Level 0 players will tend to choose option 1. Level 1 players will realize that this is what level 0 players will do, so they will tend to choose option 2 ("the first one"). Level 2 players will realize that this is what level 1 players will do, so they will tend to choose option 4 ("the second one"). Level 3 players will realize that this is what level 2 players will do, so they will tend to choose option 5 ("the fourth one"). Apparently there are lots of level 1 & 2 players, but very few level 3 players.

But this analysis does not explain why so many people chose option 3 ("the last one") - I doubt that they are level 4 players. Perhaps it's that the last answer is the second-most-salient, by virtue of being last, making them level 1 players with a twist.

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[-]AlexMennen14y40

When trying to choose randomly, people tend to avoid options with salient features. It is not so easy to sort players into levels accurately.

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[-]roystgnr14y10

You and DanielLC are right, however:

Just because a game is isomorphic to a symmetric problem doesn't mean that it is a symmetric problem. "Scissors cut Paper wraps Rock smashes Scissors" has an equivalent formalism to "Policeman arrests Murderer kills Mayor bosses Policeman" but I'd bet with the latter (played as a single-round game) you'd see some very different game play in practice.

So what CronoDAS needs isn't a game theorist, it's a psychologist.

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