Dictat 2.6 Part 6 17. The payoff function for player i depends on player i's contribution and the contributions of the others in player i's group. I=e-atmx =4 -ri +m(r + + 13 + I.) Where e, is the initial endowment of tokens held by player i, T, is player i's contribution, m is the share of the group contributions that each player receives and _,, is the sum of all contributions by each of the players in the group. treatments are referred to as 'experiments' in Herrmann, Thoni, and Gachter (2008). Suppose you have a group of / = 4 players, each player has an initial endowment of 20, and m = 0.25 (contri- butions are shared equally among all members of the group). Show that if all other players contribute their entire endowment, player i's optimal decision is to contribute nothing (to 'free-ride'). Hint: Compare the payoff when player i contributes the full endowment to the payoff when player i contributes nothing. Also show the impact of player i's decision on the other group members by comparing their payoffs when player i free rides and when player : contributes their full endowment