Exercises
Explore how economists analyze strategic interactions among individuals, businesses, and other decision-makers. This quiz covers dominant strategies, best responses, Nash equilibrium, zero-sum games, mixed strategies, backward induction, repeated cooperation, credible threats, and Pareto efficiency. Questions include payoff matrices and game trees that develop practical skills for interpreting simultaneous and sequential games.
Answer the questions below and check the explanation for each answer.
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Strategy A gives the row player a higher payoff than B whether the column player selects Left or Right. Therefore, A strictly dominates B.
At a Nash equilibrium, each player's strategy is a best response to the strategies of the others. No player benefits from a unilateral change.
Defection is each prisoner's best response to either action of the other prisoner. Consequently, mutual defection is the Nash equilibrium, despite mutual cooperation producing higher payoffs.
In a zero-sum game, the players' payoffs add to zero. Any gain received by one player is offset by an equal loss to the other.
When the row player chooses Up, the column player's payoff is 2 with Left and 4 with Right. Right is therefore the column player's best response.
Each player randomizes equally between the two strategies. A probability of 1/2 makes the opponent indifferent and prevents either player from exploiting a predictable pattern.
After entry, the incumbent prefers accommodation because 1 exceeds -1. Anticipating this response, the entrant enters because its payoff of 2 exceeds the payoff of 0 from staying out.
Cooperation is sustainable when 3/(1-δ) is at least 5 + δ/(1-δ). Simplifying gives 3 ≥ 5 - 4δ, so δ ≥ 1/2. Players must value future payoffs sufficiently.
A threat is credible only if executing it remains in the threatening player's interest when the decision point arrives. Otherwise, a rational opponent should not expect it to be carried out.
An outcome is Pareto efficient when no feasible alternative benefits at least one player without harming another. This differs from Nash equilibrium, which concerns unilateral deviations.
Stag-Stag and Hare-Hare are both pure-strategy Nash equilibria. At either outcome, neither player benefits from changing strategy alone.

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