Example 1: Alice and Bob and both necessary to produce something which has value 1500. Alice is player 1, Bob is player 2.
Example 2: Alice and Bob are each individually responsible for two different projects, each of which has value 1000. Alice is player 1, Bob is player 2.
Example 3: Newton and Leibniz invented calculus at the same time. It has a value of 100, in arbitrary units. Assumption: Nobody else could have invented calculus. Newton is player 1, Leibniz is player 2
Example 4: Netwon invented Calculus. Leibniz, mad with envy, pretended that he also invented calculus at the same time. Newton is player 1. Lebniz is player 2.
Example 5: Suppose that the Against Malaria Foundation (AMF) will spend $1M on a malaria net distribution. As a result of AMF's commitment, the Gates Foundation contributes $400,000. If AMF had not acted, Gates would have spent the $400,000 on something else, half as valuable. AMF is player 1, Gates is player 2.
Example 6: Suppose again that AMF commits $1m to a net distribution. But if AMF had put nothing in, DFID would instead have committed $500,000 to the net distribution. Now, DFID commits that money to something half as valuable. AMF is player 1, DFID is player 2.
Example 7: 7 people boil a goat in their mother's milk, independently and at the same time. According to the Kabbalah, this has terrible implications: -1000 value is lost. Suppose that all the damage is done once the first deed is done.
Example 8: Suppose that there was a position in an EA org, for which there were 6 qualified applicants which are otherwise 'idle'. In arbitrary units, the person in that position in that organization can produce an impact of 100 utility. Applicants are players 1-6, the organization is player 7.
Example 9: A small Indian state with 10 million inhabitants spends $60 million to vaccinate 30% of their population. An NGO which would otherwise be doing something really ineffective, comes in, and by sending reminders, increases the vaccination rate to 35%. They do this very cheaply, for $100,000. The government is player 1, the indian state is player 2. What if, instead, the NGO would have done something equally valuable?
Example 10 1: Same as Example 9, but now there are 6 government subagencies, each of which we consider as a distinct agent. The NGO is player 1, government agencies are players 2-7.
Example 11: An organization organizes a costless online vote to pass a measure of value 1, and it passes if it gets more than 3 votes. 7 people vote in favour