Problem set #2
1) Consider the 2-player strategic game represented by the following payoff matrix. Player 1’s actions are denoted by T and B and player 2’s actions are denoted by L and R, respectively. Each cell shows the payoff outcomes for the respective pair of actions chosen by the two players. The first numbers in the cells give player 1’s payoffs and the second numbers give player 2’s payoffs.
|
Player 1 |
Player 2 | |||
| L | R | |||
| T | 8, 8 | 2, 7 | ||
| B | 7, 2 | 3, 3 | ||
Find all Nash equilibria in pure and mixed strategies of the game. Show them in a graph that depicts the best response functions of player 1 and player 2.
2) Consider the 2-player strategic game represented by the following payoff matrix. Player 1’s actions are denoted by T and B and player 2’s actions are denoted by L and R. Each cell shows the payoff outcomes for the respective pair of actions chosen by the two players. The first numbers in the cells give player 1’s payoffs and the second numbers give player 2’s payoffs.
|
Player 1 |
Player 2 | |||
| L | R | |||
| T | 0, 2 | 6, 6 | ||
| B | 4, 4 | 2, 3 | ||
Find all Nash equilibria in pure and mixed strategies of the strategic game and show them in a graph that depicts the best response functions of player 1 and player 2. Are these strict or weak Nash equilibria?
3) Consider the 2-player strategic game represented by the following payoff matrix. Player 1’s actions are denoted by T and M, and player 2’s actions are denoted by L and R, respectively. Each cell shows the payoff outcomes for the respective pair of actions chosen by the two players. The first numbers in the cells give player 1’s payoffs and the second numbers give player 2’s payoffs.
|
Player 1 |
Player 2 | |||
| L | R | |||
| T | 2, 0 | 4, 2 | ||
| M | 3, 4 | 2, 3 | ||
Find all Nash equilibria in pure and mixed strategies of the game. Show them in a graph that depicts the best response functions of player 1 and player 2.
4) What is the subgame perfect equilibrium of the following extensive game? The first numbers give player 1’s payoffs and the second numbers give player 2’s payoffs.
5) What is the subgame perfect equilibrium of the following extensive game? The first numbers give player 1’s payoffs and the second numbers give player 2’s payoffs
6) Consider an ambitious party member who decides on whether or not to challenge the party leader’s predictions about an important issue with uncertain outcomes (“nature” randomly determines whether the leader’s prediction is correct, C, or incorrect, I, where each outcome occurs with probability ½). If the challenger’s prediction turns out to be true, her reputation within the party will increase by 3. But if her prediction turns out to be wrong, her reputation will decrease by 3. Finally, if she does not challenge the leader her reputation remains unchanged.
|
Party member |
“Nature” | |||
| p(C)= ½ | p(I) = ½ | |||
| Challenge | -3 | 3 | ||
| Don’t challenge | 0 | 0 | ||
What are the expected payoffs of the ambitious party member for each of her actions ‘challenge’ and ‘don’t challenge’? Will she challenge the leader?
Problem+set+2
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The post 1) Consider the 2-player strategic game represented by the following payoff matrix. Player 1’s actions are denoted by T and B and player 2’s actions are denoted by L and R, respectively. Each cell shows the payoff outcomes for the respective pair of actions chosen by the two players. The first numbers in the cells give player 1’s payoffs and the second numbers give player 2’s payoffs. Player 1 Player 2 L R T 8, 8 2, 7 B 7, 2 3, 3 Find all Nash equilibria in pure and mixed strategies of the game. Show them in a graph that depicts the best response functions of player 1 and player 2. appeared first on Apax Researchers.