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ECON 1001

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

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  1. ECON 1001 Tutorial 10

  2. 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

  3. 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}.

  4. 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.

  5. 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

  6. 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.

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. Q5) The game has ? Nash Equilibrium. • 0 • 1 • 2 • 3 • 4 Ans: C

  13. 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.

  14. 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

  15. By allowing a timing element, the game is now a sequential game. • 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.

  16. 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.

  17. 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.

  18. 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

  19. 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

  20. With Z joining the election, the area in green are voters voting for Z. • All voters in the green area used to vote for Y. • Hence, (D) is the answer. 0 25 50 75 100 X Y Z

  21. 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

  22. 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.

  23. 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

  24. 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)

  25. 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

  26. 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)

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