An old man is looking for help crossing the street. Only one person is needed to help her; if more people help her, this

[answerhappygod]

An old man is looking for help crossing the street. Only one
person is needed to help her; if more people help her, this is no
better. Anna and Sam are the only two people in the vicinity who
can help the old man; and they have to choose simultaneously upon
their decision. Each of the two will get pleasure worth a 3 from
seeing the old man having crossed the street (no matter who helps
him). But each one who goes to help will bear a cost of 2, this
being the value of the time taken up in helping. If neither player
helps, the pay-off for each player is zero.
Suppose now, that the nature of the players has changed. Anna
has becomes extremely altruistic (is happy when she gets to help
others and sad when she cannot) while Sam has become selfish (is
happy when he does not have to help others and sad when he has to).
Anna gets pleasure worth a 3 if she gets to help the old man having
crossed the street and pleasure worth a 1 if she doesn’t. Sam, on
the other hand, gets a pleasure of 4 if he doesn’t help and no
pleasure if he gets to help the old man. Sam also gets extremely
angry if he and Anna both help the old man together and hence gets
a displeasure worth -1. If neither player helps, the pay-off for
Anna is zero and for Sam is 4.
d) How do the pay-off change? Set this
up as a new game and write the pay-off table.
e) What would the dominant strategies
for both players now be? In case there is none, explain why.
f) Find all equilibria for this game
and explain why it is an equilibrium.