Review Questions

1. What are the three common elements of an economic game?

   All economic games have three common elements:

   1. Players, or the decision makers in a game

   2. Strategies, or a player’s plan of action in a game

   3. Payoffs, or the outcome of a game

2. What differentiates game theory from single-agent problems?

   Unlike single-agent problems, game theory is concerned with situations in which a player’s actions affect her opponents’ choices and payoffs, and not just her own.

3. How does the existence of multiple Nash equilibria complicate the solution to an economic game?

   In games with multiple Nash equilibria, just as with all games with Nash equilibria, firms’ best responses depend on competitor firms’ decisions. As a result, we can narrow down the possible outcomes but cannot determine the final outcome of the game prior to its being played.

4. How can a payoff matrix be used to find a player’s optimal strategy?

   The payoff matrix incorporates information about all three elements of a game—its players, their possible strategies, and the associated payoffs—and therefore can be used to eliminate dominant strategies as possible equilibrium outcomes and to find the players’ mutual best responses or the strategy that will lead to the Nash equilibrium or equilibria.

5. Why might a player pursue a mixed strategy?

   In some situations, it may be best for the player to choose actions randomly from the set of available pure strategies and therefore to pursue a mixed strategy. One example would be in a game in which a pure strategy does not lead to a mutual best response (i.e., two checks using the check-box method).

6. Why is the maximin strategy considered a conservative strategy?

   A player using a maximin strategy is not going for the greatest payoff, but rather is choosing the conservative strategy of minimizing her losses.

7. Define backward induction. How can backward induction be used to solve a strategic game?

   Backward induction allows us to consider all steps in a multistep game. To use backward induction, we solve first for the game’s final step, and then proceed backward.

8. Compare the grim trigger and tit-for-tat strategies.

   A player using a grim trigger strategy cooperates with her opponent so long as her opponent is also cooperative. If her opponent cheats, the player permanently ends the game. In tit for tat, the player instead mimics her opponent’s actions. When the opponent cooperates, so does she; when the opponent cheats, the player cheats in the next period.

9. Why do we use decision trees—instead of normal-form matrices—to solve sequential games?

   Unlike a normal-form matrix, a decision tree incorporates information about the timing of decisions, a piece of information that is key to the outcome of a sequential game.

10. How can side payments be beneficial to both players in a two-player game?

    In some games, a player may offer a side payment to his opponent. This payment is designed to ensure the opponent chooses the strategy optimal to the player, and provides both with a greater outcome than he would receive in a game without side payments.

11. Describe the relationship between credibility and entry deterrence to a market.

    Entry deterrence relies on credibility. Without it, the claim a firm makes about its actions once new firms enter is simply an empty threat. With credible commitment, a firm’s threat can deter entrance, and allows the firm to earn greater profits than it would in a market with more firms.

12. What are some ways in which a company uses its reputation to its advantage?

    A reputation—for fighting lawsuits, for aggressively competing against new entrants, or for being unpredictable or crazy, among other actions—signals a commitment to a game-playing strategy, and can prevent new entrants to the market, as well as affect other market behaviors of competitors.