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Find Pure Nash Equilibria
1. Consider a two-player game in which player 1 chooses the strategy x1 from the closed interval [-1, 1] while player 2 chooses the strategy x2 from the same closed interval [-1, 1]. Player 1's utility function is x21/2 + x1x2 and player 2's utility function is x2 2/2 - x1x2. Find and plot the best- response function of each player (against any pure strategy of the opponent). Is there a pure strategy Nash equilibrium of the game?
2. Consider a game in which player 1 chooses rows, player 2 chooses columns and player 3 chooses matrices. Only Player 3's payoffs are given below. Show that D is not a best response for player 3 against any combination of (mixed) strategies of players 1 and 2. However, prove that D is not dominated by any (mixed) strategies of player 3.
3. Consider the following three-player game and find all pure Nash Equilibria. Can you find any Nash equilibrium in which exactly two of the three players play a pure strategy while the other plays a mixed strategy (such as (B, R, ½X ½Y)). Explain by considering all possible cases.
4. Show that the following game has two types of NE: (i) player 1 chooses D, 2 chooses C with probability at least 1/3 and player 3 chooses L, and (ii) where player 1 chooses C, player 2 chooses C and 3 chooses R with probability at least ¾.
The interaction among rational, mutually aware players, where the choices of some players impacts the payoffs of others. A game is described by its players, every player's methods,
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A mixed strategy during which the player assigns strictly positive chance to each pure strategy.Morgenstern, Oskar,Coauthor of Theory of Games and Economic Behavior with John von N
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A non-cooperative game is one during which players are unable to form enforceable contracts outside of these specifically modeled within the game. Hence, it's not outlined as games
A form of a Japanese auction (which is a form of an English auction) in which bidders hold down a button as the auctioneer frequently increases the current price. Bidders irrevocab
For the section on dynamic games of competition, you can begin by asking if anyone in the class has played competi- tive tennis (club or collegiate or better); there is usually one
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How do I eliminate weakly dominated strategy
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