Can someone explain the concept of a min-max strategy in Game Theory? And also i
ID: 1093345 • Letter: C
Question
Can someone explain the concept of a min-max strategy in Game Theory? And also is there such thing as a min-min strategy? I have to write a paper on the concept of minmax and then also compare its effectiveness to a minmin strategy. Along with creating a running example to refer to throughout the paper. Thanks!
Below is my paper description: Describe in detail the concept of a minmax strategy. Be sure to fully elaborate including what exactly it is, what are the strategic benefits to such a strategy, and in which environments does it arise as an optimal strategy. Throughout your explanation of these ideas employ a novel
Explanation / Answer
explain the concept of a min-max strategy in Game Theory?
Minimax is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario. Alternatively, it can be thought of as maximizing the minimum gain . Originally formulated for two-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision making in the presence of uncertainty.
Minimax theorem
For every two-person, zero-sum game with finitely many strategies, there exists a value V and a mixed strategy for each player, such that
(a) Given player 2's strategy, the best payoff possible for player 1 is V, and
(b) Given player 1's strategy, the best payoff possible for player 2 is ?V.
Equivalently, Player 1's strategy guarantees him a payoff of V regardless of Player 2's strategy, and similarly Player 2 can guarantee himself a payoff of ?V. The name minimax arises because each player minimizes the maximum payoff possible for the other