Practice Quiz: Simultaneous Games

1. Which of the following statements are true?
(There can be more than 1 correct answer)
• A rational player will never play a dominated strategy.
• If each player has a dominant strategy, there will be a Nash Equilibrium in the game.
• Every game must have a dominant strategy.
• Rational players take only the payoffs into consideration when making a decision.
• Every game must have at least one Nash Equilibrium.
• Players, actions, rules and payoffs are important parts of a game (in terms of game theory).
• In a prisoner’s dilemma game the highest outcome for both players is reached.

2. Assume that two big communication companies (Secchat and Safetalk) are thinking about developing an innovative chat system for smartphones. Both companies can either develop the new technology or not. Given the dynamics and characteristics of the market, there is only room for one new chat system.
The payoffs would look like this:
How many Nash Equilibria are in this one periodic game?
• 0
• 2
• 4
• 1
• 3

3. Your business intelligence department realizes that they made a mistake in calculating the expected payoffs. Instead, they expect payoffs as shown in the game matrix below. They are not sure about what payoffs Pepsi and Cola can receive if they both do not advertise.

What payoffs would they have to receive in order to turn this game into a prisoners’ dilemma?

• 100 < X < 200
• 50 < X < 100
• X > 20
• X < −25

4. How many dominated strategies are in this game?

• 1
• 5
• 3
• 2
• 4
• none

5. Pepsi and Cola consider starting an advertising campaign. Both can either advertise or not advertise. If both decide to advertise each company gets a payoff of 50 mn Euro. If they don’t advertise, each gets a payoff of 70 mn Euro. If Cola advertises and Pepsi doesn’t, Cola gets a payoff of 100 mn Euro, whilst Pepsi makes losses of 50 mn Euros – and vice versa.

If you were responsible for marketing at Coca Cola, would you launch the advertising campaign?

(Consider this as a single stage game, in which all players act rationally.)
• Yes.
• No.

Practice Quiz: Sequential Games

1.Under which circumstances would Adam’s Pizza decide against a marketing campaign?
• x = € 1mn
• x = € 2mn
• x = € 4mn
• x = € 6mn
• x = € 7mn

2. A well-known cinema in town has offered Adam’s Pizza (A) to make advertisement on their tickets. If Adam’s Pizza declines the offer, they will approach A’s competitor Big Pizza (B) with the same offer. On the tickets, there is only space for one advertisement campaign. The actions and the corresponding payoffs are shown in the game tree below.
What is the Nash Equilibrium in this game?

• A: marketing / B: status quo
• A: no marketing / B: marketing
• A: no marketing / B: no marketing
• There is no Nash Equilibrium.

3. Which of the following statements are correct?
• Chess is an example for a sequential game.
• In a sequential game the first player can anticipate the reaction of the second player. This can be considered a first-mover advantage.
• Sequential games and simultaneous games have the same rules.
• In sequential games, threats are always credible.
• Threats always change the outcome of the game.
• Sequential games can be solved using backward induction or forward induction.

4. Let’s get back to the 1970’s: At this time, Intel is the only supplier of computer chips to IBM. At the same time, IBM is exploring the possibility of decreasing this dependency and producing computer chips on its own. In order to prevent IBM from doing so, Intel promises to decrease its price.

IBM can choose first between continuing to purchase computer chips from Intel and producing them in an own subsidiary. After that, Intel can choose whether to set a low price or a high price. If IBM opens its own subsidiary, IBM receives 40mn USD and Intel gets a payoff of 30mn USD. If IBM keeps Intel as its supplier and Intel sets a high price, then IBM gets a payoff of 10mn USD and Intel makes 90mn USD. In the case of low prices, IBM and Intel receive 50mn USD each.

Imagine you are the purchasing director of IBM. Would you open your own subsidiary producing computer chips?
• No.
• Yes.

5. Imagine now that Intel invests in a new production facility that increases its production capacity significantly. In order to utilize their capacity, Intel has to sell high quantities to set low prices. With charging high prices, Intel would now realize a payoff of 30mn USD (given that IBM doesn’t open an own subsidiary).

As the purchasing director of IBM, would you now open your own subsidiary for computer chips?
• No.
• Yes.

Quiz: Take Care of Your Competitors

1.Can a Nash Equilibrium contain dominated strategies?
• Yes
• No

2. Should Mars opt for the product placement in this game?
• Yes
• No

3. Can a game contain several Nash Equilibria?
• Yes
• No

4. You are the owner of the hair salon City Cuts.

Which price strategy would you choose given the payoffs in the matrix below? (You want to end up in a Nash Equilibrium.)
• Low Price
• High Price

5. Simultaneous games can be solved with the help of a ______.

• matrix
• game tree
• system of equations
• verbal expression

6. How many Nash Equilibria exist in this game? Please note that we only consider equilibria in pure strategies as discussed in the course.
• 0
• 1
• 2
• 3

7.Which values can be plugged in for x so that the game turns into a
prisoners’ dilemma?

• 2 < x < 5
• 4 < x < 5
• 1 < x < 3
• 2 < x < 6

8. What is a strategy according to the working definition of this course?
• The best alternatives a player has.
• The behaviour of a firm in a certain setting.
• A set of rules a player can choose from.
• A player’s plan of actions in a game.

9. British Airways is the monopolist for domestic flights in the United Kingdom. Lufthansa wants to enter the market. British Airways threatens Lufthansa to start a price war if they enter.
Is this a credible threat ?
• No
• Yes

10. Identify the dominated strategy in the following game:
• Sensodyne – Do not advertise
• Colgate – Do not advertise

Practice Quiz: Reasons for Cooperation

1. Through which mechanisms can cooperation between companies be achieved?

• Entry deterrence
• Bullying
• Commitment
• Repeated games

2.Have a look at the game matrix below. Could some kind of cooperation improve the outcome of this game?
• Yes.
• No.

3.Imagine a price setting game like in the game matrix below.
Which of the following statements is true?
• The two companies are suffering from a Prisoner’s Dilemma.
• Both companies set a low price because this is the best outcome for both of them.
• It would be best for both companies if they could commit to an outcome where one firm chooses a high price and the other firm chooses a low price.
• Both companies cannot coordinate on one Nash Equilibrium.

Practice Quiz: Finite Repetition

1. Which of the following statements is true?
• Repeated games are the only way to achieve cooperative behavior.
• In finite games it is clear from the beginning how often the game is repeated and when it ends.
• In repeated games interactions between competitors always take place in endless patterns.
• Backward induction is used to analyze repeated games with infinite repetitions.

2. If the outcome of a game is determined by the fact that in the last stage of the game there is no further threat of retaliation, this is called ___________ effect.
• equilibrium
• first- mover
• funnel
• sausage
• end-game

3. Imagine SausageKing and Hotdog-Master run hot dog stalls at the stadium of the football world championships. Both stalls exactly know that they can only sell sausages during the five weeks of the championships. After that, they have to leave the site. Mondays at 8am, they can set their prices for the coming week. The possible actions and related payoffs are as follows:

What prices will the two stalls set on the first Monday of the championships?

• SausageKing sets a Low Price and Hotdog-Master sets a High Price.
• Both set a Low Price.
• Hotdog-Master sets a Low Price and SausageKing sets a High Price.
• Both set a High Price.

4. Which of these statements are true for a game with finite repetitions?
• The players do not play a dominant strategy.
• The outcome is always the same as for a game with infinite repetitions.
• There is no endgame effect.
• In each period of the game, the equilibrium outcome is the same.
• Honor Code Agreement

Practice Quiz: Infinite Repetition

1. Which of the following factors enhance cooperation?
• The customers are heterogeneous in their preferences.
• The punishment for incorporative behavior is small.
• The number of competitors is small.
• Future payoffs are highly valued.

2. Let’s assume Saudi Arabia and Venezuela control the market for oil. Each country has enough resources and production capacity to supply the whole demand in the market. At the end of each year, the countries decide simultaneously about the prices they will charge in the following year. With probability p, the countries stay in the market and the game goes on.

If both countries charge the monopoly price the market is shared equally and the overall profit is 80mn USD. If one country charges a slightly lower price, it will serve the whole market and make profits of 60mn USD. If both countries charge a low price this will end in fierce competition and both countries will make zero profits.

The companies agreed on charging monopoly prices and punish deviation with setting a low price for all future periods.

Cooperation is achieved if…
• p<1/4
• p>1/3
• p>1/4
• p<1/3

3.Assume that there are two skis manufacturers. Every year at Christmas, they think about launching an advertising campaign. Because both companies have been in the market for quite a while and intend to stay in the market, this can be treated as a game with infinite repetitions. The possible actions of the companies and the related payoffs are as follows:
What could be a good strategy to sustain cooperation in the market?
• Flip a coin and advertise accordingly.
• Don’t advertise as long as the other manufacturer doesn’t advertise. If the other manufacturer advertises once, advertise in all future Christmas seasons.
• Choose always the action that the other company wasn’t doing in the previous period.
• Advertise at each Christmas season, no matter what the other manufacturer is doing.

4. Sweet Retreat and Flour & Faith sell cupcakes around the main university building in Los Angeles. One day, the two owners meet in secret and agree to coordinate their prices.

Their cupcake price cartel is more stable if…
• …more cupcake stores open in the area.
• …the banks charge less for credits.
• …the price for flour and other ingredients goes down.