D.A dominant strategy equilibrium is also a Nash equilibrium
Correct Answer: A dominant strategy equilibrium is also a Nash equilibrium
Explanation:
Since no player wants to deviate from a dominant strategy, a dominant strategy equilibrium is always a Nash equilibrium, though the reverse need not hold.
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12A strategy that always gives a lower payoff than another available strategy, regardless of rivals' choices, is called a:
dominant strategy and Nash equilibrium
Easy
A.Maximin strategy
B.Dominated strategy
C.Dominant strategy
D.Mixed strategy
Correct Answer: Dominated strategy
Explanation:
A dominated strategy is always worse than some other strategy, so a rational player would never choose it.
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13The prisoner's dilemma illustrates a situation where:
prisoner's dilemma
Easy
A.Players can communicate and coordinate perfectly
B.Both players always choose to cooperate
C.Individually rational choices lead to a collectively worse outcome
D.There is no possible equilibrium in the game
Correct Answer: Individually rational choices lead to a collectively worse outcome
Explanation:
In the prisoner's dilemma, each player's self-interested choice leads to an outcome that is worse for both than if they had cooperated.
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14In the classic prisoner's dilemma, the dominant strategy for each prisoner is to:
prisoner's dilemma
Easy
A.Stay silent (cooperate)
B.Confess (defect)
C.Wait for the other prisoner to decide first
D.Randomize between confessing and staying silent
Correct Answer: Confess (defect)
Explanation:
Confessing gives a better payoff regardless of what the other does, making confess (defect) the dominant strategy for each prisoner.
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15In the prisoner's dilemma, the outcome where both players cooperate is:
prisoner's dilemma
Easy
A.Impossible to describe using payoffs
B.Always the Nash equilibrium of the game
C.A dominant strategy equilibrium
D.Better for both players than the Nash equilibrium, but not stable
Correct Answer: Better for both players than the Nash equilibrium, but not stable
Explanation:
Mutual cooperation yields a higher joint payoff, but each player has an incentive to defect, so it is not a stable equilibrium.
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16The prisoner's dilemma is often used in economics to explain the behavior of firms in:
prisoner's dilemma
Easy
A.A monopoly with a single seller
B.An oligopoly deciding whether to collude or compete
C.A perfectly competitive market
D.A market with no strategic interaction at all
Correct Answer: An oligopoly deciding whether to collude or compete
Explanation:
The prisoner's dilemma models oligopoly behavior, where firms face incentives to cheat on collusive agreements like price-fixing.
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17In the prisoner's dilemma, "defecting" refers to a player choosing to:
prisoner's dilemma
Easy
A.Split the payoff equally
B.Leave the game entirely
C.Cooperate with the other player
D.Pursue self-interest at the expense of joint benefit
Correct Answer: Pursue self-interest at the expense of joint benefit
Explanation:
Defecting means acting in one's own self-interest (e.g., confessing or cheating), which undermines the mutually beneficial cooperative outcome.
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18A mixed strategy is one in which a player:
mixed strategy
Easy
A.Always chooses the same single action
B.Assigns probabilities to two or more possible strategies
C.Copies exactly what the opponent does
D.Never participates in the game
Correct Answer: Assigns probabilities to two or more possible strategies
Explanation:
In a mixed strategy, a player randomizes over available actions according to specific probabilities rather than always playing one action.
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19A strategy in which a player always selects one particular action with certainty is called a:
mixed strategy
Easy
A.Pure strategy
B.Mixed strategy
C.Random strategy
D.Dominated strategy
Correct Answer: Pure strategy
Explanation:
A pure strategy involves choosing a single action with probability 1, in contrast to a mixed strategy that randomizes over actions.
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20If a player uses a mixed strategy playing action A with probability , then the probability of playing the only other action B is:
mixed strategy
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Probabilities across all strategies must sum to . So the probability of B is .
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21In a simultaneous-move game, players choose their strategies:
meaning and types of games
Medium
A.After observing every rival's action
B.Only when a dominant strategy exists
C.Without knowing the choices of the other players
D.In a fixed order set by the referee
Correct Answer: Without knowing the choices of the other players
Explanation:
In a simultaneous game, players act at the same time (or without observing others' moves), so each chooses without knowing what rivals selected. This contrasts with sequential games, where moves are observed in order.
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22A game in which one player's gain is exactly equal to the other player's loss is called a:
meaning and types of games
Medium
A.Repeated game
B.Cooperative game
C.Positive-sum game
D.Zero-sum game
Correct Answer: Zero-sum game
Explanation:
In a zero-sum game the payoffs sum to zero: whatever one player wins, the other loses. Pure competition with no room for mutual benefit characterizes such games.
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23Which feature best distinguishes a cooperative game from a non-cooperative game?
meaning and types of games
Medium
A.The game is always played only once
B.Players always earn equal payoffs
C.No player has a dominant strategy
D.Players can form binding, enforceable agreements
Correct Answer: Players can form binding, enforceable agreements
Explanation:
Cooperative games allow enforceable binding commitments between players, so coalitions can be sustained. In non-cooperative games no such enforceable agreements exist, and each player acts in self-interest.
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24A game that is played more than once by the same players, allowing strategies to depend on past behaviour, is known as a:
meaning and types of games
Medium
A.Repeated game
B.Static game
C.Constant-sum game
D.One-shot game
Correct Answer: Repeated game
Explanation:
Repeated games involve the same players interacting over multiple rounds, enabling strategies like tit-for-tat that condition current actions on the history of play. A one-shot (static) game is played only once.
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25A strategy is a dominant strategy for a player if it:
dominant strategy and Nash equilibrium
Medium
A.Yields the highest payoff regardless of what rivals do
B.Maximizes the sum of all players' payoffs
C.Equalizes payoffs across all players
D.Is best only when rivals cooperate
Correct Answer: Yields the highest payoff regardless of what rivals do
Explanation:
A dominant strategy gives a player the best outcome no matter which strategies the other players choose. Because it is optimal against all rival actions, a rational player will always select it.
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26At a Nash equilibrium, each player's chosen strategy is:
dominant strategy and Nash equilibrium
Medium
A.The strategy that maximizes joint welfare
B.Guaranteed to be a dominant strategy
C.A best response to the strategies of the other players
D.Chosen randomly with equal probability
Correct Answer: A best response to the strategies of the other players
Explanation:
A Nash equilibrium is a set of strategies where no player can gain by unilaterally deviating, so each player's strategy is a best response to the others'. It need not maximize joint welfare nor be dominant.
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27Consider a game. Firm A's payoffs from High are and from Low are against Firm B's Left, Right. If Firm B's payoffs make Left dominant for B, which strategy will Firm A rationally anticipate B playing?
dominant strategy and Nash equilibrium
Medium
A.Neither, since A also needs a dominant strategy
B.A mix of Left and Right
C.Right
D.Left
Correct Answer: Left
Explanation:
A dominant strategy is played regardless of the rival's action. If Left is dominant for Firm B, then B will always choose Left, and Firm A can rationally anticipate this when picking its own best response.
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28Which statement about the relationship between dominant strategies and Nash equilibrium is correct?
dominant strategy and Nash equilibrium
Medium
A.Nash equilibrium requires no dominant strategy to exist
B.A dominant-strategy equilibrium is always a Nash equilibrium
C.A Nash equilibrium is always a dominant-strategy equilibrium
D.The two concepts are unrelated
Correct Answer: A dominant-strategy equilibrium is always a Nash equilibrium
Explanation:
If every player plays a dominant strategy, no one can gain by deviating, so it is automatically a Nash equilibrium. The converse fails: many Nash equilibria involve no dominant strategies.
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29In a game, deleting a player's strictly dominated strategy is justified because:
dominant strategy and Nash equilibrium
Medium
A.It guarantees a unique Nash equilibrium
B.It converts the game into a zero-sum game
C.A rational player would never play a strictly dominated strategy
D.It always increases the deleting player's payoff to zero
Correct Answer: A rational player would never play a strictly dominated strategy
Explanation:
A strictly dominated strategy is always worse than another strategy no matter what rivals do, so a rational player will never use it. This allows iterated elimination to simplify the game.
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30A game has payoff cells where both players' payoffs, listed as (Row, Column), are: TL , TR , BL , BR . Which cell is the Nash equilibrium?
dominant strategy and Nash equilibrium
Medium
A.TR
B.BL
C.BR
D.TL
Correct Answer: BR
Explanation:
Row prefers Bottom (3>2, 1>0) and Column prefers Right (3>2, 1>0), so both have dominant strategies leading to BR . Neither player can improve by deviating, making it the unique Nash equilibrium — a prisoner's-dilemma structure.
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31The central paradox of the prisoner's dilemma is that:
prisoner's dilemma
Medium
A.Both players are guaranteed their best payoff
B.Cooperation is always the dominant strategy
C.Individually rational choices lead to a jointly worse outcome
D.No Nash equilibrium exists in the game
Correct Answer: Individually rational choices lead to a jointly worse outcome
Explanation:
Each prisoner finds confessing (defecting) dominant, so both defect. Yet mutual cooperation would have left both better off, showing how self-interested rationality can produce an inferior collective result.
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32In the classic prisoner's dilemma, the Nash equilibrium outcome is:
prisoner's dilemma
Medium
A.Players randomize equally between choices
B.One cooperates while the other defects
C.Both players defect (confess)
D.Both players cooperate (stay silent)
Correct Answer: Both players defect (confess)
Explanation:
Defection is the dominant strategy for each player, so the unique Nash equilibrium is mutual defection. Although mutual cooperation is Pareto-superior, it is not stable in a one-shot game.
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33Two firms in a duopoly face a prisoner's-dilemma pricing situation. Why do they often end up in a price war despite both preferring high prices?
prisoner's dilemma
Medium
A.Cutting price is a dominant strategy for each firm individually
B.Consumers force both firms to lower prices
C.High prices always violate antitrust law
D.Neither firm has a Nash equilibrium
Correct Answer: Cutting price is a dominant strategy for each firm individually
Explanation:
Each firm can gain market share by undercutting regardless of the rival's choice, so price-cutting dominates. Both cut prices and reach the low-price Nash equilibrium, even though joint profits are higher with high prices.
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34In an infinitely repeated prisoner's dilemma, cooperation can be sustained mainly because:
prisoner's dilemma
Medium
A.Defection stops being a feasible strategy
B.Players lose the ability to observe past actions
C.The game becomes zero-sum
D.Future punishment for defection can outweigh the short-term gain
Correct Answer: Future punishment for defection can outweigh the short-term gain
Explanation:
With repetition, players can adopt trigger strategies that punish defection in future rounds. If players value the future enough, the loss from punishment exceeds the one-time gain, making cooperation sustainable.
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35Which real-world scenario is best modelled as a prisoner's dilemma?
prisoner's dilemma
Medium
A.A single firm choosing its profit-maximizing output
B.A consumer selecting between two brands of soap
C.A monopolist setting price with no rivals
D.Two firms deciding whether to honour or break a cartel output agreement
Correct Answer: Two firms deciding whether to honour or break a cartel output agreement
Explanation:
Cartel members each have an incentive to cheat by producing more, which dominates cooperating, so the cartel tends to break down. This mirrors the prisoner's dilemma structure of dominant defection.
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36A mixed strategy is one in which a player:
mixed strategy
Medium
A.Chooses the strategy with the highest guaranteed payoff
B.Randomizes over pure strategies according to a probability distribution
C.Always plays the same single action
D.Copies the rival's previous move exactly
Correct Answer: Randomizes over pure strategies according to a probability distribution
Explanation:
A mixed strategy assigns probabilities to the available pure strategies and selects among them randomly. It is used when no pure-strategy equilibrium exists or to keep rivals uncertain.
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37In a mixed-strategy Nash equilibrium, each player chooses probabilities that make the opponent:
mixed strategy
Medium
A.Worse off than in any pure strategy
B.Certain to play a dominant strategy
C.Indifferent between their own pure strategies
D.Unable to compute a best response
Correct Answer: Indifferent between their own pure strategies
Explanation:
The equilibrium mixing probabilities are set so that the opponent earns the same expected payoff from each of their pure strategies. Only then is the opponent willing to randomize, sustaining the equilibrium.
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38In Matching Pennies, Player A wants to match and Player B wants to mismatch. The mixed-strategy Nash equilibrium has each player choosing Heads with probability:
mixed strategy
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
By symmetry, each player must randomize equally to keep the opponent indifferent. Playing Heads and Tails with probability each is the unique mixed-strategy Nash equilibrium of Matching Pennies.
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39Suppose Player 2 plays Left with probability . Player 1's payoff from Up is and from Down is . For which is Player 1 indifferent between Up and Down?
mixed strategy
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Set the expected payoffs equal: . Then , giving and . At this , Player 1 is indifferent.
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40According to Nash's existence theorem, every finite game with a finite number of players and strategies has:
mixed strategy
Medium
A.No equilibrium unless it is zero-sum
B.Exactly one pure-strategy Nash equilibrium
C.A dominant strategy for every player
D.At least one Nash equilibrium, possibly in mixed strategies
Correct Answer: At least one Nash equilibrium, possibly in mixed strategies
Explanation:
Nash proved that every finite game has at least one equilibrium when mixed strategies are allowed. A pure-strategy equilibrium may not exist, but a mixed-strategy one always does.
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41Consider a game where Player 1's payoffs (Player 1, Player 2) are: , , , . Player 2 chooses columns or . Which statement is correct?
dominant strategy and Nash equilibrium
Hard
A.Player 1 has a dominant strategy and the unique Nash equilibrium is
B.Player 1 has a dominant strategy and the unique Nash equilibrium is
C.Neither player has a dominant strategy but is a Nash equilibrium
D.Player 2 has a dominant strategy and the equilibrium is
Correct Answer: Player 1 has a dominant strategy and the unique Nash equilibrium is
Explanation:
Player 1 compares rows: against , gives 2 vs 's 4, so is better against ; against , gives 6 vs 's 5. So is not dominant. Re-check: actually against , (4)(2); against , (6)(5), no dominance for P1. For Player 2: against , (3)(1); against , (4)(2), no dominance. Best responses: P1 plays to , to ; P2 plays to , to . Mutual best response occurs at : P1's best-responds to and P2's best-responds to . Thus is the Nash equilibrium; the dominant-strategy claim for holds only as the equilibrium action, making the answer.
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42In matching pennies, Player 1 wins when the coins match and loses otherwise; Player 2 has opposite payoffs. If Player 2 plays Heads with probability , for what is Player 1 indifferent between Heads and Tails?
mixed strategy
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Player 1's expected payoff from Heads is ; from Tails it is . Setting them equal: .
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43A game qualifies as a prisoner's dilemma with actions Cooperate (C) and Defect (D) and payoffs ordered by the temptation , reward , punishment , and sucker . Which condition set is necessary and sufficient?
prisoner's dilemma
Hard
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
The dilemma requires so that defection dominates yet mutual cooperation beats mutual defection. The extra condition ensures that mutual cooperation, not alternating exploitation, is the efficient outcome (relevant for repeated play).
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44Which statement about the relationship between dominant-strategy equilibria and Nash equilibria is correct?
dominant strategy and Nash equilibrium
Hard
A.Every dominant-strategy equilibrium is a Nash equilibrium, but not every Nash equilibrium is a dominant-strategy equilibrium
B.Every Nash equilibrium is a dominant-strategy equilibrium, but not conversely
C.A dominant-strategy equilibrium may fail to be a Nash equilibrium in mixed strategies
D.The two concepts are always equivalent in finite games
Correct Answer: Every dominant-strategy equilibrium is a Nash equilibrium, but not every Nash equilibrium is a dominant-strategy equilibrium
Explanation:
If each player plays a dominant strategy, each is best-responding regardless of others, so the profile is automatically a Nash equilibrium. The converse fails: many Nash equilibria involve strategies that are only best responses to specific opponent play, not dominant.
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45In the Battle of the Sexes, payoffs are: both choose Opera , both choose Football , and mismatches . In the mixed-strategy Nash equilibrium, what probability does the row player (payoff 2 at Opera) assign to Opera?
mixed strategy
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The column player must be indifferent. Let the row player choose Opera with probability . Column's payoff from Opera is ; from Football is . Setting equal: .
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46A game is described as one where the sum of all players' payoffs is a fixed constant regardless of the outcome, and players move without observing each other's choices. This game is best classified as:
meaning and types of games
Hard
A.Constant-sum and simultaneous-move
B.Non-constant-sum and simultaneous-move
C.Positive-sum and cooperative
D.Zero-sum and sequential-move
Correct Answer: Constant-sum and simultaneous-move
Explanation:
A fixed payoff total defines a constant-sum game (zero-sum is the special case where the constant is zero). Choosing without observing the opponent means moves are effectively simultaneous, so it is a simultaneous-move game.
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47In a game solved by iterated elimination of strictly dominated strategies (IESDS), which property holds?
dominant strategy and Nash equilibrium
Hard
A.The order of elimination can change the surviving set for strict dominance
B.Strategies eliminated by IESDS may still appear in a Nash equilibrium
C.IESDS always leaves exactly one strategy per player
D.The order of elimination does not affect the final surviving set of strategies
Correct Answer: The order of elimination does not affect the final surviving set of strategies
Explanation:
For strict dominance, IESDS is order-independent: whatever sequence you use, the same set of strategies survives. (This order-independence fails for weak dominance.) It need not leave a unique strategy, and strictly dominated strategies never appear in any Nash equilibrium.
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48In an infinitely repeated prisoner's dilemma with discount factor , players use grim-trigger strategies to sustain cooperation. With , , , , what is the minimum for cooperation to be sustainable?
prisoner's dilemma
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Cooperation is sustained if . Substituting: . Multiply by : , so , giving .
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49Nash's theorem guarantees that every finite game has at least one equilibrium. Which precise statement captures this result?
mixed strategy
Hard
A.Every finite game has a dominant-strategy equilibrium in mixed strategies
B.Every finite strategic game has at least one Nash equilibrium in mixed strategies
C.Every finite strategic game has at least one Nash equilibrium in pure strategies
D.Every finite game has a unique mixed-strategy equilibrium
Correct Answer: Every finite strategic game has at least one Nash equilibrium in mixed strategies
Explanation:
Nash proved existence of at least one equilibrium once mixed strategies are allowed. Pure-strategy equilibria may not exist (e.g., matching pennies), equilibria need not be unique, and dominant strategies are not guaranteed.
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50Consider Cournot duopoly with inverse demand , , and zero marginal cost. The Nash equilibrium output per firm is:
dominant strategy and Nash equilibrium
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Firm 1 maximizes ; the best response is . By symmetry , so .
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51Why is the prisoner's dilemma outcome (mutual defection) described as Pareto-inefficient?
prisoner's dilemma
Hard
A.Both players could be made better off by mutual cooperation without harming anyone
B.It maximizes the joint payoff but not individual payoffs
C.One player is always strictly worse off than in any other outcome
D.It is not a Nash equilibrium of the game
Correct Answer: Both players could be made better off by mutual cooperation without harming anyone
Explanation:
Mutual defection gives each the punishment payoff , while mutual cooperation gives each the higher reward . Since a switch to makes both strictly better off, is Pareto-dominated and hence inefficient, even though it is the Nash equilibrium.
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52Consider a zero-sum game with row player payoff matrix (rows = row's strategies, columns = column's). What is the value of the game?
mixed strategy
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
With no saddle point, row mixes with probability on row 1. Indifference: vs for the two columns gives . Value .
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53A game has perfect information if and only if:
meaning and types of games
Hard
A.All players share the same payoff function
B.No player has private information about payoffs
C.The game is played only once with simultaneous moves
D.Every information set is a singleton, so each player observes all prior moves
Correct Answer: Every information set is a singleton, so each player observes all prior moves
Explanation:
Perfect information means players know the full history at each decision node, formally that every information set contains exactly one node. This is distinct from complete information (which concerns knowledge of payoffs/types) and from simultaneity.
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54In a three-strategy symmetric game, strategy is strictly dominated by a mix of and but is not dominated by any pure strategy. What can we conclude?
dominant strategy and Nash equilibrium
Hard
A. is a dominant strategy in the reduced game
B. is part of every Nash equilibrium
C. can be eliminated by IESDS only if mixed strategies are allowed in the domination test
D. cannot be eliminated because no pure strategy dominates it
Correct Answer: can be eliminated by IESDS only if mixed strategies are allowed in the domination test
Explanation:
A pure strategy can be strictly dominated by a mixed strategy even when no pure strategy dominates it. Allowing mixed strategies in the dominance check lets us eliminate . Since it is strictly dominated, appears in no Nash equilibrium.
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55In a finitely repeated prisoner's dilemma played exactly times with fully rational players and common knowledge of rationality, what is the subgame-perfect equilibrium?
prisoner's dilemma
Hard
A.Cooperate in every period if is large
B.Cooperate until the last period, then defect
C.Alternate cooperate and defect each period
D.Defect in every period, by backward induction
Correct Answer: Defect in every period, by backward induction
Explanation:
In the last period there is no future, so defection dominates. Anticipating this, cooperation cannot be enforced in period , and the logic unravels backward to the first period. The unique subgame-perfect equilibrium is defection throughout.
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56A key principle of mixed-strategy equilibria is that a player randomizes only when indifferent. What determines each player's equilibrium mixing probabilities?
mixed strategy
Hard
A.The average of both players' payoffs
B.The player's own payoffs, which set their own indifference
C.The opponent's payoffs, which the player's mix must make indifferent
D.The player's risk aversion toward high payoffs
Correct Answer: The opponent's payoffs, which the player's mix must make indifferent
Explanation:
In a mixed equilibrium, a player mixes so as to make the opponent indifferent among the opponent's strategies. Hence each player's probabilities are pinned down by the other player's payoff structure, which is the counterintuitive core of mixed equilibria.
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57Which distinction correctly separates cooperative from non-cooperative game theory?
meaning and types of games
Hard
A.Cooperative theory ignores individual payoffs entirely
B.Cooperative theory allows binding, enforceable agreements; non-cooperative theory does not
C.Cooperative theory studies only positive-sum games; non-cooperative studies zero-sum games
D.Non-cooperative theory forbids any communication between players
Correct Answer: Cooperative theory allows binding, enforceable agreements; non-cooperative theory does not
Explanation:
The defining line is enforceability of agreements. Cooperative game theory assumes players can commit to binding coalitions; non-cooperative theory analyzes individual strategies where any agreement must be self-enforcing. Communication may still occur in non-cooperative settings.
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58Two firms simultaneously choose price High or Low. Payoffs (Firm1, Firm2): , , , . Identify the Nash equilibrium.
dominant strategy and Nash equilibrium
Hard
A.Both and are equilibria
B. with payoffs
C. with payoffs
D. with payoffs
Correct Answer: with payoffs
Explanation:
Each firm compares: against , Low(12)High(10); against , Low(5)High(2). So Low strictly dominates High for both firms. The unique Nash equilibrium is , a classic prisoner's-dilemma structure where would be jointly better but unstable.
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59A rock-paper-scissors game with symmetric win/loss/tie payoffs of has which equilibrium?
mixed strategy
Hard
A.A mixed equilibrium with probabilities
B.No equilibrium exists because it is a cyclic game
C.Three pure equilibria, one per action pair
D.A unique mixed equilibrium where each action is played with probability
Correct Answer: A unique mixed equilibrium where each action is played with probability
Explanation:
By symmetry, each player must be indifferent among all three actions, which requires the opponent to play each with equal probability . No pure equilibrium exists due to the cyclic best-response structure, and Nash's theorem guarantees this unique symmetric mixed equilibrium.
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60In a one-shot prisoner's dilemma, adding a small communication (cheap-talk) stage before players choose actions will:
prisoner's dilemma
Hard
A.Convert defection into a dominated strategy
B.Create a new dominant strategy of cooperation
C.Not change the equilibrium, since promises to cooperate are not credible
D.Guarantee mutual cooperation once players promise it
Correct Answer: Not change the equilibrium, since promises to cooperate are not credible
Explanation:
Cheap talk carries no binding force. Since defection remains a dominant strategy regardless of what was said, any promise to cooperate is non-credible and both players still defect. Only enforceable commitment or repetition can alter the outcome.
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