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EXERCISE 118.3 (Defending territory) General A is defending territory accessible by two mountain passes against an attack by General B. General A has three di- visions at her disposal, and general B has two divisions. Each general allocates her divisions between the two passes. General A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does General B; she successfully defends her territory if and only if she wins the battle at both passes. Formulate this situation as a strategic game and find all its mixed strategy equilib- ria. (First argue that in every equilibrium B assigns probability zero to the action of allocating one division to each pass. Then argue that in any equilibrium she assigns probability to each of her other actions. Finally, find A's equilibrium strategies.) In an equilibrium, do the generals concentrate all their forces at one pass, or spread them out?

EXERCISE 118.3 (Defending territory) General A is defending territory accessible by two mountain passes against an attack by General B. General A has three di- visions at her disposal, and general B has two divisions. Each general allocates her divisions between the two passes. General A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does General B; she successfully defends her territory if and only if she wins the battle at both passes. Formulate this situation as a strategic game and find all its mixed strategy equilib- ria. (First argue that in every equilibrium B assigns probability zero to the action of allocating one division to each pass. Then argue that in any equilibrium she assigns probability to each of her other actions. Finally, find A's equilibrium strategies.) In an equilibrium, do the generals concentrate all their forces at one pass, or spread them out?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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EXERCISE 118.3 (Defending territory) General A is defending territory accessible by two mountain passes against an attack by General B. General A has three di- visions at her disposal, and general B has two divisions. Each general allocates her divisions between the two passes. General A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does General B; she successfully defends her territory if and only if she wins the battle at both passes. Formulate this situation as a strategic game and find all its mixed strategy equilib- ria. (First argue that in every equilibrium B assigns probability zero to the action of allocating one division to each pass. Then argue that in any equilibrium she assigns probability to each of her other actions. Finally, find A's equilibrium strategies.) In an equilibrium, do the generals concentrate all their forces at one pass, or spread them out?
Transcribed Image Text:EXERCISE 118.3 (Defending territory) General A is defending territory accessible by two mountain passes against an attack by General B. General A has three di- visions at her disposal, and general B has two divisions. Each general allocates her divisions between the two passes. General A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does General B; she successfully defends her territory if and only if she wins the battle at both passes. Formulate this situation as a strategic game and find all its mixed strategy equilib- ria. (First argue that in every equilibrium B assigns probability zero to the action of allocating one division to each pass. Then argue that in any equilibrium she assigns probability to each of her other actions. Finally, find A's equilibrium strategies.) In an equilibrium, do the generals concentrate all their forces at one pass, or spread them out?
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