INVITATION TO CYBERSECURITY 132 Figure 6.3 shows the hacker’s dilemma represented in normal form game theory syntax. The normal form grid captures all of the essential elements of the game: the players, their interdependent choices, and their utility preferences. Each of the four squares represent combinations of choices. In Figure 6.3, the top-left square is where Eve and Trudy both choose to cooperate. The other squares represent different combinations of cooperate and defect. In each square, the numbers represent utility preferences. The higher the number the more they prefer it. Utility is like money—the more the better! Since her name is listed on the left, Eve is the row player, and since she is listed at the top, Trudy is the column player in this game. Their choices are listed by their names. In this game, they each have the same two choices: cooperate (C) or defect (D). (In other games, players may have more than two choices, and they may have different choices from each other.) Each square contains two numbers. The row player’s utility is the first number, and the column player’s utility is the second number. What combination of choices does the bottom-left square represent? (Eve: Defect, Trudy: Cooperate.) What are Eve and Trudy’s utility preferences for this outcome? (Eve: four, Trudy: one.) Are there any other outcomes that Eve prefers more than this one? (No. Four is the highest row number in the grid, so it is her top choice—this is the result where she gets no prison time.) Does Trudy prefer any outcomes above this one? (Yes. One is the lowest column number in the grid, meaning this is Trudy’s worst outcome—this combination is where Trudy has to spend ten years in prison.) It would seem natural for the players to end up with the [C, C] outcome. This is what they agreed to do ahead of time, and it is the best of the two “fair” outcomes. They both get their second best choice. However, from both players’ perspectives, if they think they might land at [C, C], there is a big incentive to defect! No prison time is much preferable to an entire year in prison. Therefore, they are both being pulled towards defecting like a magnet. Ultimately, this results in a worse outcome for both of them. Cooperating is an unstable position that is difficult to hold, especially if one player has even the slightest suspicion that the other might defect. [D, D] is the only stable outcome in this game, meaning, from this square, neither player can unilaterally change his or her choice and end up with a better outcome. For example, if either Eve or Trudy were to change to cooperate while the other remained at defect, the one who changed would receive ten years in prison rather than five—a worse outcome. This equilibrium dynamic is called the Nash equilibrium after John Nash who proved that all finite games have at least one stable point like this (although in some games, the equilibrium is in mixed strategies, meaning that the players must assign probabilities to choices). In this game, this is the only Nash equilibrium. In all the other squares, at least one of the players could unilaterally change his or her choice and end up with a better outcome. The prisoner’s dilemma story is obviously contrived and appears to be irrelevant to real life. Most of us do not anticipate ever ending up in the backseat of a cop car making an
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