Dominant Strategies

Lesson Summary

This scene represents a prisoner’s dilemma since it’s in each person’s best interest to attack, but cooperation will yield a greater collective outcome.

Clip Summary

The players have not been intentionally underfed in an effort to motivate them to attack each other. The masked leaders admit to one of the players that it was done on purpose to eliminate weaker players. The players aren’t required to kill each other since it isn’t an official game, so they must decide: stay in bed or attack other players.

 

If all players stay in their beds, no one will be killed and all can play the next official game. If someone gets out of bed, then the players who stay in bed will likely die and the attacking player(s) may be more likely to live. By eliminating players, it makes it more likely the attacking player(s) will win the final jackpot. 

Assessment Questions

Use the payoff matrix below to answer the questions that follow. These values are not from the video, but can be used in conjunction with the scene.

Attack or Sleep Matrix.png
  1. What is Player #456’s dominant strategy?

  2. What is Player #101’s dominant strategy?

  3. What is the Nash equilibrium in this situation?

  4. Is the Nash equilibrium Pareto optimal? Why/why not?

Hover over box to see suggested answers

  1. The dominant strategy for Player #456 is to attack. If Player #101 stays in bed, Player #456 will get 10 points if he attacks or 5 points if he stays in bed. Attacking is better. If Player #101 attacks, Player #456 will get -10 points if he stays in bed or 2 points if he attacks. Attacking is better.

  2. The dominant strategy for Player #101 is to attack. If Player #456 stays in bed, Player #101 will get 10 points if he attacks or 5 points if he stays in bed. Attacking is better. If Player #456 attacks, Player #101 will get -10 points if he stays in bed or 2 points if he attacks. Attacking is better.

  3. A Nash equilibrium occurs when economic decision-makers choose the best-possible strategy after taking into account the decisions of others. This means that if each player is playing the strategy according to the Nash equilibrium, neither player would want to deviate unilaterally by playing any other strategy.

  4. The Nash equilibrium of the game is NOT Pareto Optimal because there is another outcome (both remaining in bed) in which both players would be better off: they each earn a payoff of 5 (top left corner).