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A two-player “guessing game” is a game in which the first participant, the “Responder,” picks a number from a certain range. Then, the second participant, the “Questioner,” asks only yes-or-no questions in order to guess the number. We will introduce guessing games in which the Responder is allowed to lie. Guessing games with lies are closely linked to error correcting codes, which are mathematical objects that allow us to detect an error in the information that we receive and correct these errors. We will give basic definitions in coding theory and show how error correcting codes allow us to still guess the correct number even if one lie is involved. We will then introduce cost functions to guessing games. By assigning a “cost” to the games, instead of minimizing the number of questions asked, we must find a way to minimize the total cost of our game. We will discuss optimization methods for minimizing the total cost of a guessing game when the cost function is applied to the answers or when the cost function is applied to the questions.

Minimizing the Cost of Guessing Games