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From chessboards to economics: How does reverse reasoning change the rules of game strategy?
Backward reasoning is a unique way of thinking in the decision-making process, which determines the sequence of best choices by reasoning from the end of the problem back to the beginning. This method not only has applications in the fields of mathematics and computing, but also plays an important role in practical scenarios such as board games and economics. This article will explore the concept of reverse reasoning, examples of its application, and its impact on game strategy.
Backward reasoning allows decision makers to deduce earlier optimal actions from the final outcome, which is critical for precise selection of each step.
Basic concepts of reverse reasoning
The core of reverse reasoning lies in reverse thinking. Starting from a given end point, analyzing the best behavior achieved at that point, and then working backwards to the beginning of the problem, the best action can be determined for each possible situation. This method was first discovered by Arthur Kelly in 1875 to solve problems related to decision-making.
Reverse reasoning in economics
Backward reasoning is often used in economics to solve optimal stopping problems and game theory problems. In the optimal stopping problem, an individual decides when to give up and search for a better alternative. This is a typical decision-making scenario, in which reverse reasoning helps individuals consider long-term benefits.
Backward reasoning not only helps decision makers think about current situations, but also allows them to make predictions about future choices.
Applications in game theory
In game theory, backward reasoning is used to find optimal behavior, especially in sequential games. Suppose two players plan to go to the movies together. Player one prefers "Terminator" while player two prefers "Joker". Backward reasoning helps each player make optimal decisions after considering the other player's possible choices.
Multi-stage game example
Take a multi-stage game as an example. Player 1 will first choose a movie, and then player 2 will choose whether to watch it based on player 1’s decision. Through reverse reasoning, Player 2 is able to make the most beneficial choice at each stage, ultimately leading to a pivot equilibrium outcome that is most suitable for both parties.
Backward reasoning can take into account the other party's reactions and choices at every stage of decision-making. This interactivity makes the formulation of strategies more in-depth.
Limitations and Empirical Challenges
Although reverse reasoning can provide a powerful solution tool in theory, it faces many challenges in practice. For example, in some games with incomplete information, players cannot accurately predict the opponent's actions, so the effect of reverse reasoning will be greatly reduced.
Proposed example: monopoly problem
Consider the entry decision problem of a competitor in a monopoly market. If a potential entrant chooses to enter the market, existing firms decide whether to resist or tolerate the entrant. By reasoning backwards, companies can find the right combination of strategies to maximize their own interests and avoid becoming unwise because of unrealistic threats.
Accidental suspension paradox and reverse reasoning
The unexpected hanging paradox demonstrates the limitations of reverse reasoning. Suppose a prisoner relied on reverse reasoning to find a way to escape, but over-reasoned and came to the wrong conclusion. This tells us that backward reasoning, although a powerful tool, can also mislead us to arrive at erroneous results.
Conclusion
The influence of reverse reasoning reaches every corner of the chessboard and economics, transforming our understanding of strategy making. However, when faced with complex human behaviors and changing environments, can we really rely on this way of reasoning to make the best decisions?
