Consider the following strategic game with complete information. Set of players is $N = \{1, . . . , n\}$, where $n ≥ 2$. Each player $i ∈ N$ chooses action $a$ $i ∈ \{0, 1\}$. Payoff of each $i ∈ N$ from action profile $ (a_i)_{i∈N}$ is $\sum_{ j∈N} a_j−c_ia_i,$ where $c_i > 0$ is a parameter. Assume $c_i$ is not an integer for each $i ∈ N$. The interpretation of the game is as follows. Each person in a society either takes an action that benefits everyone in the society but is costly for her, or not.
The solution it gives is as follows: Payoff of each $i ∈ N$ from action profile $ (a_i)_{i∈N}$ equals $\sum_{j∈N/\{i\}} a_j+(1-c_i)a_i,$ Hence there exists unique NE in which $a_i = 0$ for any player $i ∈ N$ with $1 − c_i < 0$ and $a_i = 1$ for any player $i∈ N$ with $1 − c_i > 0.$
But I'm not understanding where this payoff came from