1) There are two alien groups living in the outer space: the Republic and the Federation. They are fighting over a planet Tatooine initially held by a troop of the Republic. The Republic has 4 troops and the Federation has 5 troops. Whenever the planet is occupied by one alien the opposing alien's troops can launch an attack. The outcome of the attack is that the occupying troop and one of the attacking troops are destroyed; the attacking alien group wins, and as long as it has troops left it occupies the planet with one troop. The president of each alien group is interested in maximizing the number of surviving troops but also regards the occupation of the planet as worth equivalent to 1,5 troop (i.e., if, after an attack, neither group has any troops left, then the payoff of each president is 0). Analyze this situation as an extensive game and predict the winner.