"The king's problem"

Proposed in:

F. V. Jensen and M. Vomlelová, "Unconstrained influence diagrams", in Proceedings of the Eighteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI'02), (San Francisco, CA), pp. 234–241, Morgan Kaufmann, 2002.

It is described as follows:

"The beautiful princess in the kingdom Lovania has a wooer. It is rather convenient for the king as he considers retirement. Furthermore, in case he starts a war with the neighbor king, he needs a good general. As customary, the king shall confront the wooer with three tasks. One of the tasks shall be either to kill a unicorn or a dragon. Another task will be to spend a night in the royal tomb or in the haunted castle tower. The third type of task is to swim across the river or to climb the highest mountain in the kingdom.

The king can decide to retire or to start a war at any time. However, he cannot start a war after retirement, and he cannot give his daughter to the wooer before he has been confronted with all three tasks."

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Result of task 1.

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Result of task 1.

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Result of task 1.

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Represents the quality of the wooer.

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Represents the quality of the wooer as a military general.

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Represents whether the wooer is of noble descent or not.

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"One of the tasks shall be either to kill a unicorn or a dragon."

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"Another task will be to spend a night in the royal tomb or in the haunted castle tower."

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"The third type of task is to swim across the river or to climb the highest mountain in the kingdom."

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Represents the decision whether to marry the king's daughter with the wooer or not.

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Represents the decision to go to war.

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Represents the decision to abdicate.

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Cost of task 1.

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Cost of task 2.

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Cost of task 3.

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Cost of marriage.

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Cost of retirement

]]> 0.0 1.0 1.0 0.0 1.0 1.0 0.0 0.0 1.0 0.97 0.03 0.75 0.25 0.75 0.25 0.25 0.75 0.9 0.1 0.2 0.8 0.75 0.25 0.25 0.75 0.6 0.4 0.4 0.6 0.55 0.45 0.45 0.55 1.0 0.0 0.0 1.0 0.5 0.5 0.5 0.5 0.85 0.15 0.15 0.85 0.6 0.4 0.6 0.4 0.9 0.1 0.2 0.8 1.0 0.0 1.0 0.0 0.6 0.4 0.2 0.8 0.0 0.0 2.0 3.0 1.0 3.0 4.0 7.0 0.0 1.0 2.0 3.0 6.0 8.0 7.0 10.0 -1.0 -0.2 -0.5 -0.2 -0.1 -0.05 0.0 -5.0