Farmers will offer the workers $40K on round 1 , which the workers will accept
6. f) The Apple Farmers will offer the workers $40K on round 1 , the workers will refuse that offer and hold out for $50 for themselves on the second round when $60K is available.

A8 (6 marks) The following payoff matrix describes a 3 person simultaneous game. The three players are R, B, and G. Each player has two moves: {T, B} for R, {L, R} for B, and {Yes, No} for G. Payoffs are in dollars, listed in order from left to right first for player R, then for player B then for player G. The Nash Equilibrium prediction(s) for the outcome of this game is/are _____(Choose your answer(s) from the list a,b,c,d,e,f,g,h that labels each of the cells in the payoff matrix and write the answer in the space provided on your multi-choice answer sheet)

A9 (6 marks) Consider the situation of two groups of firms that produce digital entertainment products: regular DVDs and new higher definition/higher capacity optical disks. Think Sony/Philips for BluRay style disks and Toshiba/Hitachi for HD-DVD style disks. (You don't need to know the technical details of these systems to appreciate the stratgeic interaction between the two groups of firms). The most important long run concern for these two firms is that they coordinate their product designs and agree on one set of technical standards (either both pick BluRay or both pick HD-DVD) so their products are compatible with new generation of DVD type players. Such coordination will leave both firms much better off than they would be with no coordination. As a secondary concern, each firm has its own favorite product design that it would most like to see both firms adopt. The game between these two firms (in which each chooses a product design simultaneously and independently ) can be best described by saying that is it most like a : (Choose one answer from the list below and write the answer in the space provided on your multi-choice answer sheet)
(a) a prisoners’ dilemma game.
(b) a centipede game with a grwoing pie to share out
(c) a battle of the sexes game.
(d) an assurance game.
(e) a stag hunt game
(f) a voluntary contributions (VCM) game

Part B :Question B1: elementary simultaneous games (16 marks)

The question for this part - and an answer template -is on the opposite side of your multi choice answer sheet, the one to be handed in. Write your answers on that answer sheet . Do not write your answers in your answer booklet.

answers here (note correction as at April 7 2008);

Part B : Question B2: Dixit and Skeath Questions defining various types of games (18 marks) (write answers in answer book)

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

 

Question B3: Trust (12 marks) (write answers in answer book)

Trust is an important part of any relationship or transaction. Without trust there are many valuable opportunities - valuable for all players - that will predictably go wasting. Many people would simply rather not be involved in a game where they are going to be ripped off, exploited, or abused, even though if they could trust the other player the game would be worth playing. The following payoff table describes payoffs and actions for a simultaneous 2 player, one-shot trust game. The column player Rachel can choose either to Trust (T) or distrust (DT) the row player Bob. Bob, the row player can choose to honour that trust (HT) by acting in an honest sincere hardworking manner or he can act opportunistically (OPP), taking advantage of the situation. Bob's payoffs are his preference ranks 1 to 4 for various combinations of actions, while Rachel's payoffs are 0 for a benchmark (she doesn't trust and Bob acts opportunistically) , and other cells are valued for her as gains or losses relative to that benchmark, higher numbers being more preferred.

B3(a) (2 marks) Use Game Theory to predict the Nash Equilibrium strategies and associated payoffs in this simultaneous version of the trust game. Does either player have a dominant strategy in this simultaneous version of the game?.

B3(b) (5 marks) Draw and clearly label the game tree for the sequential game where Rachel (column player) moves first and Bob (row player) second, Bob observing whether Rachel is committed to trusting him or not before Bob makes his choice (Please use the convention for payoffs that the player that moves first come first in the payoff list; if you are using coloured pens use Red for Rachel and Blue for Bob) . Use rollback reasoning from Game Theory to predict the path of play , the player's strategies and the player's payoffs in this sequential version of the game . Does either player have a dominant strategy in this simultaneous version of the game? Most students did the order change here quite well - except for a failure to correctly identify the rollback strategies of players (which is more than the path of play): typically this resulted in a mark of 10/12

B3(c) (5 marks) Draw and clearly label the game tree for the sequential game where Bob (row player) moves first and Rachel (column player) second, Rachel observing whether Bob is committed to acting honorably or opportunistically before she has to make her choice. (Please use the convention for payoffs that the player that moves first come first in the payoff list; if you are using coloured pens use Red for Rachel and Blue for Bob) . Use rollback reasoning from Game Theory to predict the path of play , the player's strategies and the player's payoffs in this sequential version of the game . Does either player have a dominant strategy in this simultaneous version of the game?

using methods we developed in class here are the suggested answers: note YOU should try to analyze both versions of the simultaneous games as sequential games (as per our lecture 9, 2008 in class example of the threat game).