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GAME THEORY detailed answer is needed There are five families living in the same building. They will try to collect funds to build a swimming

GAME THEORY detailed answer is needed
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There are five families living in the same building. They will try to collect funds to build a swimming pool in front of their building. If built, it can be used by anyone living in the building, so each family will derive some utility (captured by their "valuations). However, each family has different valuations for the swimming pool. Those valuations are listed in the table below: Family 1 Family 2 Family 3 Family 4 Family 5 30 $ 40 $ 50 $ 60 $ 70 $ The valuations are common knowledge, i.e., each family knows how much value other families attach to the swimming pool. The protocol for collecting money and building the pool is as follows: Today, each family simultaneously transfers some money into a bank account. Tomorrow, they will check whether the collected money is sufficient to build a swimming pool, which costs 100$. If sufficient, the swimming pool will be built right away, but if there is some excess money left in the account, it will disappear (i.e., no refunds). If it is not sufficient, the swimming pool cannot be built, and all the collected money will disappear (ie, no refunds), Note that each family only cares about the swimming pool (whether it is built or not) and the amount of money they have transferred. They do not care about anything else. This strategic interaction can be modeled as a normal form game. Find its set of Nash equilibria. Show your work and explain it clearly. There are five families living in the same building. They will try to collect funds to build a swimming pool in front of their building. If built, it can be used by anyone living in the building, so each family will derive some utility (captured by their "valuations). However, each family has different valuations for the swimming pool. Those valuations are listed in the table below: Family 1 Family 2 Family 3 Family 4 Family 5 30 $ 40 $ 50 $ 60 $ 70 $ The valuations are common knowledge, i.e., each family knows how much value other families attach to the swimming pool. The protocol for collecting money and building the pool is as follows: Today, each family simultaneously transfers some money into a bank account. Tomorrow, they will check whether the collected money is sufficient to build a swimming pool, which costs 100$. If sufficient, the swimming pool will be built right away, but if there is some excess money left in the account, it will disappear (i.e., no refunds). If it is not sufficient, the swimming pool cannot be built, and all the collected money will disappear (ie, no refunds), Note that each family only cares about the swimming pool (whether it is built or not) and the amount of money they have transferred. They do not care about anything else. This strategic interaction can be modeled as a normal form game. Find its set of Nash equilibria. Show your work and explain it clearly

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