A bidding game: Consider the following game: Two people are asked to select an i

Question

A bidding game: Consider the following game: Two people are asked to select an integer between 2 and 100 (inclusive). If the two numbers are the same, each receives that dollar amount. If they select dierent numbers, the person who chose the lower number gets that dollar amount plus two dollars, while the person who chose the higher dollar amount gets the lower number minus two dollars. That is, if A selects 56 and B selects 88, then A gets 56+2 = 58, while B gets 56-2 = 54. Find the Nash equilibrium of this game.  Hint: the strategies in a Nash equilibrium have to be best responces to each other. One might think both people choosing 100 is a Nash equilibrium. If the other person chooses 100, is selecting 100 a best responce? What about a smaller number? Try some slightly smaller integers...  What is the other person's best responce to that (slightly) smaller number? If 100 is a best responce, then that is a Nash equilibrium. If not, there are no Nash equilibria in which either person selects 100.  Can you eliminate 99 in a similar fashion? Note for the reader's interest: I have observed the bidding game

Explanation / Answer

Both players choose 2 is the only strategy that fits the definition of Nash equilibrium. Either player will not gain anything by changing his/her strategy

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