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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.
A strategy is strictly dominant if, no matter what the other players do, the strategy earns a player a strictly higher payoff than the other. Hence, a method is strictly dominant i
Named when Vilfredo Pareto, Pareto potency (or Pareto optimality) may be alive of potency. An outcome of a game is Pareto economical if there's no different outcome that produces e
Scenario Any game during which the identity of the player doesn't amendment the ensuing game facing that player is symmetric. In different words, every player earns identical pa
Matches or different objects are organized in 2 or a lot of piles. Players alternate removing some or all of the matches from anyone pile. The player to get rid of the last match w
please compute this number 885 for the swertres lotto game.
You and an opponent are seated at a table, and on the table is a square board. At each of the four corners of the board, there is a disc, each one red on one side and black on the
in a rectangular game pay off matrix of player a is as follows B1 B2 A1 5 7 A2 4 0 salve the game write down the pay off matrix of B and then solve the game.
A zero add game may be a special case of a continuing add game during which all outcomes involve a add of all player's payoffs of zero. Hence, a gain for one participant is usually
A sequential game is one during which players build choices (or choose a strategy) following an exact predefined order, and during which a minimum of some players will observe the
Two individuals, Player 1 and Player 2, are competing in an auction to obtain a valuable object. Each player bids in a sealed envelope, without knowing the bid of the other player.
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