INVITATION TO CYBERSECURITY 138 The traveling hacker’s dilemma is a cyber-themed retelling of a game theoretical game called the traveler’s dilemma. There are two players, Veryl and Ruth Ann, and they each have numerous choices—they can put down any dollar amount between $100 and $500. Their utility preferences are tied to their payout—they both want to take home as much money as possible. Figure 6.5 shows a small portion of the normal form version of this game. Interestingly, no matter which of these squares you start in, at least one of the players has an incentive to unilaterally change his or her answer. For example, in the square where both players submit $499, both of them have an incentive to change their answer to $498 because this would result in the $50 bonus. Like with the prisoner’s dilemma, there is a magnet pulling the players downward and to the right in the grid. None of these squares represent stable choices, and none of them are the solution to this game. The Nash equilibrium is actually the very bottom right square in the overall grid of the game. This is the square where both Veryl and Ruth Ann submit $100 and receive a $100 payout. From here, unlike all the other squares, neither player has an incentive to change his or her answer. If Veryl knows that Ruth Ann is going to submit $100, then any choice between $101 and $500 would result in only a $50 payout because he would have to absorb the penalty. So If Ruth Ann submits $100, then Veryl should also submit $100 so he can take home $100. The solution to the game for both players is to submit $100. Figure 6.5 The traveling hacker’s dilemma in normal form (partial game). It takes many iterations to start at the top-left square [500, 500] and find the Nash equilibrium of this game. With each iteration, strategies are eliminated. This is an example of the successive elimination of dominated strategies. Eventually, there is only one strategy remaining [100, 100]. This is the game theoretical solution to the game. However, when game theorists conduct studies with actual people and have them play this game, they never choose the Nash equilibrium strategy, and their end result is better than if they had chosen it. In other words, they deviate from what game theory says they should do and are rewarded for it. So is game theory wrong? There have been critics of analytical game theory from the beginning—those that maintained it was not accurate at predicting what real people would do in many types of strategic situations. The traveling hacker’s dilemma is a prime example of a type of game
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