Exam 24: Strategic Thinking and Game Theory

If a separating equilibrium is played in a signaling game,the receiver will "update" his beliefs during the game.

In a simultaneous move,incomplete information game in which player 1 is unsure of which of two types player 2 is,player 1's strategy must include an action for each possible type that player 2 might be,but player 2 only needs to pick one action since he knows what type he is.

If a player's strategy in a sequential game is to choose an action that stops the game early on,it is unnecessary to specify that player's plans for moves later on in the game when it would have been his turn to move again.

Suppose a player can play 2 possible actions and has 5 possible decision nodes in a sequential game.Then he has 10 possible strategies he can play.

Consider the following sequential move game: a.What are the subgame perfect equilibrium strategies in this game? b.List all possible strategies for the two players. c.Illustrate this game in a payoff matrix. d.Indicate the Nash equilibria in the payoff matrix from (c). e.What makes some of the Nash equilibria not subgame perfect?

Non-credible threats that are made in a Nash equilibrium (that is not subgame perfect)of a sequential game cannot be made in the first stage by the player who begins the game.

If a pooling equilibrium is played in a signaling game,beliefs about the sender type can take on any form along the branch of the game tree that is not played in equilibrium,but on the branch that is played,beliefs are identical to the probability distribution with which "nature" assigned types to the sender.

If players discount the future sufficiently,cooperation in infinitely repeated Prisoners' Dilemma games cannot emerge as a subgame perfect equilibrium.

Suppose a player in a sequential game has 5 potential decision nodes,with 2 possible actions at each node.Then he has 25 possible pure strategies.

If all players in a game have a dominant strategy,then there can only be one pure strategy Nash equilibrium to the game.

In a Bayesian incomplete information game,a "belief" is represented as the probability you place on your opponent playing one strategy versus another.

If everyone has a dominant strategy in a simultaneous move game,then the action that is played by that strategy is played in all stages of any finitely repeated version of that game in any subgame perfect equilibrium.

A mixed strategy in which positive probability is placed on more than one action can be a best response to another player's strategy only if the expected payoff from playing the pure strategies (over which the individual is mixing)is the same.

In any subgame perfect equilibrium to an infinitely repeated Prisoners' Dilemma game,the players will end up cooperating.