PART A

NOTE: Answer ALL questions. Each question is worth 1 mark. PART A is worth 5 marks. Write your answers clearly on the multiple-choice answer sheet.

1. In game theory, the outcome or consequence of a strategy is referred to as the:

a. payoff.

b. penalty.

c. reward.

d. end-game strategy.

2. In game theory, a choice that is optimal for a firm no matter what its competitors do is referred to as:

a. a dominant strategy.

b. a dominated strategy.

c. a game-winning choice.

d. a super-optimal strategy.

3. A plan of action that considers the reaction of rivals is an example of:

a. accounting liability.

b. strategic behaviour.

c. accommodating behaviour.

d. risk management.

NOTE: Consider the following game to answer Q4 and Q5 of PART A. Two players A and B, have two strategy choices, 1 and 2.

If both players choose strategy 1, then both receive a payoff of $25. If both choose strategy 2 then both receive a payoff of $50.

If one player chooses strategy 1, and the other player chooses strategy 2, then the player choosing strategy 2 receives a payoff of $20 while the player choosing strategy 1 receives a payoff of $70.

Both of the players must make their decision without knowledge of the other’s action.

4. Are there any dominant strategies in this game?

a. Strategy 1 is a dominant strategy for both players.

b. Strategy 2 is a dominant strategy for both players

c. Strategy 1 is dominant for Player A and strategy 2 is dominant for Player B

d. There are no dominant strategies in this game.

5. The equilibrium in this game is expressed as (Player A’s strategy; Player B’s

Strategy):

a. (Strategy 1; Strategy 1).

b. (Strategy 2; Strategy 2).

c. (Strategy 1; Strategy 2).

d. (Strategy 2; Strategy 1).

PART B

NOTE: Answer ALL questions. Each question is worth 5 marks. PART B is worth 15 marks. Write your answers clearly on the answer booklet provided.

1. Define the following:

a. Game Theory.

b. Dominant Strategy.

c. Tipping.

d. Congestion.

e. Nash Equilibrium.

(Each of these carries 1 mark, for 5 marks in total)

2. Briefly describe the basic structure of a game.

(5 marks)

3. What is the difference between:

a. an extensive form game and a strategic form game?

b. perfect information and imperfect information?

(Each carries 2.5 marks, for 5 marks in total)

PART C

NOTE: Answer ALL questions. Each question is worth 10 marks. PART C is worth 40 marks. Write your answers clearly on the answer booklet provided.

For all questions, remember to show your working.

1. Alexa and Judd live in Boston and have been dating for about a year, and are fairly serious. Alexa has been promoted to Regional Manager and been given the choice of assignments in Atlanta, Boise, and Tucson. After she makes her choice (and this is observed by Judd), he’ll decide whether to stay in Boston or follow Alexa. The payoffs associated with the six possible outcomes are in the accompanying table:

a. Write down the extensive form game. (5 marks)

b. Write down the strategic form game. (5 marks)

2. Queen Elizabeth has decided to auction off the crown jewels, and there are two bidders: Sultan Hassanal Bolkiah of Brunei and Sheikh Zayed Bin Sultan Al Nahyan of Abu Dhabi. The auction format is as follows: The Sultan and the Sheikh simultaneously submit a written bid. Exhibiting her well known quirkiness, the queen specifies that the Sultan’s bid must be an odd number (in hundreds of millions of English pounds) between 3 and 11 (that is, it must be 3, 5, 7, 9 and 11) and that the Sheikh’s bid must be an even number between 2 and 10 (that is, it must be 2, 4, 6, 8 and 10). The bidder who submits the highest bid wins the jewels and pays a price equal to his bid. The winning bidder’s payoff equals his valuation of the item less the price he pays, whereas the losing bidder’s payoff is 0. Assume that the Sultan has the valuation of 10 (hundred million pounds) and that the Sheikh has a valuation of 9 (hundred million pounds).

a. In matrix form, write down the strategic form of this game. (5 marks)

b. Find all Nash equilibria. (5 marks)