ECON 1001

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# ECON 1001 - PowerPoint PPT Presentation

ECON 1001. Tutorial 10. Q1) A dominant strategy occurs when One player has a strategy that yields the highest payoff independent of the other player’s choice. Both players have a strategy that yields the highest payoff independent of the other’s choice. Both players make the same choice.

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### ECON 1001

Tutorial 10

Q1) A dominant strategy occurs when
• One player has a strategy that yields the highest payoff independent of the other player’s choice.
• Both players have a strategy that yields the highest payoff independent of the other’s choice.
• Both players make the same choice.
• The payoff to a strategy depends on the choice made by the other player.
• Each player has a single strategy.

Ans: A

Let’s illustrate this by an example:
• Player 1’s dominant strategy is {Top}, because it gives him a higher payoff than {Bottom}, no matter what Player 2 chooses.
• Player 2’s dominant strategy is {Right}.
Therefore, a dominant strategy is a strategy that yields the highest payoff compared to other available strategies, no matter what the other player’s choice is.
• A rational player will always choose to play his dominant strategy (if there is any in the game), because this maximises his payoff.
• The other strategy available to the player that yield a payoff strictly smaller than that of the dominant strategy is called a ‘dominated strategy’ (e.g. Player 2’s [Left})
• Dominant strategies may not exist in all games. It all depends on the payoff matrix.
Q2) The prisoner’s dilemma refers to games where
• Neither player has a dominant strategy.
• One player has a dominant strategy and the other does not.
• Both players have a dominant strategy.
• Both players have a dominant strategy which results in the largest possible payoff.
• Both players have a dominant strategy which results in a lower payoff than their dominated strategies.

Ans: E

The prisoner’s dilemma is a coordination game.
• Both players have a dominant strategy, but the result of which is a lower payoff than the dominated strategies.

P

Q3) MC for both Firms M and N is 0. If Firms M and N decide to collude and work as a pure monopolist, what will M’s econ profit be?

• \$0
• \$50
• \$100
• \$150
• \$200

Ans: C

Demand

Q

P

• The monopolist maximises profit by producing a quantity where MC = MR, and set the price according to the willingness to pay (Demand)
• The profit-max output level is 100, and the profit will be \$200.
• Since each firm is halving the quantity, they each earns an econ profit of \$100.

Demand

\$2

100

Q

P

Q4) If Firm M cheats on N and reduces its price to \$1. How many units will Firm N sell?

• 200
• 150
• 100
• 50
• 0

Ans: E

Demand

\$2

100

Q

P

• If Firm M cheats and charges \$1/unit, the quantity demanded by the market would be 150.
• At this point, M is charging \$1 and N is charging \$2 for the same product.
• All customers will buy from Firm M, and hence, Firm N will have no sales at all.
• Firm M is going to make a profit of \$150.

Demand

\$2

\$1

100

150

Q

P

• If Firm N is allowed to respond to Firm M’s cheating, it may lower is price to \$0.5/unit, the quantity demanded by the market would be 175.
• At this point, if M is charging \$1, all customers will buy from Firm N, and hence, Firm M will have no sales at all.
• Firm N is going to make a profit of \$75.
• … The story continues

Demand

\$2

\$1

100

150

Q

Let’s look at the payoff matrix to find out the N.E.
• {C, C} and {D, C} are the Nash Equilibria.
• Hence, there are 2 N.E. in this game.
• The N.E. is also known as pure strategy N.E., the adjective “pure strategy” is to distinguish it from the alternative of “mixed strategy” N.E. A mixed strategy N.E. is a N.E. in which players will randomly choose between two or more strategies with some probability.
Q6) By allowing for a timing element in this game, i.e., letting either Jordan or Lee buy a ticket first and then letting the other choose second, assuming rational players, the equilibrium is ? , based on ? .
• Still uncertain; who buys the 2nd ticket.
• Now determinant; who buys the 1st ticket.
• Now determinant; who buys the 2nd ticket.
• Still uncertain; who buys the 1st ticket.
• Now determinant; who is more cooperative.

Ans: B

• That means, one player moves first, and buys the first ticket.
• The other player observes any action taken (i.e. knows what ticket has been bought), and then makes his / her decision.
• Actions are not taken simultaneously anymore.
Whoever chooses an action can now predict how the other player is going to react.
• E.g. If Lee chooses {Comedy}, he can be sure that Jordan will choose {Comedy} as well, because this gives Jordan a higher payoff than picking {Documentary}.
• Therefore, the first mover has the advantage (called First Mover Advantage) to take actions first, hence securing his or her own payoff by predicting the response from the other player.
A rational (self-interested) player will always pick the action that maximises his or her own payoff (irregardless of others’)
• Hence, if Lee is to move first, he will pick {Documentary}, because {D, D} gives him the highest possible payoff.
• If Jordan is to move first, she will pick {Comedy}, because {C, C} gives her the highest possible payoff.
• Therefore, the result is now determinant, as soon as we know who is buying the 1st ticket.
Q7) Suppose Candidate X is running against Candidate Y. If Candidate Z enters the race,
• Approximately half of the voters who were going to vote for X will now vote for Z.
• Fewer than half of the voters who were going to vote for Y will now vote for Z.
• All of the voters who were going to vote for Y will now vote for Z.
• Most of the voters who were going to vote for Y will now vote for Z.
• X will certainly win because Y and Z compete for the same voters.

Ans: D

Originally, before Z joins the election,
• Assuming voters in between 2 candidates are shared equally.
• Area covered in RED are voters voting for X.
• Area covered in BLUE are voters voting for Y

0

25

50

75

100

X

Y

• All voters in the green area used to vote for Y.
• Hence, (D) is the answer.

0

25

50

75

100

X

Y

Z

Q8) A commitment problem exists when
• Players cannot make credible threats or promises.
• Players cannot make threats.
• There is a Prisoner’s Dilemma.
• Players cannot make promises.
• Players are playing games in which timing does not matter.

Ans: A

In games like the prisoner’s dilemma, players have trouble arriving at the better outcomes for both players…. Because
• Both players are unable to make credible commitments that they will choose a strategy that will ensue a better outcomes for both players (either in the form of credible threats or credible promises)
• This is known as the commitment problem.
Q9) Suppose Dean promises Matthew that he will always select the upper branch of either Y or Z. If Matthew believes Dean and Dean does in fact keep his promise, the outcome of the game is
• Unpredictable.
• Matthew and Dean both get \$1,000.
• Matthew gets \$500; Dean gets \$1,500.
• Matthew gets \$1.5m; Dean gets \$1m.
• Matthew gets \$400; Dean gets \$1.5m.

Ans: D

If Dean will indeed goes for the upper branch, then Matthew can either earn \$1,000 by choosing the upper branch (i.e., arriving the node Y), or \$1.5m by picking the lower branch (i.e., arriving the node Z).
• As Matthew is a rational individual, he will choose a lower branch (i.e., arriving the node Z).

(1000, 1000)

Dean

Y

(500, 1500)

X

Matthew

*

(1.5m, 1m)

Z

Dean

(400, 1.5m)

Q10) Suppose Dean promises Matthew that he will always select the upper branch of either Y or Z. Dean offers to sign a legally binding contract that penalises him if he fails to choose the upper branch of Y or Z. For the contract to make Dean’s promise credible, the value of the penalty must be
• Any positive number.
• More than \$1.5m.
• Less that \$100.
• More than \$0.5m.
• More than \$500.

Ans: D

If Dean will indeed goes for the upper branch, then Matthew is better off picking the lower branch (i.e., arriving at node Z), because he can then have a payoff of \$1.5m (compared to \$1000 from the upper branch, i.e. arriving at node Y)
• As Matthew picks the lower branch (i.e., arriving at node Z), there is a tendency for Dean to the lower branch (i.e., arriving the payoff of (400 for Matthew and 1.5m for Dean) -- for a higher payoff (compared with 1m for Dean).
• The penalty of breaching the promise should then be at least \$0.5m (say \$0.6m). The penalty will reduce the payoff to Dean (becomes 1.5-0.6 = 0.9) when Dean chooses the lower branch at node Z. Thus, Dean will choose the upper branch at node Z.

(1000, 1000)

Dean

Y

(500, 1500)

X

Matthew

*

(1.5m, 1m)

Z

Dean

(400, 0.9m)