Question 2: Game Theory [10 marks; 3. 4, 3] Anusha and Bill went to the Royal Easter show where each of them bought identical toys. Both lost their toys on their way back home. Their parents decided to reimburse them. They do not know the exact price, but they know the price is either $2, or $3, or $4. They proposed the following scheme. - Anusha should write either 2, or 3, or 4 as the price, and hand it to her parents. Bill should do the same {without consulting Anusha). a If Anusha writes pa and Bill writes pb, Anusha gets pa and Bill gets pb as long as their written numbers are identical or differ by 1, Le, |p,, pbl = 0 or 1. . Else, if |p,, - phl = 2, o Anusha gets pb 1 while Bill gets p, + 1 when p3 > pt. 0 Anusha gets pb + 1 while Bill gets pa - 1 when pa