You and a friend are spending two days in the woods; you both enjoy hiking. HOWEVER, each of you believes with probability π a bear in the woods may have ingested a brick of cocaine.If a bear is high on cocaine, anyone hiking will surely be attacked. Each of you receives −c for being attacked by a bear on blow, 0 to staying at your cabin, and 1 for a day’s worth of hiking (c > 0).If either of you is attacked by the cocaine bear on the first day, then you both know the cocaine bear exists and whoever hikes will surely be attacked on the second day, and hence no one will hike, receiving 0.If at least one person hikes and is not attacked on the first day then you know the forest is safe for sure and will hike on the 2nd day, earning 1.If neither of you hike, then on the second day you have the same belief as the first (π), and hike if and only if −πc + 1 − π ≥ 0 (i.e., your expected utility from hiking is higher than not hiking).(HINT: you need to consider both the case where −πc+1−π ≥ 0 and where −πc+1−π ≤ 0. It will be easiest to model as a grid twice).You will be considering ONLY what your decision on the first day will be, knowing that (as described above) it will affect your decision on the second day. Make sure when modeling to consider the utility of both. In otherwords, use the actions in period 1 to find the expected utility in BOTH periods, then put the sum of those expected utiltiies together in the 2x2 grid.1. (10 pts) Model this situation as a normal form game in which you and your friend decide to hike or not on the first day.
You and a friend are spending two days in the woods; you both enjoy hiking. HOWEVER, each of you believes with probability π a bear in the woods may have ingested a brick of cocaine.
If a bear is high on cocaine, anyone hiking will surely be attacked. Each of you receives −c for being attacked by a bear on blow, 0 to staying at your cabin, and 1 for a day’s worth of hiking (c > 0).
If either of you is attacked by the cocaine bear on the first day, then you both know the cocaine bear exists and whoever hikes will surely be attacked on the second day, and hence no one will hike, receiving 0.
If at least one person hikes and is not attacked on the first day then you know the forest is safe for sure and will hike on the 2nd day, earning 1.
If neither of you hike, then on the second day you have the same belief as the first (π), and hike if and only if −πc + 1 − π ≥ 0 (i.e., your expected utility from hiking is higher than not hiking).
(HINT: you need to consider both the case where −πc+1−π ≥ 0 and where −πc+1−π ≤ 0. It will be easiest to model as a grid twice).
You will be considering ONLY what your decision on the first day will be, knowing that (as described above) it will affect your decision on the second day. Make sure when modeling to consider the utility of both. In otherwords, use the actions in period 1 to find the expected utility in BOTH periods, then put the sum of those expected utiltiies together in the 2x2 grid.
1. (10 pts) Model this situation as a normal form game in which you and your friend decide to hike or not on the first day.
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