Question

Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.

Answer 1

Important Note: If the payoff is (A,B) then player 1's payoff is A and playes 2's payoff is B.

Dominant Strategy means the strategy which produces a higher payoff than any other strategy the player can use for every possible combination of its rivals' strategies.

Player 1 has a dominant strategy. Answer is "True".

Because if the player 1 moves first and chooses strategy U,player 2 will have to choose strategy L.(Since player 2 can get better payoff than to choose the strategy R).

Normally it is assumed that player 1 moves first.But if the player 2 moves first, the result will be different in this case.If the player 2 moves first  then the player 2 have a dominant strategy.

Nash Equilibrium are the set of strategies such that when all other players use these strategies,no player can obtain a higher payoff of choosing a different strategy.

This game has two Nash equilibria in pure strategies.Answer is "True". Both nash equlibria payoffs are (30,20) and (20,30).

If the player 1 moves first and chooses strategy U,player 2 will have to choose strategy L.(Since player 2 will get negative payoff if he chooses the strategy R).Then the payoff will be (30,20).

If the player 2 moves first and chooses strategy R,player 1 will have to choose strategy D.(Since player 1 will get negative payoff if he chooses the strategy U).Then the payoff will be (20,30).

Player 1's payoff in each nash equlibria is 30.Answer is "False". Both Payoffs in nash equlibria are (30,20) and (20,30).Hence here we can clearly see that Player 1's payoff is 30 and 20.