Show that in a finite strategic form game. the set of strategies surviving iterative weak dominance is non-empty

Show that in a finite strategic form game. the set of strategies surviving iterative weak dominance is non-empty

 

 

answer:

1. In a finite game a set of strategies that survive iterated elimination of strictly dominated strategies is a Nash Equilibrium. Also a Nash equilibrium will always survive iterated elimination of strictly dominated strategies.

2. a. There are no strictly dominat strategy for either player. Country 2 has a weakly dominant strategy however that is to “Spy”.

b. Yes, Country 2 has a weakly dominant strategy that is to “Spy” as it has payoffs of 1>-1 and 2=2 for the two possible outcomes for Player 1.

c. There is one Nash equilibrium in pure strategies that is given by (Destroy,Spy) with payoffs of (0.2) respectively.

3. a. There are 2 Nash equilibria that are (U,L) and (D,R). However there is one one based on pure strategies that is given by (U,L).

b. Here there are three Nash equlibria that are (U,L),( D,L) and (U,R). These are all not based on weakly dominated strategies.

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