Lecture 7 Rivalry, Strategic Behavior and Game Theory

Lecture 7 Rivalry, Strategic Behavior and Game Theory 1

Overview Game Theory Simultaneous-move, nonrepeated interaction Sequential interactions Repeated strategic interactions Pricing coordination 2

Introduction So far we have used fairly static, simplistic models to study firms strategic interactions Want to begin developing tools that will allow us to analyze more complex interactions When firms interact repeatedly over multiple period Leads to more realistic outcomes 3

Game Theory To analyze manager s strategic interactions in the market we use something called Game Theory. One way economists use game theory is to address the question: If I believe that my competitors are rational and act to maximize their own profits, how should I take their behavior into account when making my own profit-maximizing decisions? 4

Game Theory Game Theory has been applied in a number of different areas by social scientists. Originally developed to analyze interactions of countries, with emphasis on the Cold War and Nuclear deterrence. Also used by Political Scientists to model the behavior of legislative bodies and why people vote. 5

Game Theory: Payoff interdependency??? Decision-theoretic vs. Game-theoretic Situations o o o o o o o o Local Water Co. is contemplating raising local water prices to cover costs of upgrading its infrastructure. Google contemplates changing the price it charges for clicks. Raywood Stelly contemplates price and output for the upcoming harvest season. KFC in downtown Athens contemplates changing the hourly wage it pays to new employees. Apple contemplates the features it makes standard on its new iphone. Honda contemplates offering a $2000 rebate on new Accords to reduce inventories on dealer lots. UPS contemplates offering weekend delivery at the same rate as weekday delivery. American Airlines contemplates raising the price of its non-stop flight from New York to Paris. With some situations the optimal strategy for a firm to pursue depends only on the market circumstances and environment in which the firm finds itself. The behavior or reactions of other parties are not a factor. There is no Payoff Interdependency. In other situations a firm s optimal strategy will depend on the actions or reactions taken by other parties. There is Payoff Interdependency. This payoff interdependency puts us in the realm of Game Theory.

Elements of a game, Types of games Elements of a game: Players Rules: timing of moves, actions available to players on each move, information available to players when they make a move Outcomes Payoffs associated with each possible outcome Types of games: Static: players move simultaneously. Examples? https://www.youtube.com/watch?v=ui-mztcmzpe https://www.youtube.com/watch?v=g6tr78d0cma Dynamic: players move sequentially. Examples? https://www.youtube.com/watch?v=gl-uwmw4yma. Information available: we will restrict our analysis to games where all players have complete information about players, rules, outcomes, and payoffs.

Game Theory Characteristics of Games 1. There are two or more players Games with one player are boring. 2. Each player maximizes her utility, called a payoff What we have been assuming all along. 8

Game Theory Characteristics of Games 3. Each player knows the other players actions can affect her payoff. No need to consider interactions if this is not true. 4. The other player s interests are neither perfectly opposed nor perfectly coincident with those of a given player. Must be some room for both gains from cooperation and competition. 9

Game Theory There are two main type of games, Cooperative Games and Noncooperative Games. 10

Game Theory Noncooperative versus Cooperative Games Cooperative Game Players negotiate binding contracts that allow them to plan joint strategies Example: Buyer and seller negotiating the price of a good or service or a joint venture by two firms (i.e. Microsoft and Apple) Binding contracts are possible 11

Game Theory Noncooperative versus Cooperative Games Noncooperative Game Negotiation and enforcement of a binding contract are not possible Example: Two competing firms take each other s likely behavior into account when independently setting pricing and advertising strategy to gain market share 12

Cooperative vs. non-cooperative games If players are able to enter into binding commitments to pursue strategies that are not in their narrow selfinterest, then they will be able to collude. We call such games cooperative. If players cannot make binding commitments, they cannot be counted on to honor any agreements that are not incentive compatible. We call this type of game non-cooperative. http://www.youtube.com/watch?v=zpahl4fu5r8 https://www.youtube.com/watch?v=s0qjk3twze8 Are contracts to collude legally enforceable in the Greece/EU? https://en.wikipedia.org/wiki/article_101_of_the_treaty _on_the_functioning_of_the_european_union

Competition Versus Collusion: The Prisoners Dilemma An example in game theory, called the Prisoners Dilemma, illustrates the problem oligopolistic firms face. 14

Competition Versus Collusion: The Prisoners Dilemma Scenario Two prisoners have been accused of collaborating in a crime. They are in separate jail cells and cannot communicate. Each has been asked to confess to the crime. 16

Payoff Matrix for Prisoners Dilemma Prisoner B Confess Don t confess Confess Prisoner A -5, -5-1, -10 Would you choose to confess? Don t confess -10, -1-2, -2 17

Strategies Before figuring out what players will do we have to talk about their strategies. A firm s strategy is based on understanding your opponent s point of view, and (assuming you opponent is rational) deducing how he or she is likely to respond to your actions. 18

Solution strategies Dominant strategy: a strategy that maximizes a player s payoffs regardless of the strategy chosen by the other player. Iterative elimination of dominated strategies: a dominated strategy is one such that there is an alternative strategy that is in all cases better to play than this strategy. Rationalizable strategies: a rational player will not play a strategy that is never a best response to any strategy the other player might choose. Nash equilibrium: a strategy profile such that each player s chosen strategy is a best response to the strategy selected by the other player. Neither player will experience ex-post regret.

Dominant Strategies Dominant Strategy One that is optimal no matter what an opponent does. Back to Prisoner s Dilemma game. Is their a dominant strategy here and if so, what is it? 20

Payoff Matrix for Prisoners Dilemma Prisoner B Confess Don t confess Confess Prisoner A -5, -5-1, -10 Would you choose to confess? Don t confess -10, -1-2, -2 21

Pricing Game Let s go over a second example. A & B sell competing products They are deciding whether to undertake advertising campaigns 22

Payoff Matrix for Advertising Game Advertise Firm B Don t Advertise Advertise 10, 5 15, 0 Firm A Don t Advertise 6, 8 10, 2 23

Payoff Matrix for Advertising Game Observations A: regardless of B, advertising is the best B: regardless of A, advertising is best Advertise Firm A Don t Advertise Advertise Firm B Don t Advertise 10, 5 15, 0 6, 8 10, 2 24

Payoff Matrix for Advertising Game Observations Dominant strategy for A & B is to advertise Do not worry about the other player Equilibrium is dominant strategy Advertise Firm A Don t Advertise Advertise Firm B Don t Advertise 10, 5 15, 0 6, 8 10, 2 25

Dominant Strategies Game Without Dominant Strategy The optimal decision of a player without a dominant strategy will depend on what the other player does. 26

Modified Advertising Game Advertise Firm B Don t Advertise Advertise 10, 5 15, 0 Firm A Don t Advertise 6, 8 20, 2 27

Modified Advertising Game Observations A: No dominant strategy; depends on B s actions B: Advertise Question What should A do? (Hint: consider B s decision Advertise Firm A Don t Advertise Advertise 10, 5 15, 0 6, 8 Firm B Don t Advertise 20, 2 28

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. 29

The Nash Equilibrium Revisited 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. 30

Implications If a Nash equilibrium exists then it is selfenforcing no firm has an incentive to deviate from the strategy Can be multiple Nash equilibria Firms have an even stronger incentive to choose a dominant strategy if one exists; in this situation you can be fairly certain how your rival will behave 31

Implications More likely to reach a Nash equilibrium when Firms have experience in similar situations Firms are better informed There is a natural focal point 32

Iterative elimination of dominated strategies Now we are ready to explore ways of solving for the outcome of games of strategy. The first thing to do is to look for dominant strategies. If a player has a dominant strategy, she will play it. The second thing to do, if there is no dominant strategy, is to look for dominated strategies and eliminate them from consideration. A dominated strategy is one such that there is an alternative strategy that is in all cases better to play than this strategy. A rational player would never choose to play a dominated strategy.

Dominated Strategies Hilton and Hyatt are both considering building a hotel on an island Three possible choices, 70, 80, or 90 beds 34

Dominated Strategies Hilton 70 Beds 80 Beds 90 Beds 70 Beds $36, $36 $30, $40 $18, $36 Hyatt 80 Beds $40, $30 $32, $32 $16, $24 90 Beds $36, $18 $24, $16 $10, $10 35

Dominated Strategies Hyatt would never build a 90 bed hotel because they always get a higher payoff with the 80 bed hotel Hilton would never build a 90 bed hotel because they always get a higher payoff with a 80 bed hotel Once we eliminate this choice we are back to the simpler 2x2 matrix 36

Iterative elimination of dominated strategies Now we are ready to explore ways of solving for the outcome of games of strategy. The first thing to do is to look for dominant strategies. If a player has a dominant strategy, she will play it. The second thing to do, if there is no dominant strategy, is to look for dominated strategies and eliminate them from consideration. A dominated strategy is one such that there is an alternative strategy that is in all cases better to play than this strategy. A rational player would never choose to play a dominated strategy.

Can you predict the outcome of this game? Column Player C1 C2 C3 Row R1 4, 3 5, 1 6, 2 Player R2 2, 1 3, 4 3, 6 R3 3, 0 9, 6 2, 8 Does either player have a dominant strategy? Are there any dominated strategies for either player? Predicted outcome: R1, C1. Note that the level of complexity went up one notch. The column player has to get inside the row player s head and understand how he will think in order to determine what strategy is best for her.

Rationalizable Strategies How would you solve this game? Column Player Left Middle Right Row Up 2, 0 3, 5 4, 4 Player Down 0, 3 2, 1 5, 2 Are there any dominant strategies? Are there any dominated strategies? Another solution concept: a strategy is a best response for player i when player j plays a certain strategy if player i s strategy choice yields the highest possible payoff among her set of choices. A rational player will not play a strategy that is never a best response.

Solution to the previous game Row player: U is the best response to L or M, and D is the best response to R. Column player: L is the best response to D, and M is the best response to U. So R is never a best response for the column player. The row player should not expect that strategy to be played if the column player is rational. That being the case, the row player should not play the D strategy, but should always play the U strategy. And if the row player plays U, then the best response of the column player is to play M. Not that we have added another layer of complexity. The column player reasons that the row player is reasoning that he will never choose R, and so as a result will have a dominant strategy of U which she will play. The column player s choice of M is wise only if he can count on the row player having gotten inside of his head.

Nash equilibrium Let s try a more complicated example: Column Player C1 C2 C3 C4 Row R1 0, 5 2, 5 7, 0 6, 6 Player R2 5, 2 3, 3 5, 2 2, 2 R3 7, 0 2, 5 0, 7 4, 4 R4 6, 6 2, 2 4, 4 10, 3

Solution to the previous game Does either player have a dominant strategy? Are there any dominated strategies? Non-rationalizable strategies? So how do we think the game will turn out? An even stronger solution concept: Nash Equilibrium A Nash equilibrium is a strategy profile such that each player s chosen strategy is a best response to the strategy selected by the other player. In other words, if my strategy choice is the best possible response to your strategy, and at the same time your strategy is the best possible response to my strategy, then this strategy pair is a Nash equilibrium. If that is true, then neither of us will experience ex post regret. In the previous game, the strategy pair R2, C2 is a Nash equilibrium.

Implications Managers often make decisions where the situations is not likely to be repeated or not repeated very often Pricing a new product Entering a new market Acquiring another firm 43

Implications Steps to follow in this situation 1. Estimate the payoff of each potential action, as well as the payoff of your rival 2. See if there are any weakly dominate strategies you can eliminate 3. Is there a dominant strategy? If yes, then take that action 4. If no, then estimate what your rival will do and identify your best action (which may be a mixed strategy) 44

Implications Steps to follow in this situation 5. Check whether the outcome is a Nash equilibrium 6. Check whether the outcome is a Nash equilibrium are you forecasting that your rival is behaving optimally? If no, then revise your forecast Assume your rival is doing the same thing Put yourself in their desk 45

Implications If you are risk adverse or have little experience in this situation, may want to consider a secure strategy Strategy that minimizes losses Not the best strategy for the long-run May be learning-by-doing 46

Prisoner s dilemma in a business setting http://www.llbean.com/llb/shop/32937?page=warm-up-jacket-fleece-lined http://www.landsend.com/products/mens-classic-squalljacket/id_287454_59?cm_mmc=139971612&source=gs&003=56492216&010=4283286&gclid=cndhivyegm4cfqm QaQodZjcMXQ Duopolists choosing a pricing strategy: Land s End High price: $89.99 Low price: $69.99 L. L. Bean High price: $89.99 π LLB = 100 π LE = 100 Low price: $69.99 π LLB = 140 π LE = 40 π LLB = 40 π LLB = 60 π LE = 140 π LE = 60 Does this outcome seem counter-intuitive to you? See: Resolving the Prisoner s Dilemma, (Chapter 4 in Dixit and Nalebuff)

Implications of the Prisoners Dilemma for Oligipolistic Pricing Observations of Oligopoly Behavior 1) In some oligopoly markets, pricing behavior over time can create a predictable pricing environment and implicit collusion may occur. 48

Implications of the Prisoners Dilemma for Oligipolistic Pricing Observations of Oligopoly Behavior 2) In other oligopoly markets, the firms are very aggressive and collusion is not possible. Firms are reluctant to change price because of the likely response of their competitors. In this case prices tend to be relatively rigid. 49

Dynamic Price Competition Price competition can be viewed as a dynamic process Decisions by a firm today will affect its behavior as well as its competitors in the future Dynamic competition can also occur in nonprice dimensions such as quality 50

Dynamic versus Static Models Dynamic models can address questions that static models cannot (Example: What determines the intensity of price competition?) What appears as short term profits (in a static model) are often followed by long term negative effects (in a dynamic model) How might Golden Ball outcome change if they played the game a number of times? 51

Dynamic Model Scenarios Static models cannot explain how firms can maintain prices above competitive levels without formal collusion In other situations, even a small number of firms are sufficient to produce intense price competition Dynamic models are useful in exploring such situations 52

Implications of the Prisoners Dilemma for Oligopolistic Pricing Price Signaling & Price Leadership Price Signaling Implicit collusion in which a firm announces a price increase in the hope that other firms will follow suit 53

Implications of the Prisoners Dilemma for Oligopolistic Pricing Price Signaling & Price Leadership Price Leadership Pattern of pricing in which one firm regularly announces price changes that other firms then match 54

Implications of the Prisoners Dilemma for Oligopolistic Pricing The Dominant Firm (Stackelberg) Model In some oligopolistic markets, one large firm has a major share of total sales, and a group of smaller firms supplies the remainder of the market. The large firm might then act as the dominant firm, setting a price that maximized its own profits. 55

Tit-for-Tat Pricing When two firms compete over several periods, a tit-for-tat strategy may make cooperative pricing possible Since each firm knows that its rival will match any price cut, neither has an incentive to engage in price cutting 56

Pricing Problem Firm 2 Low Price High Price Low Price 10, 10 100, -50 Firm 1 High Price -50, 100 50, 50 57

Pricing Problem Non-repeated game Strategy is Low 1, Low 2 Repeated game Tit-for-tat strategy is the most profitable Low Price Firm 1 High Price Firm 2 Low Price High Price 10, 10 100, -50-50, 100 50, 50 58

Tit-for-Tat Pricing with Many Firms Condition for sustainable cooperative pricing N = Number of firms i = Discount rate Π M = Monopoly profit for the industry Π 0 = Prevailing profit for the industry 59

Tit-for-Tat Pricing with Many Firms The numerator is the annuity a firm will receive by cooperating The denominator is the one time gain by not cooperating and inviting a tit-for-tat response from the rivals When the condition is met, the present value of the annuity exceeds the one time gain from refusal to cooperate 60

Coordination Problem While cooperative pricing is sustainable, the folk theorem does not rule out other equilibria Achieving a desirable equilibrium out of many possible equilibria is a coordination problem A cooperation inducing strategy that is also a compelling choice is a focal point 61

Coordination in Practice Round number price points will help with coordination Even splits of the market (or status quo for market shares) is likely to be durable Coordination easier with fewer products that are identical 62

Coordination in Practice Conventions and traditions make rivals intentions transparent and help with coordination Examples: Standard cycles for adjusting prices, using standard price points for price quotes 63

Market Structure & Cooperative Pricing Achieving cooperative pricing may depend on certain market structure conditions Some examples are: Concentration Conditions that affect reaction speeds and detection lags Asymmetries among firms Price sensitivity of buyers 64

Relevant Structural Conditions Lumpiness of orders Information availability regarding sales transaction Volatility of demand conditions 65

Practices that Facilitate Cooperative Pricing Firms can facilitate cooperative pricing by Price leadership Advance announcement of price changes Most favored customer clauses Uniform delivered pricing 66

Cooperative Pricing Conclusion Cooperation is difficult at best since these factors may change in the long-run. 67

Sequential Games Players move in turn Players must think through the possible actions and rational reactions of each player 68

Sequential Games Examples Responding to a competitor s ad campaign Entry decisions Responding to regulatory policy 69

Sequential Games The Extensive Form of a Game Scenario Two new (sweet, crispy) cereals Successful only if each firm produces one cereal Sweet will sell better Both still profitable with only one producer 70

Modified Product Choice Problem Firm 2 Crispy Sweet Crispy -5, -5 10, 20 Firm 1 Sweet 20, 10-5, -5 71

Modified Product Choice Problem Question Firm 2 What is the likely outcome if both make their decisions independently, simultaneously, and without knowledge of the other s intentions? Crispy Firm 1 Sweet Crispy -5, -5 20, 10 Sweet 10, 20-5, -5 72

Dynamic Games of Complete Information Now we turn to game theoretic situations where there can be a sequence of moves and where players may move more than once. We define a dynamic game by its extensive form, which specifies: The identity and number of players When each player can make a move The choices or options available on each move The information available when making a move The payoffs over all possible outcomes of the game The extensive form of a dynamic game can be represented by a game tree, which has: Decision nodes Branches: actions available Terminal nodes: payoffs

Example of a game tree: u 5, 2 U 2 d 1, 0 1 D u 4, 4 2 d 6, 0

Solving the previous game Player #1 moves first and has two options, UP or DOWN. If player #1 plays UP, then player #2 moves next. He has two options, up or down. If player #1 plays DOWN, then player #2 moves next. He has two options, up or down. If player #1 plays U and player #2 then plays u, the payoff to player #1 is 5 and the payoff to player #2 is 2. U and d results in payoffs of 1 and 0 to players #1 and #2. D and u results in payoffs of 4 and 4. D and d results in payoffs of 6 and 0. How would player #1 want this game to turn out? How would player #2 want the game to turn out? How is the game likely to turn out? Why?

Solving the previous game (continued) If you are player #1, which strategy do you play? Why? UP, since your likely payoff from UP is 5 while your likely payoff from DOWN is 4. If you are player #2, how might you induce player #1 to play DOWN so that you can get to a payoff of 4 instead of 2? Threaten to play down if player #1 plays UP. Is such a threat credible? No, since if player #1 plays UP, you maximize your payoff by playing up.

Solving dynamic games Let us define a subgame to be a smaller game embedded in the complete game. In other words, starting from some point in the original game, a subgame includes all subsequent choices that must be made if players actually reach that point in the game. This will allow us to test whether conjectural sub-strategies within a game are sequentially rational. In our original game, there are three subgames: the original complete game and the games that begin at player #2 s decision nodes: u 5, 2 2 2 d 1, 0 u d 4, 4 6, 0

Subgame Perfect Nash Equilibrium A strategy profile is Subgame Perfect Nash Equilibrium [SPNE] if the strategies are a Nash equilibrium in every subgame. How do we determine the subgame perfect Nash equilibrium to a dynamic game? The approach is simple: We look ahead and reason backward. In other words, we use backward induction. Backward induction involves identifying the smallest possible subgames and determining what the optimal choices are for the player involved. Then we replace these subgames with the implied payoffs, and solve the next highest level of subgames. This process is continued until the Nash moves for every possible subgame have been found.

Another example u 2, 1, 2 U 2 d 1, 3, 4 1 U 3, 0, 1 D 2 u 3 D 4, 3, 3 d U 1, 2, 6 3 D 2, 6, 0

Another example u 2, 1, 2 U 2 d 1, 3, 4 1 U 3, 0, 1 D 2 u 3 D 4, 3, 3 d U 1, 2, 6 Solution: Player #1 picks D. Player #2 picks u. Player #3 picks D. And [D, u, D ] is subgame perfect Nash equilibrium. 3 D 2, 6, 0

Modified Product Choice Problem The Extensive Form of a Game Assume that Firm 1 will introduce its new cereal first (a sequential game). Question What will be the outcome of this game? 81

Sequential Games The Extensive Form of a Game The Extensive Form of a Game Using a decision tree Work backward from the best outcome for Firm 1 82

Product Choice Game in Extensive Form Firm 1 Crispy Sweet Firm 2 Firm 2 Crispy Sweet Crispy Sweet -5, -5 10, 20 20, 10-5, -5 83

Sequential Games The Advantage of Moving First In this product-choice game, there is a clear advantage to moving first. 84

Sequential Games The Advantage of Moving First Assume: Duopoly P = 30 Q Q = Total Production = Q MC = 0 Q 1 + Q 2 = 10 and P = 10 π = 100 / 1 + Q 2 Firm 85

Sequential Games The Advantage of Moving First Duopoly With Collusion Q 1 Firm1Moves First Q 1 π 1 = Q 2 = 15 = 112.50 = 7.5 and P = 15 Q 2 = 7.5 and P π 2 = 56.25 π = 112.50 / = 7.50 Firm 86

Choosing Output Firm 2 7.5 10 15 7.5 112.50, 112.50 93.75, 125 56.25, 112.50 Firm 1 10 125, 93.75 100, 100 50, 75 15 112.50, 56.25 75, 50 0, 0 87

Choosing Output This payoff matrix illustrates various outcomes 7.5 Firm 2 7.5 10 15 112.50, 112.50 93.75, 125 56.25, 112.50 Move together, both produce 10 Firm 1 10 125, 93.75 100, 100 50, 75 Question What if Firm 1 moves first? 15 112.50, 56.25 75, 50 0, 0 88

Threats, Commitments, and Credibility How To Make the First Move Demonstrate Commitment Firm 1 must constrain his behavior to the extent Firm 2 is convinced that he is committed 89

Threats, Commitments, and Credibility Strategic Moves What actions can a firm take to gain advantage in the marketplace? Deter entry Induce competitors to reduce output, leave, raise price Implicit agreements that benefit one firm 90

Threats, Commitments, and Credibility Empty Threats If a firm will be worse off if it charges a low price, the threat of a low price is not credible in the eyes of the competitors. 91

Wal-Mart Stores Preemptive Investment Strategy Question How did Wal-Mart become the largest retailer in the U.S. when many established retail chains were closing their doors? Hint How did Wal-Mart gain monopoly power? Preemptive game with Nash equilibrium https://www.youtube.com/watch?v=jzhkvjybpks 92

The Discount Store Preemption Game Company X Enter Don t enter Enter -10, -10 20, 0 Wal-Mart Don t enter 0, 20 0, 0 93

The Discount Store Preemption Game Two Nash equilibrium Low left Upper right Enter Company X Enter Don t enter -10, -10 20, 0 Must be preemptive to win Wal-Mart Don t enter 0, 20 0, 0 94

Strategic Entry Barriers Are there actions that an incumbent firm might take to deter entry by outsiders? In certain cases there may be. If the incumbent can make some binding commitment and communicate that to potential entrants prior to their decision to enter, then the incumbent may be able to forestall entry. Consider the following example from Avinash Dixit, New Developments in Oligopoly Theory, American Economic Review, May 1982, pp. 12-17.

Consider a two-stage game between an incumbent monopolist and a prospective entrant. The first stage is the latter's entry decision. If he stays out, the incumbent earns monopoly profits P M If entry occurs, the incumbent decides whether to fight a price war, with profits P W to each, or to share the market, with profits P D to each duopolist.

At each termination point the corresponding payoffs are shown, the first component being the incumbent's. It is assumed that P M > P D > 0 > P W, that is, duopoly is profitable but not as much as monopoly, while a price war is mutually destructive In the above example, the strategy "War if entry" cannot be part of a perfect equilibrium. The entrant knows that the incumbent's optimal response to entry is sharing. Since P D > 0, he stands to gain by entering. Therefore this is the outcome in the perfect equilibrium.

Now suppose the incumbent has available a prior irrevocable commitment, such as incurring cost C in readiness to fight a price war. This does not affect his payoff if a war in fact occurs, but lowers it by C otherwise. The new three-stage game tree is shown below.

An incumbent who has made this commitment will find it optimal to fight in the event of entry if P W > P D - C. An entrant, knowing this, will stay out if the incumbent is committed, and enter if he is passive. The incumbent, knowing this in turn, will make the commitment if the ultimate payoff from doing so, P M - C, exceeds that from being passive, P D. Provided there exists a commitment whose cost satisfies P M P D > C > P D -P W, it allows the incumbent to employ a credible threat and deter entry to his own advantage. Incidentally, the example also shows how a sequential equilibrium has to be solved backwards. The availability of such a commitment is a matter for each specific case. Sunk capacity is the most cited example.

There are two essential requirements: the commitment should be made (and made known) prior to the entrant's decision, and it should be irreversible. The incumbent often has a natural advantage of the first move, although an unaware passive incumbent may find himself facing an aggressive committed entrant, when the roles are reversed and the incumbent must contemplate exit. Irreversibility is a matter of technology and institutions. For example, capacity serves the purpose only if it cannot be costlessly liquidated. Capital goods that depreciate rapidly, or ones for which an efficient resale market exists, are not useful instruments for an entry-deterring commitment.

How might this work in practice? Techdom s Two Cold Wars, WSJ, 7/22/09. http://gattonweb.uky.edu/faculty/troske/teaching/ eco411/articles/techdoms Cold War WSJ 22-07-09.pdf Haven t Shareholders Had Enough Chicken? WSJ, 4/4/01. http://gattonweb.uky.edu/faculty/troske/teaching/ eco411/articles/shareholder Chicken WSJ 04-04-01.pdf 101

How might this work in practice? Don t underestimate you rivals willingness to fight: http://gattonweb.uky.edu/faculty/troske/teaching/ eco411/articles/jet Maker Bombardier Finds Bigger Proves Far From Better - WSJ.pdf And the fight continues: https://www.wsj.com/articles/trudeau-andmay-join-forces-against-boeing-in-itsdispute-with-bombardier-1505761250. 102

First Mover Disadvantage There may be a disadvantage to being the first mover Have to make the initial investment in developing a new product. Following firms can copy what you do and avoid the investment costs Trying to set a standard 103

Flexibility and Options The value of commitments lies in creating inflexibility However, when there is uncertainty, flexibility is valuable since future options are kept open Commitments can sacrifice the value of the options 104

Commitment-Flexibility Tradeoff By waiting, a firm preserves its option value By waiting, the firm also may allow its competitors to make preemptive investments 105

Preserving Flexibility Modify the commitment as conditions evolve Delay commitment until better information is available on profitability Make unprofitable commitments today to preserve valuable options in the future 106

Flexibility and Real Options A real option exists if future information can be used to tailor decisions Better information about demand can be utilized by delaying implementation of projects Value of real options may be limited by the risk of preemption Key managerial skill in spotting valuable real options 107

Implications When operating in a sequential environment managers should 1. Carefully define the sequence of moves 2. Work backwards from the end to predict the likely outcome of the interactions, making sure you assume your rival is acting optimally 3. Decide whether there is any credible commitment you can make to change your rivals prediction of your action 108

What Game Theory Can Teach Managers Understand your business setting Identify your rivals an how you interact Place yourself behind you rivals desk Consider the entire sequence of decisions Start at the end and work backwards to determine your best strategy, as well as your rivals best strategy With a first mover advantage try and move first 109

What Game Theory Can Teach Managers With a first mover advantage try and move first If you can t move first, decide if there are credible steps you can take to induce your rivals to change their decisions and improve your outcome With a second mover advantage, avoid moving first Be unpredictable and maximize flexibility Repetition facilitates cooperation 110

Summary A game is cooperative if the players can communicate and arrange binding contracts; otherwise it is noncooperative. A Nash equilibrium is a set of strategies such that all players are doing their best, given the strategies of the other players. 111

Summary Strategies that are not optimal for a oneshot game may be optimal for a repeated game. Strategies such as tit-for-tat pricing can facilitate coordination but are difficult to implement. Market structure affects the sustainability of cooperative pricing. 112

Summary An empty threat is a threat that one would have no incentive to carry out. To deter entry, an incumbent firm must convince any potential competitor that entry will be unprofitable. 113