Lecture 7 - Game Theory - 5ECON010C PDF

Lecture 7 Game theory 5ECON010C-n Intermediate Microeconomics Game Theory & Competitive Strategy LECTURE OUTLINE 1. Gaming and Strategic Decisions 2. Dominant Strategies 3. The Nash Equilibrium Revisited 4. Sequential Games 5. Threats, Commitments and Credibility 6. Entry Deterren...

Lecture 7 Game theory 5ECON010C-n Intermediate Microeconomics Game Theory & Competitive Strategy LECTURE OUTLINE 1. Gaming and Strategic Decisions 2. Dominant Strategies 3. The Nash Equilibrium Revisited 4. Sequential Games 5. Threats, Commitments and Credibility 6. Entry Deterrence Copyright © 2016, 2012, 2009 Pearson Education, Inc. All Rights Reserved Gaming and Strategic Decisions Game: Situation in which players (participants) make strategic decisions that take into account each other’s actions and responses. Payoff: Value associated with a possible outcome. Strategy: Rule or plan of action for playing a game. Optimal strategy: Strategy that maximizes a player’s expected payoff. If I believe that my competitors are rational and act to maximize their own payoffs, how should I take their behavior into account when making my decisions? Determining optimal strategies can be difficult, even under conditions of complete symmetry and perfect information. Gaming and Strategic Decisions Noncooperative versus Cooperative Games Cooperative game: Game in which participants can negotiate binding contracts that allow them to plan joint strategies. Noncooperative game: Game in which negotiation and enforcement of binding contracts are not possible. Note that the fundamental difference between cooperative and noncooperative games lies in the contracting possibilities. In cooperative games, binding contracts are possible; in noncooperative games, they are not. It is essential to understand your opponent’s point of view and to deduce his or her likely responses to your actions. The Nash Equilibrium Revisited Dominant Strategies: I’m doing the best I can no matter what you do. You’re doing the best you can no matter what I do. Nash Equilibrium: I’m doing the best I can given what you are doing. You’re doing the best you can given what I am doing. Dominant Strategies Dominant strategy: Strategy that is optimal no matter what an opponent does. TABLE 13.1 PAYOFF MATRIX FOR ADVERTISING GAME FIRM B ADVERTISE DON’T ADVERTISE ADVERTISE 10, 5 15, 0 FIRM A DON’T ADVERTISE 6, 8 10, 2 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. The outcome for this game is that both firms will advertise. 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. Dominant Strategies Unfortunately, not every game has a dominant strategy for each player. TABLE 13.2 MODIFIED ADVERTISING GAME FIRM B ADVERTISE DON’T ADVERTISE ADVERTISE 10, 5 15, 0 FIRM A DON’T ADVERTISE 6, 8 20, 2 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. Sequential Games Sequential game: Game in which players move in turn, responding to each other’s actions and reactions. One firm sets output before the other does. The Stackelberg model is an example. In a sequential game, the key is to think through the possible actions and rational reactions of each player. TABLE 13.9 MODIFIED PRODUCT CHOICE PROBLEM FIRM 2 CRISPY SWEET CRISPY –5, –5 10, 20 FIRM 1 SWEET 20, 10 –5, –5 Suppose that both firms, in ignorance of each other’s intentions, must announce their decisions independently and simultaneously. In that case, both will probably introduce the sweet cereal—and both will lose money. In a sequential game, Firm 1 introduces a new cereal, and then Firm 2 introduces one. Sequential Games Extensive form of a game: Representation of possible moves in a game in the form of a decision tree. FIGURE 13.2 PRODUCT CHOICE GAME IN EXTENSIVE FORM Although this outcome can be deduced from the payoff matrix in Table 13.9, sequential games are sometimes easier to visualize if we represent the possible moves in the form of a decision tree. To find the solution to the extensive form game, work backward from the end. Threats, Commitments, and Credibility In the product-choice problem shown in Table 13.9, the firm that introduces its new breakfast cereal first will do best. Each has an incentive to commit itself first to the sweet cereal. Firm 1 must constrain its own behavior in some way that convinces Firm 2 that Firm 1 has no choice but to produce the sweet cereal. Firm 1 might launch an expensive advertising campaign, or contract for the forward delivery of a large quantity of sugar (and make the contract public). Firm 1 can’t simply threaten Firm 2 because Firm 2 has little reason to believe the threat—and can make the same threat itself. A threat is useful only if it is credible. FIRM 2 CRISPY SWEET CRISPY –5, –5 10, 20 Firm 1 SWEET 20, 10 –5, –5 Threats, Commitments, and Credibility Empty Threats As in Chapter 12, we will use the example in which two duopolists face the market demand curve 𝑃 = 30 − 𝑄. TABLE 13.11 PRICING OF COMPUTERS AND WORD PROCESSORS FIRM 2 FIRM 2 HIGH PRICE LOW PRICE FIRM 1 HIGH PRICE 100, 80 80, 100 FIRM 1 LOW PRICE 20, 0 10, 20 As long as Firm 1 charges a high price for its computers, both firms can make a good deal of money. Firm 1 would prefer the outcome in the upper left-hand corner of the matrix. For Firm 2, however, charging a low price is clearly a dominant strategy. Thus, the outcome in the upper right-hand corner will prevail (no matter which firm sets its price first). Question: Can Firm 1 induce Firm 2 to charge a high price by threatening to charge a low price if Firm 2 charges a low price Threats, Commitments, and Credibility Empty Threats As in Chapter 12, we will use the example in which two duopolists face the market demand curve 𝑃 = 30 − 𝑄. TABLE 13.11 PRICING OF COMPUTERS AND WORD PROCESSORS FIRM 2 FIRM 2 HIGH PRICE LOW PRICE FIRM 1 HIGH PRICE 100, 80 80, 100 FIRM 1 LOW PRICE 20, 0 10, 20 Can Firm 1 induce Firm 2 to charge a high price by threatening to charge a low price if Firm 2 charges a low price? No. Whatever Firm 2 does, Firm 1 will be much worse off if it charges a low price. As a result, its threat is not credible. Threats, Commitments, and Credibility Commitment and Credibility TABLE 13.12(a) PRODUCTION CHOICE PROBLEM RACE CAR MOTORS RACE CAR MOTORS SMALL CARS BIG CARS FAR OUT ENGINES SMALL ENGINES 3, 6 3, 0 FAR OUT ENGINES BIG ENGINES 1, 1 8, 3 Can Far Out induce Race Car to produce big cars instead of small ones? Suppose Far Out threatens to produce big engines. If Race Car believed Far Out’s threat, it would produce big cars. But the threat is not credible. Far Out can make its threat credible by visibly and irreversibly reducing some of its own payoffs in the matrix, thereby constraining its own choices. It might do this by shutting down or destroying some of its small engine production capacity. This would result in the payoff matrix shown in Table 13.12(b). Threats, Commitments, and Credibility Commitment and Credibility TABLE 13.12(b) MODIFIED PRODUCTION CHOICE PROBLEM RACE CAR MOTORS RACE CAR MOTORS SMALL CARS BIG CARS FAR OUT ENGINES SMALL ENGINES 0, 6 0, 0 FAR OUT ENGINES BIG ENGINES 1, 1 8, 3 Now Race Car knows that whatever kind of car it produces, Far Out will produce big engines. Now it is clearly in Race Car’s interest to produce large cars. By taking an action that seemingly puts itself at a disadvantage, Far Out has improved its outcome in the game. Although strategic commitments of this kind can be effective, they are risky and depend heavily on having accurate knowledge of the payoff matrix and the industry. Suppose, for example, that Far Out commits itself to producing big engines but is surprised to find that another firm can produce small engines at a low cost. The commitment may then lead Far Out to bankruptcy rather than continued high profits. Threats, Commitments, and Credibility Bargaining Strategy TABLE 13.13 PRODUCTION DECISION: Complementary Goods FIRM 2 FIRM 2 PRODUCE A PRODUCE B FIRM 1 PRODUCE A 40, 5 50, 50 FIRM 1 PRODUCE B 60, 40 5, 45 Here, the firms produce two complementary goods. Because producing B is a dominant strategy for Firm 2, (A, B) is the only Nash equilibrium. Threats, Commitments, and Credibility Bargaining Strategy TABLE 13.14 DECISION TO JOIN CONSORTIUM FIRM 2 FIRM 2 WORK ALONE ENTER CONSORTIUM FIRM 1 WORK ALONE 10, 10 10, 20 FIRM 1 ENTER CONSORTIUM 20, 10 40, 40 Suppose, however, that Firms 1 and 2 are bargaining over to join a research consortium that a third firm is trying to form, and Firm 1 announces that it will join the consortium only if Firm 2 agrees to produce product A. In this case, it is indeed in Firm 2’s interest to produce A (with Firm 1 producing B).  Bargaining power Credible threats give one party a bargaining power You know what is that if you ever visited any local market What kind of credible threats can help a buyer in bargain? 5ECON010C-n Intermediate Microeconomics EXAMPLE 13.4 WAL-MART STORES’ PREEMPTIVE INVESTMENT STRATEGY How did Wal-Mart Stores succeed where others failed? The key was Wal-Mart’s expansion strategy. To charge less than ordinary department stores and small retail stores, discount stores rely on size, no frills, and high inventory turnover. Through the 1960s, the conventional wisdom held that a discount store could succeed only in a city with a population of 100,000 or more. Sam Walton disagreed and decided to open his stores in small Southwestern towns. The stores succeeded because Wal-Mart had created 30 “local monopolies.” Discount stores that had opened in larger towns and cities were competing with other discount stores, which drove down prices and profit margins. These small towns, however, had room for only one discount operation. There are a lot of small towns in the United States, so the issue became who would get to each town first. Wal-Mart now found itself in a preemption game of the sort illustrated by the payoff matrix in Table 13.15. EXAMPLE 13.4 WAL-MART STORES’ PREEMPTIVE INVESTMENT STRATEGY This game has two Nash equilibria—the lower left-hand corner and the upper right-hand corner. Which equilibrium results depends on who moves first. The trick, therefore, is to preempt—to set up stores in other small towns quickly, before Company X (or Company Y or Z) can do so. By 1986, it had 1009 stores in operation and was earning an annual profit of $450 million. And while other discount chains were going under, Wal-Mart continued to grow. By 1999, Wal-Mart had become the world’s largest retailer, with 2454 stores in the United States and another 729 stores in the rest of the world, and had annual sales of $138 billion. In recent years, Wal-Mart has continued to preempt other retailers by opening discount and grocery stores (Wal-Mart Supercenters) all over the world. TABLE 13.15 THE DISCOUNT STORE PREEMPTION GAME COMPANY X COMPANY X ENTER DON’T ENTER WAL-MART ENTER –10 , –10 20, 0 WAL-MART DON’T ENTER 0, 20 0, 0 Entry Deterrence To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable. TABLE 13.16(a) ENTRY POSSIBILITIES POTENTIAL ENTRANT POTENTIAL ENTRANT ENTER STAY OUT INCUMBENT HIGH PRICE 100, 20 200, 0 (ACCOMMODATION) INCUMBENT LOW PRICE (WARFARE) 70, –10 130, 0 If Firm X thinks you will be accommodating and maintain a high price after it has entered, it will find it profitable to enter and will do so. Suppose you threaten to expand output and wage a price war in order to keep X out. If X takes the threat seriously, it will not enter the market because it can expect to lose $10 million. The threat, however, is not credible. As Table 13.16(a) shows, once entry has occurred, it will be in your best interest to accommodate and maintain a high price. Firm X’s rational move is to enter the market; the outcome will be the upper left-hand corner of the matrix. Entry Deterrence TABLE 13.16(b) ENTRY DETERRENCE Blank Cell Blank Cell POTENTIAL ENTRANT POTENTIAL ENTRANT Blank Cell Blank Cell ENTER STAY OUT INCUMBENT HIGH PRICE 50, 20 150, 0 (ACCOMMODATION) INCUMBENT LOW PRICE (WARFARE) 70, –10 130, 0 If you can make an irrevocable commitment to invest in additional capacity, your threat to engage in competitive warfare is completely credible. With the additional capacity, you will do better in competitive warfare than you would by maintaining a high price. Meanwhile, having deterred entry, you can maintain a high price and earn a profit of $150 million. If the game were to be indefinitely repeated, then the incumbent might have a rational incentive to engage in warfare whenever entry actually occurs. Why? Because short term losses from warfare might be outweighed by longer-term gains from preventing entry. Finally, by fostering an image of irrationality and belligerence, an incumbent firm might convince potential entrants that the risk of warfare is too high. Entry Deterrence (4 of 5) THE COMMERCIAL AIRCRAFT MARKET Suppose that Boeing and Airbus Suppose it is only economical for one firm to produce the new aircraft. TABLE 13.17(a) DEVELOPMENT OF A NEW AIRCRAFT AIRBUS AIRBUS PRODUCE DON’T PRODUCE BOEING PRODUCE –10, –10 100, 0 BOEING DON’T PRODUCE 0, 100 0, 0 If Boeing has a head start in the development process, the outcome of the game is the upper right-hand corner of the payoff matrix. European governments, of course, would prefer that Airbus produce the new aircraft. If the European governments commit to a subsidy of 20 to Airbus if it produces the plane regardless of what Boeing does, the payoff matrix would change to the one in Table 13.17(b). Entry Deterrence TABLE 13.17(a) DEVELOPMENT OF A NEW AIRCRAFT AFTER EUROPEAN SUBSIDY AIRBUS AIRBUS PRODUCE DON’T PRODUCE BOEING PRODUCE –10, –10 100, 0 BOEING DON’T PRODUCE 0, 120 0, 0 Boeing knows that even if it commits to producing, Airbus will produce as well, and Boeing will lose money. Thus Boeing will decide not to produce, and the outcome will be the one in the lower left-hand corner. A subsidy of 20, then, changes the outcome from one in which Airbus does not produce and earns 0, to one in which it does produce and earns 120. Of this, 100 is a transfer of profit from the United States to Europe. From the European point of view, subsidizing Airbus yields a high return. European governments did commit to subsidizing Airbus, and during the 1980s, Airbus successfully introduced several new airplanes. As commercial air travel grew, it became clear that both companies could profitably develop and sell new airplanes. Nonetheless, Boeing’s market share would have been much larger without the European subsidies to Airbus.  Reading Mandatory reading Pindyck & Rubinfeld (2015). “Microeconomics”, 8th edition. Chapter 13 Optional reading https://www.sciencedirect.com/science/article/pii/S157400050580013X How digital business disrupts the five forces of industry competition. (1,100), https://www.cio.com/article/2976572/digital-disruption-from-the- perspective-of-porters-five-forces-framework.html 5ECON010C-n Intermediate Microeconomics