Game Theory • Greater attention in business is being given to tactics and strategy to achieve competitive advantage. • The development of strategic and tactical choices can be analyzed using a “game theory” framework. • This chapter allows the prediction of rival firm behavior as if they were games. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 1 Oligopolistic Rivalry and Game Theory • Game Theory – a theory of interdependent decision making by the participants in a conflict of interest or opportunity-for- collaboration situation. » Examples: Pricing of a few firms; Strategic Arms Race; Advertising plans for a few firms; Output decisions of an oligopoly © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 2 Oligopolistic Rivalry and Game Theory • Strategy--is a course of action (raise price, lower price, expand output, contract output, and the like) » The PAYOFF is the outcome of the strategy. » » Listing of PAYOFFS appear in a payoff matrix. • A Strategy Game – a decision-making situation with consciously interdependent behavior between two or more participants. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 3 Simple Two Person, Zero Sum Game • • • • • ASSUMPTIONS PLAYER 2 Each player knows both his and his opponent’s alternatives c d Preferences of all players are known 3, -3 a 1, -1 Single period game PLAYER 1 Sum of payoffs are zero » Like a Poker Game b -2, 2 0, 0 An Equilibrium (or Nash Equilibrium) -- if none of the Player 1 is the first number in participants can improve their each pair. We will get to {a,c} payoff which is an Equilibrium © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 4 Dominant Strategies & Dominated Strategies • For Player 1, strategy (a) is a PLAYER 2 dominant strategy - an action that maximizes the decision maker’s c d welfare independent of the actions of the other players. 1, -1 3, -3 a » Also, strategy (b) is a dominated strategy, which is worst PLAYER 1 regardless of what others do 0, 0 b -2, 2 • Player 2 also has a dominant strategy of (c). With dominant strategies of (a) • Dominant strategies make games easy to solve. for Player 1 and ( c) for Player 2, the solution will be {a, c}, which is an Equilibrium. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 5 Two Person Game, Non-Zero Sum Game: ASSUMPTIONS TV Show Survivor Table 13. 1 • Each player can invade the territory of the other (Maraude) or Guard his own territory • Kahn’s payoff is given first. • Randle always ranks Guard above Maraude, so Randle has a Dominant Strategy • Knowing what Randle will do, Kahn decides to Guard as well. • An Equilibrium--none of the participants can improve their payoff Randle Guard Maraude st Worst, 4th Better, 1 Guard Kahn Maraude Worse, 2nd Best, 3rd We will get to {Guard, Guard} which is an Equilibrium © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 6 Unstable Games: No Equilibrium Is Found Lem • Suppose Zelda thinks c d that the solution is going to be: {b, c} a 3, - 3 1, - 1 • Then, Zelda has an Zelda b 2, - 2 4, - 4 incentive to switch to strategy-a There is no, single stable equilibrium • Then Lem has an Each player may elect a random incentive to switch to strategy strategy-d, etc., etc. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 7 Iterated Dominant Strategy • Sharp and Xerox compete in copiers. Payoffs for Xerox are in the lower triangle • The payoffs depend on the number of territories in which they compete • Sharp has a dominant strategy of 6 territories. • What should Xerox do? • We see we get to {6, 6} as the iterated dominate strategy – an action rule that maximizes selfinterest in light of the predictable dominant-strategy behavior of the other players. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 8 Other Types of Strategic Games • These are viewed as single period, but businesses tend to be on-going, or multi-period games • These are two-person games, but oligopolies often represent N-person games (N >2), • Some games are zero-sum games in that what one player wins, the other player loses, like a game of poker © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 9 Other Types of Strategic Games • Other games are non-zero sum games where the whole payoffs depend on strategy choices by all players. • Some games are cooperative that allow binding coalitions. • Some games are noncooperative that prohibit coalitions. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 10 The Prisoner’s Dilemma: most famous non-zero sum game • Often the payoffs vary depending on the strategy choices • The Prisoner’s Dilemma » Two suspects are caught & held separately • Their strategies are either to Confess (C) or Not Confess (NC) » a one period game » Suspect 1’s payoffs are in the lower triangle (underlined and in bold ) • Noncooperative Solution » both confess: {C, C} • Cooperative Solution » both do not confess {NC,NC} • Off-diagonal represent a Double Cross suspect 2 NC C 1 yr NC suspect 1 C 1 yr 15 yrs 0 yrs 0 yrs 15 yrs 6 yrs 6 yrs Table 13.3 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 11 Solving the Prisoner’s Dilemma • Suppose each suspect is pessimistic and follows the Maximin Strategy » This is the strategy that minimizes the absolute losses. » Look at each strategy, find the worst thing that can occur, and then selects the Best among the worst. • For suspect 1, the worst case scenario for Not Confessing is 15 years in prison. The worst case scenario for Confessing is 6 years in prison. Therefore, the Maximin Strategy would be to CONFESS. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 12 Solving the Prisoner’s Dilemma • The maximin strategy for suspect 2 is also CONFESS • It turns out that { Confess, Confess } is also an equilibrium, since switching to Not Confess is undesirable for each player separately. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 13 Why is it called a Paradox? • The Prisoner’s Dilemma highlights the situation where both parties would be best off if they cooperated • But the logic of their situation ends up with a noncooperative solution • The solution to cooperate appears to be transforming a one-period game into a multi-period game. • The actions you take now will then have consequences in future periods. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 14 Cruise Ships $450 • When all players make their best reply responses (so changing Carnival $450 $300 their choices cannot improve their position) then the game is in an Equilibrium. $275 $375 • Royal Caribbean’s payouts are in the bottom triangles. $350 $50 Royal • The cooperative solution is for Caribbean both to charge $450, but $60 $185 Carnival has a dominant strategy of charging $300 $320 $175 • Knowing this, Royal Caribbean also charges $300. The outcome Table 13.4 is the Prisoner’s Dilemma again. • {$300, $300} is an Equilibrium $300 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 15 Business Strategy Games • When an oligopolistic rival alters its product or pricing, our firm must react or adapt. • Best would be proactive behavior that could anticipate actions. • A simultaneous game occurs when all players must chose their actions at the same time. • A sequential game is one in which there is an explicit order of play. » A sequential example is when one firm has announced a price cut, your decision to respond or not is sequential. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 16 Coke & Pepsi and Price Discounting Maintains Price Discounts Price • Pepsi’s payouts are in the Table 13.5 bottom triangles. • The cooperative solution is for both to maintain high prices. COKE • No dominant strategies exist. Maintains Price Discounts Price $13,000 $16,000 • Both Coke and Pepsi have an incentive to switch to discount price, making this similar to $12,000 $9,000 the Prisoner’s Dilemma PEPSI $10,500 $8,000 • But {Discount Price, Discount Price} is not an equilibrium, since both are better off $14,000 $6,300 switching to a high price. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 17 Renegade Discounting Maintains Price Discounts Price • If either player discounts, the other player is better off maintaining high Table 13.5 prices. • Indeed, there are two equilibria at {Maintain, Discount} and {Discount, Maintain}. COKE • The best-reply response – is an Maintains Price Discounts Price action that maximizes self-interest $13,000 $16,000 from among feasible choices. • A Nash equilibrium game – is an equilibrium concept for $12,000 $9,000 nondominant strategy games. PEPSI $10,500 $8,000 • With two equilibria, Coke and Pepsi may want to randomize their pricing $14,000 $6,300 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 18 Randomized Pricing Maintains Price • Suppose “p” is the probability that Pepsi maintains price & (1-p) is probability that Pepsi discounts price • If Coke maintains price, Coke gets 13,000p + 10,500(1-p) COKE • If Coke discounts price, Coke gets Maintains Price Discounts Price 16,000p + 8,000(1-p) $13,000 $16,000 • The two strategies are identical for Coke when they are equal $12,000 $9,000 • 13,000p + 10,500(1-p) = 16,000p + 8,000(1-p) PEPSI $10,500 $8,000 • This occurs at p=.454 » Pepsi randomizes by this probability and Coke is $14,000 $6,300 indifferent. • In the same manner, Coke can find a way to randomize its discounting of price to make Pepsi indifferent. Discounts Price © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 19 The Escape From Prisoner's Dilemma: Repeated Games • If the games are repeated, there is greater expectation that firms will achieve the cooperative solution. • Each firm "shows" by its behavior each period that it wants to cooperate. • Firms that expand production "show" that they do not want to cooperate. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 20 Repeated Prisoner’s Dilemma Table 13.6 with new Payoffs • Best is the cooperation solution, where both players maintain price. • This is the grim trigger strategy which has an infinitely long punishment. Maintains Price Discounts Price $12,000 $17,000 $12,000 $6,000 PEPSI Discounts Price • Suppose Coke announces that it will always Maintain Price unless it finds Pepsi defects to discount pricing, in which case it will always Discounts. COKE Maintains Price • The Dominant Strategy is for both to Discount. We fall into the noncooperative solution, which is 8,000+8,000=16,000. $6,000 $17,000 $8,000 $8,000 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 21 Repeated Prisoner’s Dilemma Table 13.6 with new Payoffs • With low enough interest rates, it is in Pepsi’s interest to Maintain its Price too. COKE Maintains Price • Pepsi must decide whether it wants to keep $12,000 or end up with a perpetuity of just $8,000 each period. • If the rival acts noncooperatively once, perhaps you can forgive. But fool me twice, and then watch out! Discounts Price • Some game theorists have wondered if the slight defections could go unpunished, called a trembling hand PEPSI trigger strategy. Maintains Price Discounts Price $12,000 $17,000 $12,000 $6,000 $17,000 $6,000 $8,000 $8,000 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 22 The Unraveling Problem Finite Lived Games Infinitely Lived Games • In a two period game, the incentive to double-cross is huge in the second period. • Knowing this, the other player double-crosses in period one. • The Unraveling Problem is this failure of cooperation in games of finite length. • Games that last forever have usually has a greater chance of cooperation. • The Chain Store Paradox involves a game tree of Accommodate or Fight entry (Figure 13.2) of new stores. • The prediction is that chain stores will always accommodate, since in the last period it pays to accommodate. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 23 Figure 13.2 The Chain Store Paradox • Consider only the last choice of Enter or Stay Out decision • With Incumbent payoff first, potential entry (PE) will expect that incumbent (I) to PE accommodate. • Backward induction leads to prediction of always accommodate. Accommodate {80,10} ENTER I Fight {-10,-10} Accommodate {100,0} I STAY OUT 20th Store Fight {60, 0} © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 24 Mutual Forbearance and Cooperation • Can even cooperate in a 2 period game if uncertain ending to game. • Payoff to firm 1 is given first in each pair. • p is the probability that the game goes to period 2 • If keep small output both periods, payoff is: 100 + p 100 • If produce a large output and double-cross in first period, payoff is: 150 + p (20) • The larger is “p” the greater is the chance of cooperation. FIRM 2 S S L 100, 100 10, 150 150, 10 20, 20 FIRM 1 L Expect to reach cooperative solution if: 100 + p 100 > 150 + p (20) or 80 p > 50 or p > 62.5% © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 25 Other Strategies in Multi-period Games • When games involve 3 or more players, coalitions of players can "win" the game. These n-person games have complex solutions. • A tit-for-tat strategy can lead to cooperation. If two cruise ship firms were competing on the price of staterooms, one ship line could match the price announced by the other. Each time the other cut its price, the other would too. Soon the first cruise line ‘learns’ to pick a price that is best for both lines. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 26 Other Strategies in Multi-period Games • A conspicuous focal point is an outcome that attracts mutual cooperation. » Living Without and Vegetarian Times magazines both sell in the specialty cooking category at the newsstand for $5.95. This is a focal point, where higher prices kill sales and lower prices do not help much. » This reduces the chance of a price war. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 27 Cruise Ships with Price Matching • • Match • $300 • $450 $450 • Carnival is in the upper triangle in each pair. In the 2x2 figure 13.4, Carnival has a $300 dominant strategy. With a Tit-for-Tat (TFT) strategy, Carnival can Royal announce a $450 stateroom Caribbean policy. Royal Caribbean can match whatever Carnival says and both payers achieve {$350, $275} If Royal Caribbean announces $450, Carnival can also match. Carnival $300 $275 $350 $375 $50 $350 $185 $175 $275 $275 $350 $60 $320 Matching $185 $175 $185 $175 $275 $350 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or Table in part. 13.8 Slide 28 Analyzing Sequential Games Table 13.9 Increase Margins • A Truck manufacturer and a retail distributor (which sometimes services & repair Truck Manufacturer trucks) Price Increase No Price Increase • Payoffs for the retail distributor are in the lower $280,000 $150,000 triangles • Neither player has a dominant strategy $130,000 Retail $120,000 • If the truck manufacturer selects Price Increase, the best decisionDistributor is to continue service of trucks at $300,000 $380,000 the retail distributor • If the truck manufacture doesn’t raise price, the best decision is to $180,000 $60,000 discontinue the service • This shows that sequential decisions influence outcomes Continue Service © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 29 Game Tree An Illustration of a Sequential Game • A game tree is like a decision tree. It is a schematic diagram of a sequential game. • Solutions to games parallels board games like chess or checkers. • One way to solve a decision problem is to use end-game reasoning, where we start with the final decision and use backward induction to find the best starting decision on the game tree. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 30 Two Accounting Firms Bid on Audit Illustrated as a Sequential Game Tree • Alpha & Daughters () is the incumbent auditor at $200 per hour. • Omega & Sons () could bid the same or less (say $50 increment reductions) to unseat the incumbent in year 1. Alpha Matches $150 $200 Alpha wins bid $150 Omega wins bid Alpha Cuts price to $100 If this pattern continues, the price could be driven too low for either firm © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 31 Subgames in Game Trees • Since game trees have several branches, we can examine the concept of equilibrium in each part of the tree, called a subgame » example: If Alpha always matches any cut by Omega (tit for tat style), this would be a “branch” or a subgame. • When all players make their best reply responses then the game is in a Nash equilibrium. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 32 Subgames in Game Trees • Looking to the end-game, it may be that both offering $150/hour is an equilibrium • If keep cutting prices, this ends in losses. » Optometrists, accountants, insurance, and other homogeneous suppliers of services seem to recognize this. » Avoid price wars through recognition of its outcome. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 33 Business Rivalry as a Sequential Game • The first to introduce a product, lower price, etc., often achieves recognition and an advantage, called a first-mover advantage.. • When games last several periods, the actions by firms in one period can be punished or rewarded in future period. » If a new firm enters a market, the threat is that the incumbent firm may drop prices down to levels that are unprofitable. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 34 First Mover Games • Andrew Carnegie: B civilian military The first person gets 30, 15 the oyster, the second civilian -10, -10 person gets the shell. A military 15, 30 -10, - 10 • Assume markets are too small for multiple firms. • First number in each pair is for firm A. • Game with Military and Civilian markets for “water-land vehicles” (DUCKS). In a simultaneous game, both would want the civilian market. But in a sequential game, the first to get the civilian market preempts it. The other firm takes the military market. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 35 Figure 13.5 Second Best Advantages • Two incumbents I1 and I2 react to an entrant in two different markets. • Being first has strategic advantages, but being second lets you know what the other firm did with entrant. PE • With Incumbent's payoff first, being second leads the entry to pick a low price strategy. • Incumbent 2, comes back with high price. High price {$0, $80} ENTER I1 Moderate price {35,50} Low price { $50, $40}* High price{$80,$30} I 2 moderate price {70,60} STAY OUT Or License Low price {$40, $60} © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 36 Credible Threats & Commitments • A credible threat is a conditional strategy that is perceived as a possible penalty in a noncooperative game. » Its existence sometimes induces cooperative behavior » Example: If you cut your price, I will cut my price too! If believed, the parties tend to avoid price wars. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 37 Credible Threats & Commitments • A credible commitment is a conditional strategy for establishing trust by promising to make the promise-giver worse off by violating that trust. » Such as a reward for good behavior in a noncooperative game. » Example: If any of my products fail to work, I will pay the buyer three-times their purchase price in recompense! Clearly, this commitment makes the firm worse off if they sell shoddy goods. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 38 The Tactical Advantage of Licensing and Leasing • There is a tactical advantage in leasing and renewal licenses between sellers of major capital equipment and their customers. • The renter fears that the equipment will become quickly obsolete. • The seller is in a better position to know what changes are occurring in technology. • A lease or license works for both parties in the contract. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 39 Pricing Techniques and Analysis • Value-based more than cost-based pricing often helps build profits. • Firms charge different customers different prices, which is known as differential pricing or price discrimination. • This chapter explains pricing used by many multi-product firms, such as full-cost pricing and target return pricing. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 40 Proactive Value-based Pricing • If the price doesn’t fit what customers are willing to pay, then the product may not be profitable. • Customer value is the focus for pricing, not just the costs associated with producing the good or service. • For a time, Apple Computer lost market share by ignoring customer value, but it has been gaining trend-setting customers through style and functions of its products. • The Ford Mustang was a success, as Ford found that people wanted a sports car, but didn’t want it to be too expensive. They started with a price and then designed the product. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 41 Prestone and Zerex Radiator Fluid • Zerex matches competitors price so long as price exceeds its costs. • Rather than use cost-based pricing, Zerex should consider segmenting customers, and design products for these segments. • Value-in-use – the difference between the value the customers place on something versus the cost of acquiring it. » Water has a high value in use, whereas diamonds are relatively low in value-in-use. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 42 Pricing of Coated Coronary Stents: An Example of Value-Based Pricing • Clogged arteries can be repaired using an $800 stent, but 1530% of the time anther open-heart surgery is needed to repair scaring caused by the stent some years later. • Coated stents reduce the likelihood of scar tissue and thus having to go through a second surgery that costs about $42,000 • What would you be willing to pay to reduce the need for a second surgery to less than 3%? • A reduction to a 27% chance of another surgery is worth: .27($42,000) = $11,340. It is no wonder that the price of coated stents is higher than then uncoated by an extra $1,165 (or about $1,965 in all). © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 43 EMR is the equal marginal revenue from each class equals MC © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 44 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 45 Differential Pricing and the Price Elasticity of Demand • • • Using elasticities MR P( 1 + 1/ ED ) = MC In two regions: MR1 = P1( 1 + 1/ E1 ) = MC MR2 = P2( 1 + 1/ E2 ) = MC Therefore: P1( 1 + 1/ E1 ) = P2( 1 + 1/ E2 ) or: P1/ P2 = ( 1 + 1/ E2 )/( 1 + 1/ E1 ) • • • If the price elasticity in region 1 is -1.25 and if the price elasticity in region 2 is -2.5, then P1/ P2 = (1+1/ -2.5)/(1+1/ -1.25 ) = 3. Hence, P1 = 3P2. The price is three times higher in region 1, which the less elastic region. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 46 An Example: Differential Pricing at Taiwan Instrument • Japan: P1 = 12 – Q1 and US: P2 = 8 – Q2 • Total cost: C = 5 + 2(Q1 + Q2) • In differential pricing, maximize profits: p= P1Q1 + P2Q2 – C = (12 – Q1)Q1 + (8–Q2)Q2 - 5 - 2(Q1 + Q2) = 10Q1 - Q12 +6Q2 - Q22 -5. Find ∂p/∂Q1 = 10 – 2Q1 = 0, or Q1= 5 Find ∂p/∂Q2 = 6 – 2Q2 = 0, or Q2= 3 • So, P1 = $7 and P2 = $5 and p = $29 (million) • When prices uniform at $6, p = $27 (million) © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 47 Differential Pricing in Target Market Segments • If at peak rush hour, the toll is higher than at the offpeak, we are using different prices at different time periods. • The peak toll can encourage shifting travel patterns to off-peak times or discourage some commuting altogether. • Differential pricing appears more frequently than one thinks. Aside from earning greater tolls, it can relieve congestion. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 48 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 49 Direct Segmenting with “Fences” • Price differentiation is difficult if products are easily arbitraged • Ralph Lauren sells in upscale stores and sells some goods in discount outlet malls • Customers of the boutiques seldom frequent outlet malls along highways. The two groups of customers are separated or “fenced” away from each other. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 50 Price Discrimination Price Discrimination- Goods which are NOT priced in proportion to their marginal cost, even though technically similar Some Necessary Conditions: 1. Have Some Monopoly Power • Otherwise, in pure competition, P = MC 2. Be Able to Prevent Arbitrage • Separate customers and prevent reselling • Think of a “Fence” that prevents reselling to others. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 51 Arbitrage • Buy Low to Sell Higher Arbitrage of Goods is fairly Easy » Price Discrimination of goods is typically ineffective. The price is the same for all customers found in grocery items • Arbitrage of Services is often Difficult » Price Discrimination of services is often effective, so it is found at restaurants by age, as restaurant food is a service » Lawyers charge different prices for wills, based on ability to pay © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 52 Why practice differential pricing and price discrimination? • In Simple Monopoly, there is only one price • Consumers receive a CS consumer surplus (CS) PSM • In differential pricing, the incentive is to SCOOP OUT all consumer surplus • The object is to earn greater profits. MC Simple Monopoly D QSM © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q Slide 53 Perfect Price Discrimination (or 1st Degree Price Discrimination) • Charge the MOST that a person is willing to pay for each good • Zero consumer surplus • Produce MORE than in Simple Monopoly • Output the same as in Competition Price Discriminating Monopoly MC D Q1st © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q Slide 54 Notice: Incentives to Understate One’s True Willingness to Pay • The conditions for In Second Degree Price perfect price Discrimination: discrimination are Units are Grouped seldom met • Hence, some close • There are a variety of approximations ways to group units to exist attempt to scoop out consumer surplus © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 55 An Example of “Second Degree” Price Discrimination © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 56 Bundling: Another Example of Second Degree Price Discrimination Time Warner could offer the History Channel (H) and Showtime (S) individually or as a bundle of both. Suppose the reservation prices of customers 1& 2 are presented in the boxes below. CASE A : Preferences are negatively correlated S H 1 9 2 11 2 3 8 11 9 8 = $17 Selling separately $22 If the cost to Time Warner is $1 per customer for licensing fees, the profits of bundling is 22 – 4 = $18, In contrast, the profits of selling Bundling each separately is 17-2= $15. generates more revenue Bundling is more profitable! © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 57 Changing the preferences: Bundling Suppose, however, that everyone likes Showtime more than the History Channel, such that preferences are positively correlated as given below. CASE B: Preferences are positively correlated If the cost to Time Warner is $1 per customer for licensing fees, the profits of bundling is 20 – 4 = $16, In contrast, the profits of selling each separately is 22-3= $19. Selling separately is more profitable! S H 1 9 1 10 2 8 6 14 20 16 6 = 22 Selling separately © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 58 Mixed Bundling • McDonalds sells Extra Value Meals, as a bundle of sandwich, fries, and a soft drink for less than it sells them separately. But selling both bundles and items separately is mixed bundling. » Suppose that Bob would pay $3 for a burger and $1 for a soft drink » Mary would pay $2 for a burger and $2 for a soft drink » Jim would pay $3.50 for burger and nothing for a soft drink © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 59 Mixed Bundling • If the individual price of a burger is $3 and the individual price of a drink is $1.50, then Bob buys a burger, Mary buys a soft drink, and Jim buys a burger. With only ala carte pricing, the revenue $3 (Bob) + $1.50(Mary) + $3(Jim) = $7.50. • If the extra value meal bundle (of a burger and drink) costs $4, both Bob and Mary buy the bundle, but Jim buys nothing. Hence, with only bundling, the revenues is $4 (Bob) + $4 (Mary) = $8. • Mixed Bundling yields revenue of $4 (Bob) + $4 (Mary) + $3(Jim) = $11, which is the highest revenue. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 60 Nine Ways to Separate Customers for Price Discrimination 1. Geography as when the price in the East-side and West-side differ 2. Income as the American Economics Association charges more to professors than students 3. Gender as when jeans for women are priced higher than similar jeans for men 4. Age as when kids get in at lower prices for movies 5. Time of day or season © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 61 Nine Ways to Separate Customers for Price Discrimination 6. Versions as when software for home use is slightly different but priced much differently than business use. 7. Language as when products printed in Spanish are priced differently than those in English 8. Transient/Resident as when contractors pay less at hardware stores than other customers 9. Ability to Haggle when those who ask for a lower price get it © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 62 Couponing • Some customers use coupons. These customers identify themselves as being highly price sensitive • Other customers seldom bother to use coupons. They demonstrate that they are less price sensitive. • The customers that use coupons pay less. • The customers don’t bother pay more. • Both are buying the same items. • This is an efficient way to price discriminate. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 63 Pricing in Practice • In practice, pricing strategy involves the whole life-cycle pricing of the product. » A plan to start with a high price when it is new, with the idea of lowering the price when it is no longer as fashionable (e.g., demand falls). • An example of this life-cycle pricing is price skimming. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 64 Price Skimming • Price declines over time • Those who wish to get it first pays the highest price, others are willing to wait • Examples: P D » Hardcover & Paperback Books » New electrical, computer products, PDAs, iPhone, etc. • Sometimes, in the long run the product fills a small niche, and the producer can raise its price in the long run to fill this niche pricing. TIME © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 65 Cost-Based Pricing Methods • Managers also report wide use of cost-plus pricing methods because it: » Streamlines pricing of multiple products » Streamlines pricing of retail prices • P = ACn + Markup or P = ACn(1 + m) » where ACn is average cost at a normal output and m is a percentage markup » Notice: This procedure does not use MC pricing or use elasticities, as in: P( 1 + 1/Ep ) = MC. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 66 Cost-Plus Pricing: Advantages & Disadvantages • Cost-plus is simple • It is easy to delegate to others • Easy to apply to thousands of items » Can use categories of markups for different classes of products • But cost-plus ignores demand changes • Pricing may be based on poor cost data • Output varies in business cycle Hybrid Method: Variable Cost-Plus Pricing -- the markup can vary over the season, or business cycle © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 67 Full Cost & Target Rate of Return on Investment Pricing • Full Cost Pricing: » Covers all Costs at the standard or normal output » Plus a return on the investment which is the markup • Target Rate of Return: P = ACN + p K / QN » Where ACN is the AC at a normal amount of output (which is average variable cost plus average fixed cost). » where p K is the target amount of profit, and pis the desired profit rate and K is gross operating assets and QN is the number of units expected to be produced over this time horizon. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slide 68