Consider a sequential-move game with two players. The game tree with order of payoffs (Player 1, Player 2) is provided above. Choose the answer that is consistent with it.

Question

BlackTom AI · Accepted Answer

To evaluate the options, we first interpret the game from the tree. If Player 1 plays U, Player 2 responds by choosing between L (payoffs -1 for Player 1, 2 for Player 2) and R (payoffs 2 for Player 1, -1 for Player 2). Hence, after U, Player 2 prefers L since 2 > -1 for them. If Player 1 plays D, Player 2 faces L (1 for Player 1, 0 for Player 2) and R (0 for Player 1, 1 for Player 2). Here, Player 2 prefers R since 1 > 0.

Now consider Player 1’s decision anticipating Player 2’s responses. If Player 1 chooses U, the subsequent equilibrium payoff to Player 1 is -1 (since Player 2 will pick L after U). If Player 1 chooses D, the subsequent equilibrium payoff to Player 1 is 0 (since Player 2 will pick R after D). Since 0 > -1, Player 1’s best move is D, given Player 2’s best responses.

With Player 1 choosing D, the consistent continuation for Player 2 is R after D (as established), and with Player 1 choosing U, the consistent continuation for Player 2 is L after U. Therefore, the strategy profile where Player 1 plays D, and Player 2 plays L after U and R after D is the one that aligns with backward induction and subgame perfection.

Option a: Proposes D for Player 1 and Player 2 responds R after U and L after D. This contradicts the best responses described: after U, Player 2 would choose L, not R, and after D, Player 2 would choose R, not L.

Option b: States there is no Nash Equilibrium. The game has a well-defined sequential structure with best responses in each subgame, so a Nash Equilibrium (indeed a subgame-perfect one) exists. This makes the statement incorrect.

Option c: Proposes D for Player 1 and Player 2 responds L after U and R after D. This matches the backward-induction-based reasoning: P2 picks L after U and R after D, and P1 prefers D given those responses. This option is consistent with the game’s equilibrium analysis.

Option d: Proposes U for Player 1 with P2 choosing L after U and R after D. While P2 would choose L after U, Player 1 would not choose U because D yields a higher anticipated payoff (0 vs -1). Hence this profile is not a best response for Player 1 and is inconsistent with equilibrium behavior.

In summary, evaluating each choice against the players’ best-response logic and the subgames, only the option describing Player 1 choosing D with Player 2 responding L after U and R after D aligns with the equilibrium reasoning.

SESS0007_24-25 LSA Test

Consider a sequential-move game with two players. The game tree with order of payoffs (Player 1, Player 2) is provided above. Choose the answer that is consistent with it.

View Explanation

Log in for full answers

Similar Questions

The advertising agency raises its prices, causing a firm that chooses to run ads to earn $200 less in profits. Once the firms adjust to the higher advertising prices, what is the total combined profit of the two firms in the new Nash equilibrium?

Consider a matrix form game between two players, A and B. Player A can choose between Up and Down, and Player B can choose between Left and Right. If the payoffs are represented using this matrix, what is the pure Nash equilibrium?

In the following duopoly game, the two firms can either set the price of their product high or low. For each firm, the final profit depends on the price they set as well as the price the other firm sets. The game is represented in the table below. The Nash equilibrium for this game is for:

Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the statement that is consistent with it.

Consider the payoff matrix below. Which is correct for the following payoff matrix? Player 2 A B C Player 1 A (3,2) (3,1) (2,2) B (1,3) (2,2) (0,2) C (5,1) (8,1) (1,7)

Which pure strategy profiles are Nash equilibria? Select all that apply.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler