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List all the consistent assessments, and all the sequentially rational assessments of the following game.
What is the corresponding belief of Player II at his information sets? Justify your answer.
Find all the sequential equilibria of the following game. Provide complete and step by step solution for the question and show calculations and use formulas.
The following example shows that the set of sequential equilibria is sensitive to the way in which a player makes decisions: it makes a difference.
In an extensive-form game with perfect recall, is every Nash equilibrium part of a sequential equilibrium?
Pre-trial settlement A contractor is being sued for damages by a municipality that hired him to construct a bridge, because the bridge has collapsed.
Describe this situation as an extensive-form game, where the root of the game tree is a chance move that determines whether Caesar is brave.
Henry seeks a loan to form a new company, and submits a request for a loan to Rockefeller.
Prove Theorem for every Nash equilibrium s* in a strategic-form game, the probability distribution ps* that s* induces on the set of action vectors S.
Prove that if a player in an extensive-form game has only one information set, then his set of mixed strategies equals his set of behavior strategies.
Suppose that there is a strategy vector s-i of the other players such that ?(x; si, s-i) > 0 for each leaf x in the game tree.
Let i be a player with perfect recall in an extensive-form game and let bi be a behavior strategy of player i.
In the following two-player zero-sum game, find the optimal behavior strategies of the two players. (Why must such strategies exist?)
Compute the value of the following game, in mixed strategies, and in behavior strategies, if these values exist.
Adding information to one of the players does not increase the maxmin or the minmax value of the other players.
Suppose that a symmetric two-player game, in which each player has two pure strategies and all payoffs are nonnegative.
Explain why the evolutionarily stable strategy is that at which the number of male leopards born equals the number of females born.
Prove that if the payoff matrix of a two-player zero-sum game is antisymmetric, then the value of the game in mixed strategies is 0.
Is si chosen with positive probability in each of player i’s maxmin strategies? Prove this claim, or provide a counterexample.
Is si chosen with positive probability in one of player i’s maxmin strategies? Prove this claim, or provide a counterexample.
Find a mixed strategy of Player I that guarantees him the same payoff against any pure strategy of Player II.
What inequalities must the numbers a, b, c, d satisfy? Find the value in mixed strategies of this game.
Prove that in any n-person game, at Nash equilibrium, each player’s payoff is greater than or equal to his maxmin value.
For each of the following games, where Player I is the row player and Player II is the column player-Write out the mixed extension of the game.
The value of the two-player zero-sum game given by the matrix A is 0. Is it necessarily true that the value of the two-player zero-sum game.