Question

Will Up Left Centre Right 2,8 0,9 4,3 3,7 -2,10 2,15 John Down Problem 2 Consider the following simultaneous game given above. 1. What is the set of strategies for each player? 2. Define dominant strategy. Is there a dominant strategy for John? Is there a dominant strategy for Will? Find all dominant strategy equilibria in this game. 3. Define Nash equilibrium. Find all Nash equilibria in this game. 4. Are dominant strategy equilibria always Nash equilibria? Are Nash equilibria always domi- nant strategy equilibria?

Answer 1

1) Strategy set of john

• SJ = { up, down}

• SW = { left, centre, right}

2) dominant strategy is the Strategy which a player selects always, irrespective of the action choice of other player .

Thus dominant Strategy always provides the highest playoff ,in comparison to all other strategies available, for any action

Choice of all other players

Payoff matrix :

John/ Will	left	Centre	Right
Up	(2,8)	(0*,9•)	(4*,3)
Down	(3*,7)	(-2,10)	(2,15•)

John doesn't have dominant Strategy

Will doesn't have a dominant Strategy

No dominant Strategy eqm exists

3) Nash eqm : it's the set of strategies, so that no player wants to deviate from the chosen strategies

Each player's Strategy is best response to all other players' chosen strategies

NE: ( John plays up, Will plays Centre )

4) yes, dominant Strategy eqm is always A NE

But a NE is not always a dominant Strategy eqm