494 PART • Market Structure and Competitive Strategy Ocean 200 yards A Y C Beach Figure 13.1 BEACH LOCATION GAME You (Y) and a competitor (C) plan to sell soft drinks on a beach If sunbathers are spread evenly across the beach and will walk to the closest vendor, the two of you will locate next to each other at the center of the beach This is the only Nash equilibrium If your competitor located at point A, you would want to move until you were just to the left, where you could capture three-fourths of all sales But your competitor would then want to move back to the center, and you would the same The “beach location game” can help us understand a variety of phenomena Have you ever noticed how, along a two- or three-mile stretch of road, two or three gas stations or several car dealerships will be located close to each other? Likewise, as a U.S presidential election approaches, the Democratic and Republican candidates typically move close to the center as they define their political positions Maximin Strategies The concept of a Nash equilibrium relies heavily on individual rationality Each player’s choice of strategy depends not only on its own rationality, but also on the rationality of its opponent This can be a limitation, as the example in Table 13.4 shows In this game, two firms compete in selling file-encryption software Because both firms use the same encryption standard, files encrypted by one firm’s software can be read by the other’s—an advantage for consumers Nonetheless, Firm has a much larger market share (It entered the market earlier and its software has a better user interface.) Both firms are now considering an investment in a new encryption standard Note that investing is a dominant strategy for Firm because by doing so it will better regardless of what Firm does Thus Firm should expect Firm to invest In this case, Firm would also better by investing (and earning TABLE 13.4 MAXIMIN STRATEGY Firm Don’t invest Firm Don’t invest Invest Invest 0, ؊10, 10 ؊100, 20, 10