A beauty contest game, each player (more than 2) simultaneously choose an intege

Question

A beauty contest game, each player (more than 2) simultaneously choose an integer between 0 and 20. Whoever chose the number that is closest to the mean (average) of all players win. If multiple players play strategies that are equally close to the mean, one player is randomly chosen as the winner.

1. Is playing 20 a dominated strategy in this version of the game? Explain.

2.Is everyone playing the same number, say 20, a Nash equilibrium?

3.Consider the following outcome. The number of players is even, e.g. n = 4. Half players play one integer, the other half plays the next integer. Is this outcome a Nash equilibrium?

Explanation / Answer

No. Playing 20 cannot be a dominated strategy as the mean can be averagely close to the number which every player selects..

Yes playing the same number 20 is a Nash equilibrium as the average will come to the same number and it would be a dominant strategy for every player.

If half players select a number and other half select the next then the mean would be the middle number of the two hence all players would be equally close to mean. Hence this outcome is a Nash equilibrium.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.