Consider the following two-player extensive form game with complete infor- mation. In this game, colony A...
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Consider the following two-player extensive form game with complete infor- mation. In this game, colony A is controlled by country B. Country B receives revenue from both direct taxes on the population of A as well as revenue from the control of A's natural resources. In the first stage of the game, colony A decides whether to Revolt (R) or continue to Consent (C) to the status quo arrangement. If A revolts, country B must decide whether to grant independence G or suppress S the revolt. If B suppresses the revolt, the situation will escalate into a costly war over control of the natural resources worth a payoff of "4" to whoever wins. Let the probability that colony A wins the war be denoted by p. Starting a revolution costs colony A "1" if country B does not suppress. In the event country B does suppress the revolt, it costs both A and B "6." If A does not revolt, B can continue to tax T the residents of colony A for a transfer of "2" or it can eliminate E the taxes. The structure and payoffs can be described in the following game tree. If we assume that pe (0, 1) i.e., 0 < p < 1 what is the SPNE of the game? country B grant independence, 3, 0 revolt suppress colony A 4p-6-2(1-P). 6(1-P) - 6 consent -2, 6 tax country B eliminate taxes 0. Consider the following two-player extensive form game with complete infor- mation. In this game, colony A is controlled by country B. Country B receives revenue from both direct taxes on the population of A as well as revenue from the control of A's natural resources. In the first stage of the game, colony A decides whether to Revolt (R) or continue to Consent (C) to the status quo arrangement. If A revolts, country B must decide whether to grant independence G or suppress S the revolt. If B suppresses the revolt, the situation will escalate into a costly war over control of the natural resources worth a payoff of "4" to whoever wins. Let the probability that colony A wins the war be denoted by p. Starting a revolution costs colony A "1" if country B does not suppress. In the event country B does suppress the revolt, it costs both A and B "6." If A does not revolt, B can continue to tax T the residents of colony A for a transfer of "2" or it can eliminate E the taxes. The structure and payoffs can be described in the following game tree. If we assume that pe (0, 1) i.e., 0 < p < 1 what is the SPNE of the game? country B grant independence, 3, 0 revolt suppress colony A 4p-6-2(1-P). 6(1-P) - 6 consent -2, 6 tax country B eliminate taxes 0. Consider the following two-player extensive form game with complete infor- mation. In this game, colony A is controlled by country B. Country B receives revenue from both direct taxes on the population of A as well as revenue from the control of A's natural resources. In the first stage of the game, colony A decides whether to Revolt (R) or continue to Consent (C) to the status quo arrangement. If A revolts, country B must decide whether to grant independence G or suppress S the revolt. If B suppresses the revolt, the situation will escalate into a costly war over control of the natural resources worth a payoff of "4" to whoever wins. Let the probability that colony A wins the war be denoted by p. Starting a revolution costs colony A "1" if country B does not suppress. In the event country B does suppress the revolt, it costs both A and B "6." If A does not revolt, B can continue to tax T the residents of colony A for a transfer of "2" or it can eliminate E the taxes. The structure and payoffs can be described in the following game tree. If we assume that pe (0, 1) i.e., 0 < p < 1 what is the SPNE of the game? country B grant independence, 3, 0 revolt suppress colony A 4p-6-2(1-P). 6(1-P) - 6 consent -2, 6 tax country B eliminate taxes 0. Consider the following two-player extensive form game with complete infor- mation. In this game, colony A is controlled by country B. Country B receives revenue from both direct taxes on the population of A as well as revenue from the control of A's natural resources. In the first stage of the game, colony A decides whether to Revolt (R) or continue to Consent (C) to the status quo arrangement. If A revolts, country B must decide whether to grant independence G or suppress S the revolt. If B suppresses the revolt, the situation will escalate into a costly war over control of the natural resources worth a payoff of "4" to whoever wins. Let the probability that colony A wins the war be denoted by p. Starting a revolution costs colony A "1" if country B does not suppress. In the event country B does suppress the revolt, it costs both A and B "6." If A does not revolt, B can continue to tax T the residents of colony A for a transfer of "2" or it can eliminate E the taxes. The structure and payoffs can be described in the following game tree. If we assume that pe (0, 1) i.e., 0 < p < 1 what is the SPNE of the game? country B grant independence, 3, 0 revolt suppress colony A 4p-6-2(1-P). 6(1-P) - 6 consent -2, 6 tax country B eliminate taxes 0.
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