Two farmers, Joe and Giles, graze their animals on a common land. They can choose to use the common resource lightly or heavily and the resulting strategic interaction may be described as a simultaneous-move game. GILES light heavy JOE light 40, 40 20, 55 heavy 55, 20 30, 30 The payoff matrix is the following: Joe Giles light heavy light 40, 40 20, 55 heavy 55, 20 30, 30 1. Find the Nash equilibrium of the game and show that it is an example of "Prisoners' Dilemma" games. 2. Suppose that the same game is repeated infinitely. Is the {light, light} outcome a Nash equilibrium if both players play a Grim strategy and have a discount factor of 0.7? Distinguish simultaneous-move games and dynamic games in terms of information. Explain why in dynamic games Nash equilibria may not be subgame perfect. Using examples, show how non-credible threats are ruled out using backward induction.
Two farmers, Joe and Giles, graze their animals on a common land. They can choose to use the common resource lightly or heavily and the resulting strategic interaction may be described as a simultaneous-move game.
| GILES | |||
| light | heavy | ||
| JOE | light | 40, 40 | 20, 55 |
| heavy | 55, 20 | 30, 30 |
The payoff matrix is the following: Joe Giles light heavy light 40, 40 20, 55 heavy 55, 20 30, 30
1. Find the Nash equilibrium of the game and show that it is an example of "Prisoners' Dilemma" games.
2. Suppose that the same game is repeated infinitely. Is the {light, light} outcome a Nash equilibrium if both players play a Grim strategy and have a discount factor of 0.7?
Distinguish simultaneous-move games and dynamic games in terms of information. Explain why in dynamic games Nash equilibria may not be subgame perfect. Using examples, show how non-credible threats are ruled out using backward induction.
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