General A is defending territory accessible

by two mountain passes against an attack by General B. General A has three

divisions 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

equilibria. (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 1 2 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?