Strategy: Multistage Games

1. Strategy: Multistage Games

2. Key issues • preventing entry: simultaneous decisions • preventing entry: sequential decisions • creating and using cost advantages • advertising

3. Preventing entry • consider a market with either 1 or 2 firms • simultaneous entry decision: neither firm has an advantage that helps it prevent other firm from entering • sequential decision: incumbent may have an advantage over firm deciding whether to enter

4. Simultaneous decisions • initially no gas stations • physical space for at most 2 gas stations • 2 firms consider opening a gas station at a highway rest stop

6. Simultaneous Decisions • Room for 2 firms • firms have pure (dominant) strategies: both enter • unique, pure strategy equilibrium • Room for only one firm • game is similar to game of chicken • neither firm has a dominant strategy

7. Problem with pure strategies • game has two Nash equilibria in pure strategies: • Firm 1 enters and Firm 2 does not • Firm 2 enters and Firm 1 does not • players don’t know which Nash equilibrium will result • could collude: firm that enters could pay other firm to stay out of market • these pure Nash equilibria are unappealing because identical firms use different strategies

8. Mixed strategies • mixed strategies: firm chooses between its possible actions with given probabilities • firms may use same strategies if their strategies are mixed • in our game, each firm enters with 50% probability • result: Nash equilibrium in mixed strategies

10. Mixed strategy equilibria

11. Firm 2’s response • if Firm 1 uses this mixed strategy, Firm 2 cannot do better using a pure strategy • if Firm 2 enters with certainty, it earns • $1 half of the time time • loses $1 other half • so its expected profit is $0 • if Firm 2 stays out with certainty, Firm 2 earns $0

12. Nash equilibria • firms play mixed strategy • one firm plays pure strategy of entering and other firm plays pure strategy of not entering

13. Games without pure-strategy equilibria • some games have no pure-strategy Nash equilibrium, so mixed strategies must be used • theorem (Nash, 1950): every game with a finite number of firms and a finite number of actions has at least one Nash equilibrium, which may involve mixed strategies

14. Preventing entry: Sequential decisions • incumbent (monopoly) firm knows potential entrant is considering entering • stage 1: incumbent decides whether to take an action to prevent entry • stage 2: potential entrant decides whether to enter, and firms choose output levels • no entry: incumbent earns monopoly profit • entry: each firm earns duopoly profit • assume potential entrant does not enter if it breaks even or loses money

15. Three possibilities • blockaded entry: market conditions make profitable entry impossible so no action necessary 2. deterred entry: incumbent acts to prevent an additional firm from entering because it pays 3. accommodated entry: doesn't pay for incumbent to prevent entry • incumbent does nothing to prevent entry • reduces its output (or price) from monopoly to duopoly level

16. Incumbent’s advantage • Because incumbent is already in market, • its fixed entry cost is sunk • so it ignores its sunk cost in deciding whether to operate • potential entrant • views fixed cost of entry as avoidable cost • incurs cost only if entry takes place

17. Output commitment • incumbent can commit to large quantity of output before potential entrant decides whether to enter • 3 possibilities • no commitment: entry occurs, Cournot equilibrium • commit to Stackelberg-leader quantity: entry occurs, Stackelberg equilibrium • commit to larger quantity: deters entry, monopoly equilibrium

18. Commitment and fixed cost • incumbent's decision depends on potential entrant's fixed cost of entry, F • illustrate role that F plays in incumbent's decision by looking at demand and cost structure that underlie game tree:

19. Game Trees for the Deterred Entry and Stackelberg Equilibria

21. Cournot and Stackelberg Equilibria

22. Incumbent Loss If It Deters Entry

23. Raising rivals' costs • by raising its rivals’ variable costs relative to its own, firm may increase its own profit • firm can raise rivals’ variable costs either directly or indirectly

24. Preventing customers from switching • incumbent makes it difficult for customers to switch to entrant to discourage entry • industrial customers of Pacific Gas and Electric (PG&E) were told that they'd have to pay a fee to stop buying from PG&E

25. Raising all firms' costs • incumbent may raise costs of all firms, including its own • incumbent wants to raise costs if its cost is sunk and potential rivals' entry costs are avoidable

26. Monopoly advertising • successful advertising campaign shifts market demand curve by • changing consumers' tastes • informing them about new products • if advertising convinces some consumers they can't live without product, demand curve may • shift out • become less elastic at new equilibrium • firm charges a higher price for its product

27. Decision whether to advertise • even if advertising shifts demand, it may not pay to advertise • if demand curve shifts out or becomes less elastic, firm's gross profit (= profit ignoring cost of advertising) must rise • firm undertakes advertising campaign only if it expects net profit (= gross profit - cost of advertising) to increase

28. Advertising

29. How much to advertise • How much should a monopoly advertise in order to maximize its net profit? • level of advertising maximizes firm’s net profit if last $1 of advertising increases its gross profit by $1

31. Shifts in the Marginal Benefit of Advertising

32. Advertising that helps rivals • firm informs consumers about a new use for its product increasing demand for its own and rival brands (pink toothbrush) • some industry groups advertise collectively to increase demand for their product: • raisin growers (dancing raisins) • milk producers (milk mustache)

33. Advertising that hurts rivals • firm's advertising may increase demand for its product by taking customers from rivals • firm may use advertising to differentiate its products from those of rivals (possibly spuriously)

34. 1. Preventing entry: Simultaneous decisions • firm's strategies depend on size of market and possibly on chance • if market is large enough that 2 firms can make a profit, both enter • if only one firm can profitably produce, there are many possible Nash equilibria

35. 2. Preventing entry: Sequential decisions • incumbent firm that can commit to producing large quantities before another firm decides whether to enter market • may deter entry: first-mover advantage • incumbent acts to prevent entry only if it pays to do so (depends on entry costs): • blockaded market: no action needed • incumbent deters entry if it is profitable to do so • incumbent accommodates entrant

36. 3. Creating and using cost advantages • firm with a lower MC • has a larger market share and a higher profit than a higher-cost rival • may prevent entry by a higher-cost rival • thus, firms benefit from lowering their marginal costs relative to those of rivals • firm invests in technology that raises its total cost of production if it lowers its MC substantially • by lowering its MC, firm credibly commits to producing relatively large levels of output, and thereby discourages entry

37. 4. Advertising • firms advertise to • shift out their demand curve, and/or • reduce equilibrium elasticity of demand • advertising may • differentiate a firm's product, or • inform consumers about new products or new uses for a product