QUESTION: Two pigs, one dominant and the other subordinate, are put in a pen. There is a lever at one end of the pen which, when pressed, dispenses 6 units of food at the opposite end. It "costs" a pig 1 unit of food to travel from the food to the lever and back.
If only one pig presses the lever, the pig that presses the lever must run to the food; by the time it gets there, the other pig has eaten 4 of the 6 units. The dominant pig can push the subordinate pig away from the food, and cannot be moved away from the food by the subordinate pig.
If both pigs press the lever, the subordinate pig is faster, and eats 2 of the units before the dominant pig pushes it away.
QUESTION: If each pig plays rationally, optimally, and selfishly, which pig will press the lever?
To answer the question, construct a simultaneous game, where the "payoffs" to the pigs are the net amount of grain consumed.
ANSWER: The subordinate pig always does better by not pulling the lever, regardless of what the the other pig does. This is called a "dominant strategy." The dominant pig's best response to this strategy is to pull the lever. The unique equilibrium is for the dominant pig to pull the lever and consume 1 net unit of food while the subordinate pig consumes four.
Pull Don't Pull
Pull (3,1) (1,4)
Don't Pull (6,-1) (0,0)
Ironically, with these payoffs, the subordinate pig will soon become dominant. Then the equilibrium will change.