Florida B.E.S.T. MA.912.LT.2.7

MathGrades 9–12Apply optimization and techniques from Graph Theory to solve problems.

The Standard

Solve problems involving optimal strategies in Game Theory.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students analyze the possible moves and payoffs for two players. They choose strategies that produce the best result while accounting for what the other player may do.
What Mastery Looks Like: Students can read a payoff matrix, compare possible responses, and identify a strategy that gives the best guaranteed result. They can justify the choice using payoffs and recognize when a mixed strategy is needed.
Common Misconceptions: Students may choose the move with the largest possible payoff without considering the opponent’s response. They may also confuse a best response with an optimal strategy or assume an optimal strategy always guarantees a win.
How to Assess It: Give this payoff matrix for Player A: Up gives 4 or 1, and Down gives 2 or 0. Ask students to name each player’s optimal strategy, state the game value, and justify both choices.

Lesson moves

Pairs play a two-choice token game, record outcomes in a payoff matrix, then identify each player’s safest strategy.
Ask students, “Should you chase the highest possible payoff or protect against the worst outcome?” Support the answer with a payoff matrix.
Run a payoff-matrix tournament where students earn points for correctly predicting optimal strategies before each round is played.
Compare pricing choices by two competing snack stands, using a payoff table to decide whether each should charge a high or low price.

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