Maximize the function 
subject to the constraint 
.
Definitions:
Proportion
A mathematical relation between parts, quantities, or amounts that expresses how much one is relative to the other.
Equilibrium
A state in which supply and demand are balanced, or a situation in which conflicting forces cancel each other out, resulting in a stable outcome or condition.
Hawk-Dove Game
A model in game theory that explores the conflict between aggressive (hawk) and peaceful (dove) strategies.
Payoff
The return or reward received as a result of an action or decision, particularly in the context of games or economic models.
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