Lecture 13

1. Lecture 13 ECON 4100: Industrial Organization Dynamic strategic interaction and credible commitment

2. Introduction • The question as to how the incumbent credibly commits to produce QD a quantity that will create problems for the other company • The Chain-Store Paradox

3. Credibility and Predation • Take a simple example • two companies Microhard (incumbent) and Newvel (entrant) • Newvel makes its decision first • enter or stay out of Microhard’s market • Microhard then chooses • accommodate or fight • pay-off matrix is as follows:

4. What is the equilibrium for this game? An Example of Predation There appear to be two equilibria to this game The Pay-Off Matrix But is (Enter, Fight) credible? Microhard (Enter, Fight) is not an equilibrium Fight Accommodate (Stay Out, Accommodate) is not an equilibrium (0, 0) Enter (0, 0) (2, 2) Newvel (1, 5) Stay Out (1, 5) (1, 5)

5. Credibility and Predation • Note that options listed are strategies not actions • Thus, Microhard’s option to Fight is not an action of predatory nature but a strategy that says Microhard will fight if Newvel enters but will otherwise remain placid • Similarly, Accommodate defines what actions to take depending, again, on Newvel’s strategic choice

6. Credibility and Predation • The question is: Are the actions called for by a particular strategy credible? • In particular, is the promise to Fight if Newvel enters believable • If not, then the associated equilibrium is suspect • To put it differently, the matrix-form ignores timing. We can see this by representing the game in its extensive form to highlight sequence of moves

7. What if Newvel decides to Enter? The Example Again Fight is eliminated Microhard had better Accommodate (0,0) (0,0) Fight Fight (2,2) Accommodate Enter, Accommodate is the unique equilibrium forthis game Enter M2 Enter (2,2) Newvel Newvel will choose to Enter since Microhard will Accommodate N1 Stay Out (1,5)

8. Sequential games • A sequential game is one in which players make decisions following a certain predefined temporal order, and in which at least some players can observe the moves of players who preceded them • If no players observe the moves of previous players, then the game is simultaneous (like Cournot or Bertrand)

9. Sequential games • If every player observes the moves of every other player who has gone before her, the game is one of perfect information • If some (but not all) players observe prior moves, while others move simultaneously, the game is one of imperfect information • Sequential games are represented by game trees (the extensive form) and solved using the concept of subgame- perfect equilibrium

10. Some extra notions within sequential games • Sequential rationality: A player’s strategy, which is part of a proposed strategy profile for playing the game, is sequentially-rational if starting at any decision point (information set) for a player in the game (including ones that may not be reached if the game is conducted according to the strategy profile), his or her strategy from that point on represents a best response to the choices of the other players

11. Some extra notions within sequential games • A subgame: A subgame is any part of a game tree (extensive form) that begins with an information set that has a single node (a singleton) and includes all successor nodes of that branch of the game • Note that the game as a whole is also considered a subgame

12. Some extra notions within sequential games • Subgame perfect: A strategy that is a Nash equilibrium is also subgame perfect if the choices of actions specified for each node in a subgame represent a strategy profile that is a Nash equilibrium for the subgame • Some Nash equilibria are not subgame perfect. The concept allows the players in the game to reason that they can ignore Nash equilibria that are not subgame perfect. • Reinhard Selten (in 1975) introduced this notion of subgame perfection

13. Some extra notions within sequential games • Illegitimate threats or empty threats • Subgame perfection rules out threats of illegitimate threats. These are a claim that the player will make choices at certain points in the game that change the responses of other players so that they avoid sending the game to those decision nodes (ie: do not enter my soup market or I will dump prices to fight you off) • If these decisions are against the interest of the player who makes the threat, others will reason that he or she will not carry through with them if the decision nodes are actually reached

14. Some extra notions within sequential games • Backward induction • With common knowledge each player can start at the end of the game and solve backwards through the different subgames to identify equilibria that are both Nash and subgame perfect • Basically backward induction is an iterative process for solving finite extensive-form or sequential games.

15. Some extra notions within sequential games • Backward induction • First, one determines the optimal strategy of the player who makes the last move of the game. • Then, the optimal action of the next-to-last moving player is determined taking the last player's action as given. • The process continues in this way backwards in time until all players' actions have been determined. • Note that it is important that we know when the game finishes (it must have a finite number of rounds)

16. The Chain-Store Paradox • What if Microhard competes in more than one market or with more than one rival? • threatening one may affect the others • But: Selten’s Chain-Store Paradox arises • 20 markets established sequentially • will Microhard “fight” in the first few as a means to prevent entry in later ones?

17. The Chain-Store Paradox Trivia: Reinhard Selten first refined the Nash equilibrium concept for analyzing dynamic strategic interaction. He also applied these refined concepts to analyses of oligopolistic competition. In 1994, he shared the Nobel Prize with John F. Nash and John C. Harsanyi (proving that if your first name is John you are more likely to get a Nobel Prize )

18. The Chain-Store Paradox • 20 markets established sequentially • will Microhard “fight” in the first few as a means to prevent entry in later ones? • No: this is the paradox • Suppose Microhard “fights” in the first 19 markets, will it “fight” in the 20th? • With just one market left, we are in the same situation as before • “Enter, Accommodate” becomes the only equilibrium • Fighting in the 20th market won’t help in subsequent markets . . There are no subsequent markets • So, “fight” strategy will not be adapted in the 20th market

19. The Chain-Store Paradox • Now consider the 19th market • Taken by itself, we know that the equilibrium for this market would be “Enter, Accommodate” • The only reason to adopt “Fight” in the 19th market is to convince a potential entrant in the 20th market that Microhard is a “fighter” • But as we have just seen, Microhard will not “Fight” in the 20th market regardless as to what has happened in earlier markets • “Fighting” in the 19th market will therefore not convince anyone that Microhard will “fight” in the 20th. • With the only possible reason to “Fight” in the 19th now removed, “Enter, Accommodate” becomes the unique equilibrium for this market, too

20. The Chain-Store Paradox • What about the 18th market? etc • Microhard’s threat to “Fight” in these markets is simply not credible. “Enter, Accommodate” is again the equilibrium • By repetition, we see that Microhard will not “Fight” in any market

21. The Chain-Store Paradox • Using backward induction, we see that the strategy is always to • LIVE AND LET LIVE!

22. Capacity Expansion and Entry Deterrence • Central point of previous discussion • For predation to be successful—and therefore rational—the incumbent must somehow convince the entrant that the market environment after the entrant comes in will not be a profitable one • How can the incumbent credibly make this threat?

23. Capacity Expansion and Entry Deterrence • One possible mechanism is to install capacity in advance of production • Installed capacity is a commitment to a minimum level of output • The lead firm can manipulate entrants through capacity choice • the lead firm may be able to deter entry through its capacity choice We need, however, to make sure that the investment in capacity is not reversible, it must be sunk. After installing the capacity you need to burn the bridges (or burn the ships, if you are a Spanish conqueror )allowing a way back (incumbent invest in highly specialized equipment, enter into contracts to take the decision on output off our hands)

24. Capacity Expansion and Entry Deterrence • The incumbent needs to make sure that the entrant is aware of the commitment to fight • http://www.gametheory.net/html

25. Capacity Expansion and Entry Deterrence • An example Practice problem 12.2: • P = 120 - Q = 120 - (q1 + q2) • marginal cost of production $60 for incumbent and entrant • cost of each unit of capacity is $30 (so $30 is the per unit cost of capacity) • firms also have fixed costs of F • incumbent chooses capacity K1 in stage 1 • NOTE: incumbent will always produce at least K1 in stage 1 otherwise it throws away revenue that could help cover the cost of installed capacity • entrant chooses capacity and output in stage 2 • firms compete in quantities in stage 2.

26. The Example (cont.) Equate marginal cost and marginal revenue • Consider the best response function of the entrant This is the entrant’s best response function Residual demand is P = (120 - q1) - q2 Marginal revenue is: MR2 = (120 - q1) - 2q2 Marginal cost is: MC2 = 60 (120 - q1) - 2q2 = 60 so q2 = 30 - q1/2 • What about the incumbent? • If we ignore any installed capacity it has a similar best response function q1 = 30 - q2/2 • What if the incumbent had a monopoly? (q2 = 0) Then with marginal costs of $60 it would produce 30 units.

27. The Example (cont.) The incumbent’s best response function ignoring any installed capacity q2 Suppose that the incumbent can act as a Stackelberg leader 60 R1 Here P=$120-$30-$15=$75. Therefore, the entrant earns a profit of ($75-$60)15=$225 less its fixed cost F in the Stackelberg equilibrium. The entrant will then choose output and capacity of 15 units A Stackelberg leader always chooses the monopoly output, in this case, 30 units 30 The entrant’s best response function S 15 R2 q1 30 60

28. The Example (cont.) If the incumbent has installed capacity of K1 , its marginal cost up to K1 is 30, not 60. So, its best response function up to K1 is shifted out to q1 = 45 – q2/2. q2 90 60 There is a kink in the incumbent’s best response function at output Q=K1. NOTE: The incumbent will never let installed capacity stay idle, it can credibly commit to produce at least K1 in the production stage R1 30 R2 q1 30 45 60 K1

29. The incumbent can credibly commit to an outputequal to the level of capacity installed in Stage 1. This permits it to act as a Stackelberg leader. So, it will never choose an initial capacity K1 < 30, i.e., less than that chosen by the Stackelberg leader. The Example (cont.) q2 90 The choice of K1 = 30 would lead to the Stackelberg outcome. Is this predation? Does the incumbent have any incentive to choose K1 > 30? 60 R1 30 15 R2 q1 30 45 60

30. The entrant’s profit at S is ($75 - 60)15 - F = $225 – F.Then profit is null if F=$225 and if F > $225, Then the entrant cannot Enter when the incumbent installs capacity K1 = 30 But this is not predation. The incumbent is simply acting as a monopolist (q1 = 30) . It is not producing an output that is profitable only because it prevents entry. The Example (cont.) q2 60 R1 If F $225, then there is a break in the entrant’s best response function. The entrant’s response function for q130, is q2 = 0. What if fixed costs are F > $225? The entrant needs to produce more than 15 units is order to be able to enter 30 S 15 R2 R’2 q1 30 60

31. The Example (cont.) q2 Profit of the entrant at S is ($75 - 60).15 - F = $225 - F If F < $225, say $200, then the entrant can still enter if its output is 15 units. The kinkin its reaction function occurs at an output q2 < 15. 60 R1 Does the incumbent want to deter entry by installing additional capacity? Can the incumbent deter entry by installing additional capacity? What if fixed costs are F = $200? The break in the entrant’s best response function now lies to the right of S 30 S 15 R2 R’2 q1 30 60

32. The Example (cont.) Up until the break-even point, the entrant’s best response function is described by: q2 = 30 - q1/2 If the incumbent installs 32 units of capacity it will deter entry So if the incumbent has capacity q1 total output is Q = q1 + q2 = 30 + q1/2 Does the incumbent want to do this? What does q1 have to be for this to be negative? Price is then P = 120 - Q =120-30- q1/2 = 90 - q1/2 Profit of the entrant is (P - 60)q2 - F = (90 - q1/2-60)(30 - q1/2) - 200 = 700 - 30q1 + q12/4 Suppose q1 = 32. Then the entrant’s profit would be 700 - 960 + 256 = $-4

33. Entry deterrence by adding capacity is profitable in this case. The Example (cont.) Suppose that F = $200 and that the incumbent accommodates entry. Acting as a Stackelberg leader, the incumbent installs 30 units of capacity in the first period. Profit to the incumbent in the production stage will then be: ($75 - $60)x30 = $450 less F = $250. NOTE: the incumbent’s cost per unit is also $60 but $30 of that is the per unit cost of installed capacity If the incumbent deters entry by installing 32 units, profit in the production stage is then: ($88 - $60)x32 = $896 less F = $696

34. q2 The Example (cont.) 90 By installing capacity of 32, the incumbent shifts out its best response function to pass through this output level. Effectively this commits the incumbent to q1 = 32. The entrant’s best response to q1 = 32 is q2 = 14. This would lead to P = $74 and operating profit of $196 to the entrant. Yet that operating profit does not cover its $200 overhead. If the entrant’s best response is not profitable, it will not enter. R1 60 30 S 15 R2 R’2 q1 30 60 32

35. The Example (cont.) • Note that entry deterrence by adding capacity is not always profitable. • Suppose that the entrant has no fixed costs. • Then the incumbent would need to install 60 units of capacity to deter entry. • Incumbent profit in the operating stage would be ($60 - $60)x60 – F = -$200 • Now entry deterrence is not an attractive option. • However, at a minimum, the incumbent can always act as a Stackelberg leader (q1 = 30)

36. Next Further issues on predation Read Ch. 13 and 14