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}. 2 1 Left Right Top (100, 30) (80, 90) Bottom (60, 60) (70, 100)

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. 2 1 Confess Deny (-3, -3)* (0, -6) (-6, 0) (-1, -1)

Q3). MC for both Firms M and N is 0 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 P Demand Q

The profit-max output level is 100, and the profit will be $200. 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. P Demand $2 100 Q

Q4). If Firm M cheats on N and reduces its price to $1 Q4) If Firm M cheats on N and reduces its price to $1. How many units will Firm N sell? 200 150 100 50 Ans: E P Demand $2 100 Q

Firm M is going to make a profit of $150. 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. P Demand $2 $1 100 150 Q

Firm N is going to make a profit of $75. 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 P Demand $2 $1 100 150 Q

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

Jordan Lee Comedy Documentary (3, 5) (1, 1) (2, 2) (5, 3) 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. Jordan Lee Comedy Documentary (3, 5) (1, 1) (2, 2) (5, 3)

Q6). By allowing for a timing element in this game, i. e 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

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.

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 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 25 50 75 100 X Y

All voters in the green area used to vote for Y. 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. 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

This is known as the commitment problem. 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 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)