# Game theory challenge: Can you predict human behavior?

by **Lee Ho Sung**

게임이론의 K-level 추정을 통해서 다른 사람들과 함께 하는 상황에서 더 좋은 선택을 할 수 있습니다.

Let’s think of a simple social experiment. Given a range of integers from 0 to 100, guess the number closest to 2/3 of the average of all numbers guessed. If the average guessed by all other participants is 60, the answer will be 40. But everyone in this experiment guesses similarly they will choose 40 as an answer instead of 60. In that case, 2/3 of the average would be 26.6. This logic can be able to extend further and further. With each step, the logical answer keeps getting smaller. Finally, when everyone chose zero, the game would reach what’s known as a Nash Equilibrium. This concept is a state where every player has selected the best possible strategy for themselves, considering an opponent’s choice, and no individual player has an incentive to change their decision.

But in the real world, people aren’t perfectly rational, and they don’t expect others to be logically perfect. When this game is played in real-world settings, the average tends to be somewhere between 20 and 35.

Economic game theorists have a model called k-level reasoning, which explains this interplay between rationality and practicality. K-level reasoning is defined recursively. K stands for the number of times a cycle of reasoning is repeated. A person playing at k-level 0 would approach a game without thinking about the other players. At k-level 1, a player would assume everyone else was playing at level 0.

The evidence that the number guessed at k-level 2 is 22 suggests the most people stop at 1 or 2 k-levels. That is useful to know. For example, during penalty kicks in soccer, both the shooter and the goalie decide whether to go right or left based on what they think the other person is thinking like a rock paper scissors.

1 or 2 k-levels is by no means a strict and fast rule. But, remembering this way of thinking can help you choose a better answer by adjusting your expectations.

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