Dominance can be a very useful and intuitive way to find the likely outcome of a game.

Consider, for example, the following game between Bobbi and Gary:

Gary

Left Center Right

High $4,47,55,2$

Middle $8,32,41,12$Bobbi

Low $10,69,14,3$

a$.$ Are there any dominant strategies in this game?

b$.$ Finding the likely outcome of this complex game appears difficult. Can you simplify the

game by finding a strategy that Bobbi should never reasonably play? Redraw the game

with that strategy eliminated. $($Hint: Look for dominated strategies.$)$

c$.$ In your simplified game, find a strategy that Gary should never reasonably play. $($Again$,$

look for dominated strategies.$)$ Did that strategy appear to be unreasonable in the

original game? Redraw the simplified game.

d$.$ In your twice$-$simplified game, find a strategy that Bobbi should never reasonably play

and redraw the game with that strategy removed from consideration.

e$.$ Eliminate the one strategy remaining that Gary is unlikely to use. The only outcome

remaining is the likely outcome of the game.