Rückwärtsbeweis

Rückwärtsbeweis, also known as backward induction, is a method of reasoning used in game theory and other decision-making processes to determine the optimal strategy in sequential games. It involves starting from the end of the game and working backward to the beginning, determining the optimal decision at each stage.

The core idea of Rückwärtsbeweis is to identify the optimal action for the last player to move, assuming they will act rationally to maximize their payoff. Once this is established, the reasoning proceeds to the second-to-last player, who will then choose their action knowing how the last player will respond. This process continues backward until the first player's move is determined.

This technique is particularly useful for analyzing finite games with perfect information, where all players know the current state of the game and all previous moves. By anticipating the rational choices of future players, current players can make informed decisions to achieve the best possible outcome for themselves.

Rückwärtsbeweis assumes that all players are rational and seek to maximize their own utility. If players are not perfectly rational or if there are elements of chance or incomplete information, the standard application of backward induction may not yield the true optimal strategy. However, it remains a fundamental tool for understanding strategic decision-making in a wide range of contexts.