Game Theory Quiz

Game Theory: ten questions on strategic choices, equilibria, and payoff calculations. Every answer is explained.

Free, with no sign-up.

For High school students and adults reviewing the topic.

About 12 minutes. 10 questions.

How does it work?

Choose one answer or enter a number as requested, then check it.
Read the explanation before continuing.
Round only the final answer to the precision requested.

What will you get?

See your score and review the reasoning behind each answer.

Question 1The row player chooses Up or Down; the column player chooses Left or Right. Payoffs (row, column) are Up-Left (6, 2), Up-Right (1, 5), Down-Left (4, 3), and Down-Right (7, 0). At Down-Left, what is the row player’s payoff? Enter a whole number.

Enter a number.

Answers within 0.5 of the expected value are accepted.

Question 2The row player chooses Up or Down; the column player chooses Left or Right. Payoffs (row, column) are Up-Left (8, 1), Up-Right (2, 4), Down-Left (3, 6), and Down-Right (5, 2). Row chooses Up. Column chooses Left with probability 0.25 and Right with probability 0.75. Find Row’s expected payoff, rounded to two decimals.

Enter a number.

Answers within 0.005 of the expected value are accepted.

Question 3The row player chooses Up or Down; the column player chooses Left or Right. Payoffs (row, column) are Up-Left (9, 0), Up-Right (1, 6), Down-Left (−2, 5), and Down-Right (4, 3). Row chooses Down. Column chooses Left with probability 0.4 and Right with probability 0.6. Find Row’s expected payoff, rounded to two decimals.

Enter a number.

Answers within 0.005 of the expected value are accepted.

Question 4A sports player randomizes deliberately to prevent an opponent from anticipating the next move. What is the role of a mixed strategy?

It chooses the action with the best previous outcomeIt conceals a permanent preference for one repeated actionIt specifies a probability distribution over available actionsIt replaces the payoffs with the opponent’s preferences

Question 5A supplier expects future orders to depend on how it treats today’s customer. Why does repetition matter?

Past business turns the customer’s choices into fixed rulesRepeated contact makes the supplier’s preferences match the customer’sFuture orders replace the immediate payoff in the calculationThe prospect of repeat custom changes the reward for present behavior

Question 6A strategy yields a better payoff against each action an opponent could choose. What supports choosing it?

Its success depends on being chosen before the opponent movesIts success requires the opponent to copy the same actionIts advantage comes from raising the sum of both payoffsIts advantage survives a change in the opponent’s action

Question 7A seller threatens an expensive retaliation that would leave the seller worse off once a rival enters. How should a sequential analysis assess it?

Check the seller’s incentive at the later decision pointAccept the threat because it was announced before entryJudge the threat by the loss it would impose on the rivalAverage the seller’s payoffs across both announced actions

Question 8Two negotiators divide a fixed payment, with a larger share for either leaving a smaller share for the other. Which feature identifies the fixed-sum part?

A failed agreement leaves both negotiators with greater rewardsA party’s extra reward subtracts an equal amount from its counterpart’sA fair division requires the two shares to have equal sizeA negotiator’s gain increases the total amount being divided

Question 9Two firms settle on choices that neither wants to change unilaterally. What has been established?

Each choice is a best response to the other choiceEach choice maximizes the firms’ combined earningsEach choice gives both firms an equal share of earningsEach choice beats its alternatives against both rival actions

Question 10Why does the prisoner’s dilemma create a conflict between individual incentives and cooperation?

Mutual cooperation pays both players less than mutual defectionThe players choose without preferences over the possible rewardsThe individually preferred moves lead to lower joint rewardsThe opponent’s move has no effect on either player’s reward

Answer every question to see and share your score.

Read the topic guide