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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.
Scenario To determine who is needed to try to to the nightly chores, 2 youngsters simultaneously build one among 3 symbols with their fists - a rock, paper, or scissors. straigh
1. Consider two firms producing an identical product in a market where the demand is described by p = 1; 200 2Y. The corresponding cost functions are c 1 (y 1 ) = y 2 1 and c 2
A pure strategy defines a selected move or action that a player can follow in each potential attainable state of affairs in a very game. Such moves might not be random, or drawn fr
A game frequently displayed in tv police dramas. 2 partners in crime are separated into separate rooms at the police station and given an identical deal. If one implicates the oppo
Equilibrium payoffs a) The reward system changes payoffs for Player A, but does not change the equilibrium strategies in the game. Player A still takes the money at the fir
Scenario As described by William Poundstone, imagine that you just notice that electricity has gone out for your entire neighborhood. the electrical company can send somebody to
Ship, Captain and Crew (sometimes called Ship, Captain and Mate) was a popular bar game played for drinks with five dice and throwing cup. Each player gets three throws. He has to
Borel was maybe the primary to outline the notion of games of strategy. He printed many papers on poker, incorporating themes of imperfect data and credibility. Whereas his writing
Tower defense - is a subgenre of real-time strategy games. The goal of tower defense games is to try to stop enemies from crossing a map by building towers which shoot at them as t
Computer Game Zenda This game was invented by James Andreoni and Hal Varian; see their article, "Pre-Play Contracting in the Prisoners 'Dilemma".The paper also contains some co
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