Minimax theorem guarantees a saddle point strategy in zero-sum games
Image: Екатерина Волкова, CC BY-SA 2.0, via Wikimedia Commons
Minimax theorem guarantees a saddle point strategy in zero-sum games
The minimax theorem is a fundamental concept in game theory that ensures a stable strategy exists for players in zero-sum games. This theorem provides a way to minimize potential losses for a player, even in the worst-case scenario.
Example
In a two-player zero-sum game like chess, the minimax theorem helps players determine their best moves by calculating the minimum gain for the opponent and maximizing their own minimum gain.
Remember this
Understanding the minimax theorem is crucial for developing strategies in competitive environments where outcomes are directly influenced by the actions of others.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Zero-sum game
Zero-sum game: one player's gain equals another's loss
Convex optimization
Convex functions have only one global minimum
a dominant strategy is: optimal regardless of what other players do
A dominant strategy maximizes payoff irrespective of opponents' actions
Kolmogorov complexity
Kolmogorov complexity is uncomputable
the optional stopping theorem says about martingales and stopping times
Martingale: E[X_{n+1} | X_1, X_2, ..., X_n] = X_n
approximation algorithms guarantee: solution within factor α of optimal
Can we always find the best solution quickly?
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