Santa Claus and the Snow Maiden share the fee for the New Year's party of 6000 rubles using a sequential procedure of alternating proposals. First, Santa Claus offers a division, if the Snow Maiden agrees, then the negotiations end. If the Snow Maiden does not agree, then she will be able to offer her division, then Santa Claus, and so on. But the problem is that starting from the second period of time, the director of the House of Culture, where they work, can come at any minute, and with the probability a (0, 1), take away the entire amount from them and give Santa Claus 1000 rubles, and Snow Maiden 500. Players do not have discounts from decreasing utility over time, but they are under pressure from the possibility of the directors. What division will the players make in equilibrium? What happens when a 0?