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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.
An auction during which bidders simultaneously submit bids to the auctioneer while not information of the number bid by different participants. Usually, the very best bidder (or lo
Scenario The French thinker, Jean Jacques Rousseau, presented the subsequent state of affairs. 2 hunters will either jointly hunt a stag (an adult deer and rather massive meal)
A sub game excellent Nash equilibrium is an equilibrium such that players' methods represent a Nash equilibrium in each sub game of the initial game. it should be found by backward
Ordinal payoffs are numbers representing the outcomes of a game where the worth of the numbers isn't vital, however solely the ordering of numbers. for instance, when solving for a
In any game, payoffs are numbers that represent the motivations of players. Payoffs might represent profit, quantity, "utility," or different continuous measures (cardinal payoffs)
Combining Simultaneous and Sequential Moves The material in this chapter covers a variety of issues that require some knowledge of the analysis of both sequential- move
Players 1 and 2 are bargaining over how to split one dollar. Both players simultaneously name shares they would like to keep s 1 and s 2 . Furthermore, players' choices have to be
. A bid is an sign by a potential buyer of the price the buyer is ready to pay for the object being auctioned. In a Procurement Auction, the bid is an sign of the price a seller is
Rollback shows that Boeing chooses peace over war if Airbus enters, so Airbus will enter. Rollback equilibrium entails Airbus playing “Enter” and Boeing playing “Peace if entry”; e
1. Two firms, producing an identical good, engage in price competition. The cost functions are c 1 (y 1 ) = 1:17y 1 and c 2 (y 2 ) = 1:19y 2 , correspondingly. The demand functi
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