CHAPTER 13 • Game Theory and Competitive Strategy 491 TABLE 13.1 PAYOFF MATRIX FOR ADVERTISING GAME Firm B Firm A Advertise Don’t advertise Advertise 10, 15, Don’t advertise 6, 10, What strategy should each firm choose? First consider Firm A It should clearly advertise because no matter what firm B does, Firm A does best by advertising If Firm B advertises, A earns a profit of 10 if it advertises but only if it doesn’t If B does not advertise, A earns 15 if it advertises but only 10 if it doesn’t Thus advertising is a dominant strategy for Firm A The same is true for Firm B: No matter what firm A does, Firm B does best by advertising Therefore, assuming that both firms are rational, we know that the outcome for this game is that both firms will advertise This outcome is easy to determine because both firms have dominant strategies When every player has a dominant strategy, we call the outcome of the game an equilibrium in dominant strategies Such games are straightforward to analyze because each player’s optimal strategy can be determined without worrying about the actions of the other players Unfortunately, not every game has a dominant strategy for each player To see this, let’s change our advertising example slightly The payoff matrix in Table 13.2 is the same as in Table 13.1 except for the bottom right-hand corner—if neither firm advertises, Firm B will again earn a profit of 2, but Firm A will earn a profit of 20 (Perhaps Firm A’s ads are expensive and largely designed to refute Firm B’s claims, so by not advertising, Firm A can reduce its expenses considerably.) Now Firm A has no dominant strategy Its optimal decision depends on what Firm B does If Firm B advertises, Firm A does best by advertising; but if Firm B does not advertise, Firm A also does best by not advertising Now suppose both firms must make their decisions at the same time What should Firm A do? To answer this, Firm A must put itself in Firm B’s shoes What decision is best from Firm B’s point of view, and what is Firm B likely to do? The answer is clear: Firm B has a dominant strategy—advertise, no matter what Firm A does (If Firm A advertises, B earns by advertising and by not advertising; if A doesn’t advertise, B earns if it advertises and if it doesn’t.) Therefore, Firm A can conclude that Firm B will advertise This means that Firm A should advertise (and thereby earn 10 instead of 6) The logical outcome of the game is that both firms will advertise because Firm A is doing the best it can given Firm B’s decision; and Firm B is doing the best it can given Firm A’s decision TABLE 13.2 MODIFIED ADVERTISING GAME Firm B Firm A Advertise Don’t advertise Advertise 10, 15, Don’t advertise 6, 20, • equilibrium in dominant strategies Outcome of a game in which each firm is doing the best it can regardless of what its competitors are doing