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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.
Rollback (often referred to as backward induction) is an iterative method for solving finite in depth kind or sequential games. First, one determines the optimal strategy of the pl
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
An auction associates who submits offers (or bids) to sale or buy the goods being auctioned.
While ancient auctions involve one seller and plenty of consumers, a reverse auction typically involves several sellers and one buyer. for instance, procurement auctions are used t
A collection of colluding bidders. Ring members comply with rig bids by agreeing to not bid against one another, either by avoiding the auction or by putting phony (phantom) bids
A strategy is dominated if, no matter what the other players do, the strategy earns a player a smaller payoff than another strategy. Hence, a method is dominated if it's invariably
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
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
In any game, payoffs are numbers that represent the motivations of players. Payoffs might represent profit, quantity, "utility," or different continuous measures (cardinal payoffs)
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
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