INVITATION TO CYBERSECURITY 140 he uses level-k reasoning to an absurd degree as he goes back and forth eliminating each cup as a possibility. In order to perform level-k reasoning, the level-0 strategy must be clearly defined. In some games, the level-0 strategy is not obvious, so not all games lend themselves to this type of analysis. Additionally, in repeated play games, the level-k strategies change after each play. This is because players learn from one another and their expectations for the level-0 strategy (i.e., the most obvious strategy) are reset. For example, in rock paper scissors, for the first play, scissors is the level-2 strategy, but in subsequent plays, the winning strategy from the previous play arguably becomes the level-0 strategy for the next play. Experimental results show that most people choose level-0 or level-1 strategies and rarely if ever go beyond the level-3 strategy. They may stop descending because going deeper becomes too confusing or because they assume others will not keep going. Studies show that level-2 and level-3 strategies are the sweet spot because this anticipates what most people are going to do and one-ups them. As is hopefully clear, level-k reasoning is helpful in performing a strategic analysis, but it is not an exact science. It would suggest that in the traveling hacker’s dilemma, Veryl should submit either $498 (level-2) or $497 (level-3), but of course, this does not guarantee an optimal outcome. However, it is highly likely that applying level-k reasoning in such a game would result in a much better outcome than the Nash equilibrium solution. 6.3.1 Level-k Reasoning in Security Games The hide and seek game is helpful for thinking about various ways that level-k reasoning can apply to strategic situations.4 In this game, one player (the hider) has hidden money in one of four boxes arranged in a row (see Figure 6.6). The other player (the seeker) has one chance to guess where the money is hidden. If the seeker guesses correctly, he wins the money, otherwise the hider gets to keep the money. Game theory predicts that the seekers will win 25% of the time since there are four choices, and technically, all four choices are equally likely. But experiments show that seekers win 33% of the time. Clearly, the second box changes the dynamics of this game. It illustrates focal point biases—people tend to focus on unusual features. In this game, players immediately focus on the B box because it is different from the other three. 4 This section draws on findings from the following journal article: A. Rubinstein, “Experience from a course in game theory: pre- and post-class problem sets as a didactic device,” Games and Economic Behavior, vol. 28, iss. 1, pp. 155-170, 1999.
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