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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 other. You are blindfolded, and thus cannot see the configuration of the discs, but you claim that you can flip the discs such that they are all facing with the same color up. On each move, you can flip either one or two discs (either adjacent or diagonal to each other). If this results in a winning state, your opponent must announce that. Otherwise, your opponent may choose to rotate the board 0°, 90°, 180°, or 270°. Find the shortest sequence of moves that is guaranteed to win the game, no matter what rotations of the board are made. Be sure to include a proof that your solution is correct and that it is the shortest possible.
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
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
A strategy defines a collection of moves or actions a player can follow in a very given game. a method should be complete, defining an action in each contingency, together with peo
1. The publishing industry in the country of Font, where the local currency is the stet, is dominated by two companies, the Arial Book Co. and Verdana Works Ltd.. Currently, both o
Find Pure Nash Equilibria 1. Consider a two-player game in which player 1 chooses the strategy x 1 from the closed interval [-1, 1] while player 2 chooses the strategy x 2 fr
Three flowcharts and the game board for your mousetrap game should be submitted. You can use board_design.pdf to help you lay out your board. Basically, you can use any shapes you
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An item of information of data in a very game is common grasp ledge if all of the players realize it (it is mutual grasp ledge) and every one of the players grasp that each one dif
The 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 rows or column
Scenario Two corporations should simultaneously elect a technology to use for his or her compatible merchandise. If the corporations adopt totally different standards, few sales
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