Payoff Calculation in the Irrigation Game with Two Other Contributors

Kim's Dominant Strategy in the Irrigation Game: Not to Contribute

Figure 4.9: Kim's Payoffs in the Irrigation Game

Payoff from Full Cooperation in the Irrigation Game

Four farmers are deciding whether to contribute to a shared irrigation project. For each farmer who contributes, all four farmers (including non-contributors) receive an $8 benefit. The personal cost for an individual to contribute is $10. Suppose you are one of the farmers, and you know that exactly two of the other three farmers have decided to contribute. Analyze your two possible outcomes: what is your final payoff if you decide to contribute, versus if you decide not to contribute?

Payoff Calculation Error Analysis

A game involves four farmers deciding whether to contribute to a shared irrigation project. The personal cost to contribute is $10. For every single farmer who contributes, all four farmers (including any who did not contribute) receive an $8 benefit. True or False: Holding the actions of the other three farmers constant, an individual farmer's net payoff is always exactly $2 lower if they choose to contribute than if they choose not to contribute.

Deducing Contributions from Payoffs

Individual vs. Group Outcomes in a Public Project

In a public project scenario involving four participants, the personal cost to contribute is $10. For every individual who contributes, all four participants (including non-contributors) receive a benefit of $8. If a particular participant decides to contribute, and a total of three participants (including them) end up contributing, that participant's final net payoff is $____.

A scenario involves four farmers deciding on a shared project. Contributing costs a farmer $10. For each contribution made (by any farmer), all four farmers receive an $8 benefit. Consider the perspective of one specific farmer who has decided NOT to contribute. Arrange the following scenarios in descending order, from the one that results in the highest payoff for this non-contributing farmer to the one that results in the lowest payoff.

Advising a Farmer on Project Contribution

In a collaborative project, four participants can each choose to contribute. A contribution costs the individual $10. For every contribution made by any participant, all four participants (including non-contributors) each receive an $8 benefit. From the perspective of a single participant, what is the minimum number of other participants who must contribute for that single participant's own decision to contribute to result in a positive net payoff (i.e., a payoff greater than $0)?