Selfish Altruistic Individuality

Selfish altruistic individual, i_sa, mostly prefers u^ip, or sometimes indifferent for which c_i>0. Reciprocal altruistic individual, i_ra, is indifferent between u^ip and u^sp, and minimum or equal contribution of c_(-i) would made c_i positive where c_i depends on c_(-i), and changing with c_(-i). Warm-glow giver, i_wg, is similar as pure altruistic contributor but they are motivated by additional utility from ‘act of giving’ where u^ip essentially includes this undefined component.
To exhibit how the magnitude of μ and c affects the i’s payoff, we argue that following Prediction 1 can show the comparative statics with respect to μ based on Proposition 1.

Prediction 1. Under all equilibrium and non-equilibrium strategies, u_i nondecreasing