Question

Player B- Heads Player B- Tails

Player A- Heads 1, -1 -1, 1

Player B- Tails    -1, 1 1, -1

Suppose both players use maximin strategies for this game. Is there a clear equilibrium outcome to the game in this case?

Explain answer

Answer 1

Answer:

No. The players in this game do not have a clear equilibrium outcome although both of them use maximin strategy.
Reason: Each player's response depends on the other player's move. This is a game that has the second mover's advantage. For example, (a) if Player 1 moves Heads, Player 2 must respond with Tails. (b) But if Player 2 moves first and plays Tails, he will get -1 in the strategy mentioned in (a).
Maximin strategy will not work in a game that has second mover advantage because the players cannot predetermine their strategies before the first move is made by one of the players. They must check what the other player has moved and then maximise their payoffs. Secondly, in this game, players must respond with the opposite move of the first player. If the first player has played Heads, the second player must move Tails, and vice versa. Thirdly, each player's outcome can be reversed by the move of the player that was not anticipated.

Thus, by using maximin strategies, the players cannot have a clear equilibrium outcome. There is only half a chance that they will get a positive result (their best outcome).