Question

+3. (5 points) Use the following matrix to answer the following questions. Player 2 Strategy с D Player 1 A -10, -10 200, B -100, 220 140, -100 180 Assume that this is a simultaneous move one shot game. (a) Determine the dominant strategy for player A and Player B. If such a strategy does not exist, explain why not. (b) Determine the secure strategy for player A and player B. If such a strategy does not exist, explain why not. (C) Determine if a Nash equilibrium exists in this game and explain why it exists (or why not).

Answer 1

question (3) Rayer-2 С D A -10,- 10 Player 1 200 - 100 B. -100, 220 140, 180 dominant strategy it is a strategy for a player hayer That gives maximum payaff To him compared to strategies irrespective what other players are choosing. others available u Secare strategy in the absence of dominant strategy The strategy that gumantees The Highest Payoff given the worse Strategy where Prayer Player can Avoid The worst possible outcome. Payaffs.

0 A To is (a) player a-t has dominant Strategy A. why it is dominant 2 Because strategy gives maximum Payays Player - A irres fective what layer-2 choosing it is best action for player- of for any every action of f-2 Prayer-2 has dominant Strategy or C. Because С gives - lo more Than - 100 220 Payaff P- chooses A Payoff more Than 180 if li chooses B. Botn Prayer has dominant Stoutegy. (b) Since both Prayers has the dominant Stoategy which insures. The maximum payass To both the players So they does Not ceeded Strategy that Prevents them to get worst payoff & (C) Dominant Strategy Leads us The dominant where pri chooses A and P-2 chooses c NE = (A,C) Such a Strategy wash there yove
for part (b) we doesn't have the secure strategy due to the presence of dominant strategy.

Part (C) the nash equilibrium is the unique nash where player-1 Will choose A and player-2 will choose C.