An old man is looking for help to cross the street. Only one person is needed to help him; two persons can help him, but the help is not of any higher quality. Two friends, who are on the same path, are the only people who can help him and they both decide simultaneously if whether they do help him or not. Each one obtains three units of utility if the old man receives help (regardless of who helped him). However, if one of them does decide to help him, he incurs a cost that's equal to one unit of utility, resulting from the time spent provided on giving aid.
a. Write the payoff matrix associated with this strategic interaction situation.
b. Find the Pareto optimal (more than one might exist)
c. Find all pure-strategy Nash equilibria (if any).