There are five people in a village. Each has $10. The village is prone to flooding. Flooding is reduced if people contribute to flood control efforts. In particular, each person in the village receives $0.50 of benefits when someone contributes $1 to flood control (flood control is a public good). So suppose, for example, each person contributes $4 to flood control. Total contributions will equal 5 × $4 = $20, each person will be left with $10 - $4 = $6 to purchase goods such as food and clothing, and each person will receive 0.5 × $20 = $10 in benefits from flood control. Everyone in the village makes their decision about contributions without talking to anyone else in the village.
a. Suppose people care only about their consumption of goods and their benefits from flood control. Show that contributing $0 is a dominant strategy.
b. Now suppose that each person cares about the total consumption of goods in the village and everyone’s benefits from flood control. Show that everyone in the village will contribute their entire $10 to flood control.