### Game Theory Decision Tree and Nash EquilibriumThe diagram displayed is a decision tree representing a two-player game. Each player has two choices: "Up" or "Down".**Player 1's Options:**- **Up:** - Both Player 1 and Player 2 receive $100 each.- **Down:** - Player 2 now has their own choice: - **Up:** - Player 1 receives $10, Player 2 receives $110. - **Down:** - Player 1 receives $65, Player 2 receives $10.**Question:**Given the game above, what is/are the sub-game perfect Nash equilibrium?**Answer Choices:**- (up, up)- (up, down)- (down, up)- (down, down)- No equilibrium existsThis setup illustrates the concept of sub-game perfect Nash equilibrium where the players make optimal decisions at every point in the game.

Backward induction is the process of solving a game from the end of a game. Subgame perfect Nash…

Up Down Player 1 Up Down Up Down Player 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No equilibrium exists P1 gets $100 P2 gets $100 P1 gets $10 P2 gets $110 P1 gets $15 P2 gets $15 P1 gets $65 P2 gets $10

Up Down Player 1 Up Down Up Down Player 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No equilibrium exists P1 gets $100 P2 gets $100 P1 gets $10 P2 gets $110 P1 gets $15 P2 gets $15 P1 gets $65 P2 gets $10

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

### Game Theory Decision Tree and Nash Equilibrium

The diagram displayed is a decision tree representing a two-player game. Each player has two choices: "Up" or "Down".

**Player 1's Options:**
- **Up:**
- Both Player 1 and Player 2 receive $100 each.
- **Down:**
- Player 2 now has their own choice:
- **Up:**
- Player 1 receives $10, Player 2 receives $110.
- **Down:**
- Player 1 receives $65, Player 2 receives $10.

**Question:**
Given the game above, what is/are the sub-game perfect Nash equilibrium?

**Answer Choices:**
- (up, up)
- (up, down)
- (down, up)
- (down, down)
- No equilibrium exists

This setup illustrates the concept of sub-game perfect Nash equilibrium where the players make optimal decisions at every point in the game.

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