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Select all statements that are false.[Note that this quesiton allows partial marks. Each correct answer is awarded equal marks, but if you choose a wrong answer you will be awarded negative marks, with a lower bound 0, so you do not receive negative score in any question. For example, if there are two true statements, then you are awarded 1 mark for each true statement you choose, and you are awarded -1 mark for each false statement you pick.] In an extensive-form game, a Nash equilibrium cannot include non-credible threats If there are more than one subgame perfect equilibria, then a player must be indifferent between their actions at some node In an extensive-form game, the whole game tree is also a subgame. The number of subgames in an extensive form game tree equals the total number of nodes in the tree, including the terminal nodes ('leaves')

Question

Select all statements that are false.[Note that this quesiton allows partial marks. Each correct answer is awarded equal marks, but if you choose a wrong answer you will be awarded negative marks, with a lower bound 0, so you do not receive negative score in any question. For example, if there are two true statements, then you are awarded 1 mark for each true statement you choose, and you are awarded -1 mark for each false statement you pick.] In an extensive-form game, a Nash equilibrium cannot include non-credible threats If there are more than one subgame perfect equilibria, then a player must be indifferent between their actions at some node In an extensive-form game, the whole game tree is also a subgame. The number of subgames in an extensive form game tree equals the total number of nodes in the tree, including the terminal nodes ('leaves')

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Solution

The following statements are false:

  1. "In an extensive-form game, a Nash equilibrium cannot include non-credible threats." This statement is false. In an extensive-form game, a Nash equilibrium can include non-credible threats. However, these threats are not credible in subgame perfect equilibrium.

  2. "The number of subgames in an extensive form game tree equals the total number of nodes in the tree, including the terminal nodes ('leaves')." This statement is also false. The number of subgames in an extensive form game tree does not necessarily equal the total number of nodes in the tree. A subgame is defined by a single decision node (not at the beginning of the game) and all its successor nodes. Therefore, not every node in the game tree will necessarily be the start of a new subgame.

This problem has been solved

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