Practice Question

Question 5 [15 points] Two players i = 1, 2 are fighting over an object. The value of the object to player i is r, > 0. The values v, and vz are known by both players. Time is continuous and start at 0, and runs indefinitely. Each player chooses when to stop the fight. If player i is the first to stop the fight at time t, then player j gets the object at that time. If both players stop the fight at the same time, they share the object equally and player i receives the value w/2. Time is valuable: if the first player to stop the fight does so at time t, then both players suffer a cost of t. (a) [5 points] Formulate this situation as a game. (b) [10 points] Show that in all Nash equilibria, one of the players concedes immediately