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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.
Consider the electoral competition game presented in Lecture 6. In this game there are two candidates who simultaneously choose policies from the real line. There is a distribution
In any game, utility represents the motivations of players. A utility perform for a given player assigns variety for each potential outcome of the sport with the property that a be
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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Identification is a problem of model formultion, rather than inf nlnde! estimation or appraisal. We say a model is identified if it is in a unique statistical form, enabling unique
write a program in c that takes n number finite players using gambit format and output is to be all pure strategy nash equilibrium
The strategic (or normal) kind may be a matrix illustration of a simultaneous game. for 2 players, one is that the "row" player, and also the different, the "column" player. every
A priori knowledge usually enables us to decide that some coefficients must be zero in the particular equation, while they assume non-zero values in other equations of the system.
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