Question

7. Solving for dominant strategies and the Nash equilibrium Suppose Sam and Teresa are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Sam chooses Right and Teresa chooses Right, Sam will receive a payoff of 5 and Teresa will receive a payoff of 3. Teresa Left Right Left 4, 4 6,3 Sam Right 5, 4 5,3 The only dominant strategy in this game is for Sam to choose Right The outcome reflecting the unique Nash equilibrium in this game is as follows: Sam chooses and Teresa chooses Grade It Now Save & Continue Continue without saving

Answer 1

Dominant strategy of a player is the strategy that will make the player better off, no matter what it's opponent chooses.

In this game, when Sam plays left, it is the best for Teresa to choose left because 4 > 3. And when Sam plays right, Teresa will choose left because she gets higher payoff. Therefore, no matter what Sam chooses, Teresa is always better off by choosing left. So, left is the dominant strategy for Teresa.

For Sam, when Teresa plays left, Sam will choose right because 5>4. And when Teresa plays right, Sam will choose left because 6>5. Therefore, there is no particular strategy that will make Sam better off. Sam has no dominant strategy.

So, the only dominant strategy in this game is for Teresa to choose Left.

Teresa's dominant strategy is left. So, she'll choose left and when she chooses it, Sam will be better off by playing Right because payoff 5 is greater than payoff 4. So, the Nash equilibrium is Sam chooses Right and Teresa chooses Left .