omewor ue July 4th at 4:45pm on Assignment 1) An old lady is looking for help cr
ID: 1163820 • Letter: O
Question
omewor ue July 4th at 4:45pm on Assignment 1) An old lady is looking for help crossing the street. Only one person is needed to help her, if more people help her, this is no better. You and I are the two people in the vicinity who can help: we have to choose simultaneously whether to do so. Each of us will get pleasure worth a 3 from her success (no matter who helps her). But each one who goes to help will bear a cost of 1, this being the value of our time taken up in helping. If neither player helps, the payoff for each player is zero. Set this up as a game. Write the payoff table, and find all pure- strategy Nash equilibria. 2) In each of the following games, how many pure strategies (complete plans of action) are available to each player?List out all of the pure strategies for each player (al SCARECHOWSCARECROWs TINMAN TINMAN 3,2 TINMAN,1, N 2,3 SCARECROW0,0,2 3.3 N 1,24 LIONExplanation / Answer
ans:
the payoff table will look like this:
ME
HELP DO NOT HELP
HELP (3-1 , 3-1) (3-1, 0)
YOU DO NOT HELP (0, 3-1) (0,0)
the one who help will get a payoff of 3 less a cost of 1 and the one who do not help will get a 0 payoff.
finding pure strategy nash equilibrium:
when I choose to help , your payoff will be max when you also choose to help (as 3-1 >0), when I choose not to help then your payoff will be max when you choose help (as 3-1 >0) . thus we underline both 3-1 payoff of your's.
now, when you choose to help my payoff will be max when I also choose to help( as 3-1 >0) hence we underline my 3-1 payoff; now when you choose not tohelp my payoff will be max when I choose to help ( as 3-1 >0). hence, again we underline my 3-1 payoff.
after this which ever cell gets two underline is considered to be the nash equilibrium. here, (help, help ) strategy is the pure strategy nash equilibrium.
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