An Economics Experiment (test your intuition)

[bobman0330]

I don't agree that the dot in that triangle is a NE position because 1 and 2 (or 1 and 3) can move it to 2 (or 3) and do better. That's not a NE either though, because the odd man out can move it to a point on the opposite side of the triangle. I'm not quite sure where that ends up.

In the pentagon example, there are better points other than the other vertices. For example, if you take a triangle consisting of the two opposite points and one of the other two and place the game in the center of that triangle, a majority improves its lot.

I actually don't see how a displacement of one player affects the situation. There's still not an equilibrium point that I can see.

[madnak]

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I don't agree that the dot in that triangle is a NE position because 1 and 2 (or 1 and 3) can move it to 2 (or 3) and do better.

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How so? Let's say player 1 is at position 0,15. Player 2 is at position 100,30. Player 3 is at position 100, 0. The red dot is at position 100,15.

Now, the red dot is 100 away from Player 1, and 15 away from players 2 and 3. If you move the token to player 2's location, that's obviously desirable for player 2. But now the distance from player 1 has increased to 30, and the distance to player 3 has increased to ~101.12 (sqrt(10225)). So such a move is bad for the majority of the players. I challenge you to find any point that isn't less desirable for at least two of the players.

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In the pentagon example, there are better points other than the other vertices. For example, if you take a triangle consisting of the two opposite points and one of the other two and place the game in the center of that triangle, a majority improves its lot.

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Not compared to the point between the closest two, it doesn't. That point will always compare the lot of a majority based on any other point.

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I actually don't see how a displacement of one player affects the situation. There's still not an equilibrium point that I can see.

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Two players, two players. That one player was a mistake.

[madnak]

Also, if you don't agree the red dot is the NE solution, where do you put it? To me it seems rational to place the dot at 67,15. That's definitely the equitable ("central") position.

[bobman0330]

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Also, if you don't agree the red dot is the NE solution, where do you put it? To me it seems rational to place the dot at 67,15. That's definitely the equitable ("central") position.

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I was wrong about 2 and 3 being good spots, but there are points on the line between 1 and 2 where both improve. I suspect now that the two NEs in that setup are the two points along the sides of the triangle 15 away from 2 and 3. The red dot might be an equilibrium too, because the players should know that they can't ultimately do better by switching.

I'm not following your comments on the pentagon example though.