Defining Nash Equilibrium 91 which ensures that a player’s strategy is optimal, given the other players’ strate- gies. Thus, all players are simultaneously doing their best. A violation of one or more of those conditions means that a strategy profile is not a Nash equilib- rium. Unlike the game of horseshoes, you don’t come “close […]
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Defining Nash Equilibrium Defining Nash Equilibrium DreamWorks initially threw down the gauntlet in the clash of the ’toon titans way back in June 2002, claiming a release date of November 5, 2004 for Sharkslayer. . . . The studio’s staking out of the November date was seen as a slap at Disney, which has traditionally
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Appendix: Rationalizability (Advanced) 85 the game that is derived by deleting strictly dominated strategies from the original game. Continuing in this manner, we derived the strategies that sur- vive the IDSDS. As just described, the IDSDS eliminates what players would not do if ra- tionality were common knowledge. But what is it that they would
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Prove that abstaining is not a weakly dominated strategy. �12 1 2 1 2 1 2 7 8 1 8 e μ 3.5 Appendix: Strict and Weak Dominance CONSIDER A GAME WITH n players: 1, 2, . . ., n. Let Si denote player i’s strategy set, and read as “strategy is a member of
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CHECK YOUR UNDERSTANDING Exercises 79 auction—the presence of a weakly dominant strategy is a good choice for the cautious player. A procedure known as the iterative deletion of strictly dominated strate- gies (IDSDS) builds on the idea that a rational player does not use a strictly dominated strategy. The key assumption of IDSDS is that
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Reduced Game After Two Rounds of IDSDS 3,2 5,1 1,3Player 1 Player 2 a c d 0,4 1,4 4,2 w z FIGURE 3.26 Reduced Game After Three Rounds of IDSDS 5,1 1,3 Player 1 Player 2 c d 1,4 4,2 w z Summary This chapter outlines methods for solving a game when players are rational,
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The IDSDS algorithm is defined by the following series of steps: Step 1 Delete all strictly dominated strategies from the original game. (This step is predicated on the assumption that players are ra- tional.) Step 2 Delete all strictly dominated strategies from the game derived after performing step 1. (This step is predicated on the
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If Bonds did take steroids, was it a reaction to remaining competitive with the other top home-run hitters in baseball? Suppose each of the athletes is rational and each believes that the others believe that he is rational. However, each athlete is unsure whether the other athletes are rational. For example, Carl is rational and
What will these athletes do? What will these athletes do? Rationality doesn’t shed any light on what Carl and Maurice will do, as their usage depends on what the other athletes are ex- pected to do. However, Ben has a dominant strategy of taking steroids, as shown in FIGURE 3.18. If neither Carl nor Maurice
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The Doping Game: Is It Rational for Athletes to Use Steroids? The Doping Game: Is It Rational for Athletes to Use Steroids? On August 7, 2007, baseball player Barry Bonds hit his 756th career home run, surpassing the career record of 755 home runs by Henry Aaron. Although this should be a time of awe
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