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John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush
John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. if one of them runs away and the other fights, then the one who ran will get away unharmed (Payoff being 0) while the one who fights will be killed (Payoff being -100). If they both run, then the bear will chase down one of them and eat them, but the other one will get away unharmed. Assuming they don't know which one will escape, we will call this payoff -50 for both. If they both fight then they will successfully drive off the bear but they may be injured in the process (-10.)
Construct a payoff matrix for the game and identify pure strategy Nash equilibrium. (Indicate in words, do not draw a circle.)
Expert Solution
Pure strategy Nash equilibrium is (Run away, Run away)
Here both have a dominant strategy of Run away
When Paul runs away, John will have a higher payoff of -50 by running away. When Paul fights, John still has a higher payoff of 0 in running away. The same is true for Paul as well. Hence both have dominant strategies of running away
| Paul | |||
| Run away | Fight | ||
| John | Run away | (-50, -50) | (0, -100) |
| Fight | (-100, 0) | (-10, -10) | |
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