Two athletes i 1,2 are jointly preparing for the upcoming world championships. The athletes simultaneously decide...

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Two athletes i 1,2 are jointly preparing for the upcoming world championships. The athletes simultaneously decide on their training levels 1, € 10. 1]. The performance p at the world championships depends on their training levels ti and ta as well as on the health condition of athlete 2 who has recently been injured. Athlete 2 knows the own health condition but athlete 1 only knows that athlete 2's health condition could be bad, okay, or good with equal probability. The performance p at the world championships is described by the function 5-4+5-1₂ 5 +7.5 ta 5:4₁ +10 1₂ The utility of athlete i is described by if athlete 2's health condition is bad if athlete 2's health condition is okay if athlete 2's health condition is good (n) (13 points) Solve for the equilibrium training levels of both athletes. (b) (8 points) Suppose that it is common knowledge that athlete 2 reveals the own health condition if and only if it is good. This revelation takes place before both athletes decide on their training levels. How do equilibrium training levels change for both athletes if athlete 2 has the health condition okay? (c) (12 points) Suppose now that athlete 2 has the option to credibly reveal or not to reveal the own health condition before both athletes decide on their training levels. Show that athlete 2 credibly reveals the own health condition if it is bad. Would athlete 2 credibly reveal the own health condition if it is okay? What happens in case of a good health condition? Two athletes i 1,2 are jointly preparing for the upcoming world championships. The athletes simultaneously decide on their training levels 1, € 10. 1]. The performance p at the world championships depends on their training levels ti and ta as well as on the health condition of athlete 2 who has recently been injured. Athlete 2 knows the own health condition but athlete 1 only knows that athlete 2's health condition could be bad, okay, or good with equal probability. The performance p at the world championships is described by the function 5-4+5-1₂ 5 +7.5 ta 5:4₁ +10 1₂ The utility of athlete i is described by if athlete 2's health condition is bad if athlete 2's health condition is okay if athlete 2's health condition is good (n) (13 points) Solve for the equilibrium training levels of both athletes. (b) (8 points) Suppose that it is common knowledge that athlete 2 reveals the own health condition if and only if it is good. This revelation takes place before both athletes decide on their training levels. How do equilibrium training levels change for both athletes if athlete 2 has the health condition okay? (c) (12 points) Suppose now that athlete 2 has the option to credibly reveal or not to reveal the own health condition before both athletes decide on their training levels. Show that athlete 2 credibly reveals the own health condition if it is bad. Would athlete 2 credibly reveal the own health condition if it is okay? What happens in case of a good health condition?