EBK MICROECONOMICS
2nd Edition
ISBN: 8220103679701
Author: List
Publisher: YUZU
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Question
Chapter 13, Problem 11P
To determine
The equilibrium using backward induction in the “centipede game”.
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Consider the following sequential strategic situation, called the centipede game. The game has 100 stages. Two players take turns making decisions, starting with player 1. At stage t = 1,...,99, player 1 (if the stage is odd) or player 2 (if the stage if even) chooses whether to "Terminate the game" or to "Continue the game." If the game is terminated instage t = 1,...,99, the player terminating the game receives a payoff of t, while the other player receives a payoff of zero. Finally, at stage t = 100, player 2 chooses between action A with a payoff of 99 for each player, or action B with a payoff of zero for player 1 and a payoff of 100 for player 2. Draw the game tree for this situation. What is the SPNE?
A payoff matrix is shown below. With the payoffs in each field indicated in the form (Player 1’s payoff, Player 2’s payoff).
Player 2
Left
Right
Player 1
Up
($1, $1)
($2, $4)
Down
($7, $8)
($3, $3)
Which of the following is true?
The only Nash Equilibrium is Player 1 playing ‘Up’ and Player 2 playing ‘Right’.
The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Left’.
The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Right’.
None of the other answers provided are true.
The London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing.
consider James as ‘row player’ and Robert as ‘column player).
a) Model the situation as a strategic game, assuming both ‘James’ and ‘Robert’ care only about their own comfort. Find the Nash equilibrium (equilibria) if it exists. Also, does a dominant strategy exist for either ‘James’ or ‘Robert’? show ALL steps and working in support to the answer
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