Wednesday, April 25, 2012

Classes #25 and 26 Highlights

Pocket Aces
In our last unit of game theory, we studied signaling. The goal of a signal is to influence the beliefs of the rival about some payoff relevant characteristic. In our setting, that characteristic was the worker's productivity. In firm settings, the characteristic is typically the quality of the item or service. To work, a signal must be understood by the receiver of the signal. That is, the message must meaningfully convey some information about the characteristic.

Most of the time, a firm or individual is interested in separating their product or service from the competition. The key to a good signal is one that a firm possessing the characteristic can send but which cannot be sent by someone lacking this characteristic. Often, this boils down to a difference in the cost of sending the signal. For instance, a car manufacturer with a low probability of breakdown can issue a comprehensive warranty that lasts for a long time whereas an unreliable manufacturer will find such a warranty too expensive to issue.

An MBA has some of these same characteristics. While the monetary cost of the degree is the same regardless of the quality of an individual, a low type will struggle to get through the courses, and this extra work effort will be costly in terms of quality of life, balance, and so on. A high type will not have to work as hard to get through the curriculum and hence will find the experience more pleasant and less costly.

Even though a separating equilibrium exists, it may not be optimal for anyone. Recognizing this, industry groups might agree not to permit certain types of signaling thus leaving all members better off. For instance, the industry council of distilled spirits manufacturers agreed not to advertise on television for many years. This agreement amounts to the enforcement of a pooling equilibrium over this signal.

Key Learnings

1. A signal works by changing beliefs about a payoff relevant characteristic. Thus, it is only effective if thie connection is readily understood by its recipient.
2. Using a signal to differentiate requires that the signal cannot be easily imitated by low quality types. This may be because it is prohibitively costly for them to do so or because it is technologically infeasible.
3. A signal is not useful simply because it is costly to send. It must be differentially costly, i.e. cheaper for high types than for low types to send.

Tuesday, April 24, 2012

Class 23 & 24 Results


In these classes, we studied mixed strategy equilibria. While usually your strategy is designed to maximize your profits given your mental model of the rival, there are some situations where the optimal strategy is simply to jam the signals your rival gets about what you intend to do. The use case is a circumstance where you are competing for price sensitive customers who buy at the lowest price. This happens in e-retail as well as in procurement contexts. Clearly, if your rival can predict your bid/price, she will simply undercut you and win the business. Thus, your job is to make the job of prediction as difficult as possible. The way to do this is through strategic ambiguity--building enough randomness into your actions that prediction is difficult.

But it's not enough simply to be random, you have to be smart about your randomness. In the e-retail situation, this consisted of using hit and run pricing strategies. Either you want to maintain a high price so as not to sacrifice margin to loyals while giving yourself a chance to win or you wanted to go low to ensure a good chance of capturing shoppers. Less good (against experienced players) is pricing in the middle, which sacrifices margin while risking defeat should your rival offer a "sale" in this period.

This is another example of the distinction between inward and outward thinking. Inward thinking says that you offer promotions to gain share, acquire customers, or introduce new customers to your product. The thinking has nothing to do with rivals. Outward thinking shows that sales promotions are a key tool in maintaining strategic ambiguity and jamming the signals of the rival.

Class #24 formalized how to do this. Your goal was to choose randomness so as to leave the rival indifferent among her strategies. Your rival acts in the same fashion and hence, in equilibrium, both sides are randomizing such that neither side gains from choosing any particular pure strategy. We showed this in the Beautiful Game example.

This strategic randomness can also lead to unintended consequences. In the Kitty Genovese game, we showed how rational players acting optimally give rise to a sort of collective madness---the larger is the team, the less likely each individual is to work hard (help) and the more likely the team is to fail at its job. The lesson for managers is to be careful about adding more people, even really good people, to teams. The logic of mixed strategies helps to explain why things like Amazon's 2PT (2 pizza team) rule makes sense despite the complexity of many business decisions.

Key Learnings:

1. Analyze games to determine is signal jamming is called for.
2. Optimal signal jamming leaves the rival indifferent among strategies.
3. When both sides are indifferent, we've found a mixed strategy equilibrium.
4. The logic of indifference can lead to perverse consequences such as diffusion of responsibility and ultimately failure despite the fact that everyone personally and collectively benefits from helping.

Final Presentation Schedule

Here is the schedule for final presentations. The rules are 10 minutes for the presentation, 2 minutes for Q&A. Please send me the slides 2 hours in advance of class so I can preload them on my laptop.

Wednesday  5/2
Monday 5/7
Good Swimmers
Latin Gambits
Nashty Equilibrium
4 Young Men
JM Hypnotherapist
Beautiful Minds
4 Men & a Baby Mama

Value of Education Results

Shapes: Cube and Cylinder

 Your colleague Abhishek Singhal was kind enough to create a results sheet for the Value of Education experiment. Check it out here:

Value of Education Results

Genius Play in the Prisoner's Dilemma

From Game Theory alumnus, Andrew Stadlen, comes this gem from the British game show, Golden Balls.

Penalty Kicks

Your colleague, Bradley Okamoto, offers this piece from the Freakonomics podcast for a follow up to the beautiful game.

Monday, April 23, 2012

How to Make a Good Final Project

Domino Theory

 Here are some tips for making a good final project. I'll be adding to this document as I think of more tips.

Tips for a Great Final Project

Monday, April 16, 2012

Thursday, April 12, 2012


Some miscellaneous goodies for your reading pleasure:

1. We saw a lot of kinked bidding functions played in first-price auctions in class. How should you bid against these: The answer is still v/2 but with "jumps" in the bidding function at each of the kink points. Your colleagu Patrick Schneider was curious about the analysis, so here it is
 Kinked Bidding Strategies in First-Price Auctions

2. In the Judo unit, I highlighted Red Bull as a Judo Master, your colleague Caroline Mock called my attention to this interesting piece. Here's the killer quote:

"Red Bull is a media company that sells drinks instead of ads, and I get the impression they think of themselves that way."

3. Answers to problem set 4 are now posted in the handouts section of the course website.

4. Slides from Elizabeth Churchill's talk are now posted on the main page of the course website.

Class #22 Highlights

Band of Brothers

 Wars of attrition are ubiquitous. Common advice is to avoid them; however, this assumes that such games are all negative sum (i.e. there are no winners). This is simply false.

A war of attrition can be thought of as a type of auction. As such, we can use the RET to determine the expected cost of the war as well as the value, if any, to be gained there. This is a key input of any cost/benefit analysis of entering into a war in the first place.

The concession decision in the WoA comes down to comparing the cost of persisting in the war for the next time interval against the benefit = value * hazard rate of rival conceding conditional on the current duration of the war. So long as the benefit exceeds the cost, then it is better to continue than concede.

Two key lessons emerge from this cost/benefit analysis:
1. Past payments in the war do not matter. These are sunk costs and should not be used in the determination of the continue/concede strategy.
2. Influencing the rival's mental model about the hazard rate of concession is critical to winning the war. There are various ways to do this:
a. Credibly signal you have a high value.
b. Employ an agent with a reputation for toughness to pursue the war on your behalf.
c. Signal cognitive biases like overoptimism to persuade the rival that you will not concede.

The last is especially noteworthy--while we usually think of behavioral biases as things to be avoided, this reflects inward thinking. We obviously do not want to perform a decision analysis with bias. Using outward thinking, however, behavioral biases can become valuable tools for commitment strategies.

For instance, if I am overconfident that my rival will concede, then I will not concede myself and this creates a credible commitment that my hazard rate is low. The result is a self-fulfilling prophecy---faced with a low hazard rate, my rival is likely to concede thus justifying my initial overconfidence.

Strategy and Game Theory:
To build on the Bitter Competition case, notice that flexibility to scale operations can undermine commitment not to concede. For instance, HSC started with a small production and left open the door for either expansion or cheap exit. From an inward thinking perspective, this is a sensible strategy. Outward thinking, however, shows that this gives Nutrasweet good reason to believe that there is a high hazard rate of concession on HSC's part; thus, bolstering Nutrasweet's willingness to prosecute a war or attrition and win it through force of will.

Key takeaways:
1. Recognize that a war of attrition is a kind of auction. It is a second-price all-pay auction.
2. Use the RET to compute the expected costs and expected payoff. Use these estimates to determine whether it is worth entering into the war or not.
3. If in the war, use the cost benefit calculus shown above to determine the time to concede.
4. To gain an advantage in the war, use every means possible to credibly signal a low hazard rate of concession.

Class #21 Highlights

In this class, we heard from an ethnographer who designs technology products. Her concerns are with empathy--utilizing survey and long-form interview methods to learn what needs are not being met by existing products as well as strategizing by consumers seeking workarounds for limitations in existing products.

The key lesson here is that she is, in effect, building mental models of consumers and other stakeholders interacting with a product or service. The job of the designer is then to utilize these mental models and then best respond in terms of product design and development--the identical outward thinking process we have emphasized in the course.

Utilizing a range of techniques, from reading financial reports and transcripts of conference calls, to implementing long-form interviews with ex-employees of the rival can yield useful insights in the construction of a complete mental model. For strategic decisions where getting the mental model correct is critical to success or failure, drawing on methodologies across a variety of fields (i.e. metacognition) is a key attribute of leaders.

Key takeaways:
1. Outward thinking is critical to innovation/new product development.
2. Psychology/ethnography offers a variety of techniques to build better mental models.

Class #20 Highlights

In this class, we studied auctions. Our taxonomy for types of auctions was:

1st Price
2nd Price

We also compared auctions for cash and shares.

Strategic Equivalence
Two auctions are strategically equivalent, if bidders follow the same bidding/drop out strategies. We easily deduced that Dutch and Yankee auctions are strategically equivalent since the decision about when to stop the clock in a Dutch auction was identical to the bid in a Yankee auction.

When bidders know their own values, then Vickrey and English auctions are also strategically equivalent. Clearly, you drop out of an English auction when the bid exceeds your value and you bid your value in a Vickrey auction.

While bidding in a Vickrey auction was easy to determine, bidding in a first-price auction is much trickier, it depends on your mental model of the rival. Under an optimal bid, the marginal benefit of increased chance of winning times the surplus gained is equal to the marginal cost of paying $1 more in all circumstances that you win the auction.

The result of this tradeoff was that, in equilibrium, you bid up to your best guess as to the value of your highest rival, conditional on the fact that her value is below yours. Intuitively, imagine you knew the value of your rival. Call this amount x, and suppose that it is less than your value, v. Then you would want to bid x + a little bit to just beat your rival. Since you do not know your rival's value, in equilibrium you make your best guess at it conditional on the fact that it is lower than your value. The reason this conditioning makes sense is that, when your rival's value is higher, you lose the auction, so these circumstances are irrelevant.

Revenue Equivalence
Now that we know the equilibrium under a first price auction, we can compare the revenues with the Vickrey. In the Vickrey, the high bidder pays the value of the highest rival. In the first price auction, the high bidder pays her bid, which is equal to the expected value of the highest rival. On average, the payment of the high bidder is exactly the same in the two auctions.

It turns out this is a general property. Here is one statement of the revenue equivalence theorem (RET):
Any pair of auctions where:
1. The allocation is efficient (i.e. the highest value bidder gets the item)
2. There is free opt-out.
3. Payment is in cash.
4. Risk-neutral bidders draw values from the same distribution
are revenue equivalent. Moreover, the expected payments of each of the bidders is the same in the two auctions.

The theorem extends to the case where there are k identical items, so long as each bidder can get only one item. It also extends to the case where there is a reserve price, so long as the two auctions exclude the same set of low-valued bidders. It can also extend to situations where bidders do not know their values exactly.

The RET is a very powerful tool. It lets us analyze all sorts of things, even things that do not seem like auctions. Examples include R&D races, lobbying, legal battles, queuing, sales contests, and price wars. However, one should be careful not to take it too seriously. It's a starting point. In most circumstances, things do not quite satisfy the RET.

Cash versus Shares
One example where the RET does not apply is cash versus shares auctions. In an English shares auction, the payment of the winning bidder depends on her value precisely. In a cash auction, it does not (the payment equals the bid of the highest rival). This creates a linkage between the payment of the winner and her value. The linkage principle says that, on average, the greater the linkage, the more the revenue to the seller. We saw that VCs do better with shares than with cash.

Another example of the linkage principle concerns disclosure of information concerning the value of the item up for auction. A policy of committing to disclose  this information will also produce higher revenues on average. The commitment aspect is important since there will be a temptation not to disclose information if it is bad news. It turns out there is a disclosure game that, under some conditions, we can do without the commitment assumption, but we'll leave that aside for now.

Key takeaways:
1. A market designer has a choice of payment rule and auction type. There are pros and cons to each possibility though some choices are strategically equivalent with sophisticated bidders who know their values.
2. The RET is a benchmark identifying conditions where the revenues are the same for common auction forms.
3. A useful lever to increase revenues is the linkage principle--the more closely payments are linked to the value of the winning bidder, the more money the auctioneer makes. Shares auctions create linkage through the value of the equity stake.

Monday, April 9, 2012

VC Auction Results

The P&L results are now posted. Please transfer your total P&L to the overall P&L spreadsheet. Thanks!

VC Results

Wednesday, April 4, 2012

Class #19 Highlights


In this class, we concluded Judo with some practical examples and then we studied VC financing.

Our first practical example of Judo was Dell. Dell chose a niche strategy of operating only in the "direct" market. Initially, this consisted of phone and catalog sales and then later expanded to online sales. Dell also kept prices low, at least initially. It exploited pricing inflexibility on the part of HP, Compaq, and IBM. Owing to resistance from the retail channel, these firms could not price discriminate by channel. Dell then benefited from the fact that the online channel turned out to have meteoric growth, ultimately surpassing the retail channel as the main way people buy desktops and laptops.

We also studied Red Bull, who chose a niche channel (discos) and exploited a brand inflexibility on the part of Coke and Pepsi. To compete with Red Bull, they needed a brand that seemed dangerous, but maintaining separate brand images across channels is extremely difficult.

We then studied how competition and the form of the contract can help VCs sort out the quality of entrepreneurs' ideas. Several facts emerged from the discussion:
1. In a second price or English auction, it is a dominant strategy to bid up to the point where you are indifferent between winning and losing regardless of whether the auction is for cash, shares, or any other payment method.
2. The English and Vickrey (second price) auctions are strategically equivalent when bidders known their values.
3. In a first-price auction the bidding strategy was less clear. It involved a trade-off between bidding higher to win versus bidding lower to make more conditional on winning. How these two forces play out was a matter of dispute among the teams.

Tuesday, April 3, 2012

Class # 18 Highlights


In this class, we studied Judo strategies. These strategies use a combination of look forward, reason back along with marketing mix and inflexibility of an incumbent to make profits even under extremely unfavorable industry settings.

The key is to choose a marketing mix to provoke an accommodate rather than a fight response from the incumbent. To do this, one needs either a low price, a niche presence, or both. The other ingredient is some exploitable inflexibility on the part of the incumbent. While the experiment focused on the inability of the incumbent to price discriminate, other inflexibilities are possible such as brand inflexibility or cannibalization inflexibility.

This "puppy dog ploy" strategy allows success even when a firm has no competitive advantage whatsoever, a common situation for a new entrant.

Key Takeaways

  • Use LFRB to choose a marketing mix that provokes an accommodate response.
  • Success is a mix of niche presence and low prices.
  • An inflexibility on the part of the incumbent is required for this to work.
  • In a suitable setting, competitive advantage is not needed for a firm to make profits using this strategy.

Class #17 Highlights

In this class, we debriefed the OPEC game. Several key points emerged from the discussion. First, in the initial summit, it is especially important to agree on thresholds where punishment will occur and the exact punishment that will be undertaken. The threatened punishment must be credible, so threats to punish forever will rarely be successful.

One problem with designing punishment is the tradeoff between being forgiving and inviting individuals to cheat. By building in a cheating "buffer" market A undercut the power of their punishment strategy by inviting cheating up to the buffer.

After the summit, communicating is crucial. Even if the lines of communication are open, without constant attention given to this channel, mistrust can build. Here, there was a significant difference between the two markets. Communication proved key to success.

What motivates people to cooperate? Part of it is financial interest in doing so, but another part, which is very important, is the power of relationships, honor, and trust. Appeals are most successful when they align the financial interests with intangibles. Much like GE's unilateral disarmament strategy in its dealings with Westinghouse, Saudi B's strategy of publicly vowing never to punish worked well in sharpening its appeal to honor and other intangibles. Thus, it gave up power using financial instruments to gain it through moral instruments.

Key Takeaways

  • Coordination works best when good behavior and bed behavior are well defined and known to all. Punishments need to be swift, forgiving, and credible.
  • Forgiveness works best in terms of the punishment, not in terms of waffling about what constitutes bad behavior. The latter simply invites cheating.
  • Use all the tools available to achieve coordination, including non-pecuniary tools. Appeals to honor, integrity, and other moral attributes, with punishments denominated in these same terms, can be powerful means of aligning incentives.

Class # 14 Highlights

The Joy of Text
In this class, we studied commitment strategies in network markets. This was illustrated in the battle between Microsoft and Netscape for browser supremacy. We saw that the network effects in this market mainly stemmed from the developer ecosystem. The larger the install base of a browser, the more likely that developers would cluster and add value. This naturally leads to tipping in favor of a single dominant player in the market. Initially, Netscape was that leader. It had a superior browser. It was cheap for developers to build on the platform, and it had a vastly larger install base than Microsoft.

The key difficulty for Microsoft is that, even if it gave away its browser, the value proposition from Netscape was still higher for consumers. What Microsoft needed was a credible way to "sell" its browser for a negative price. The problem is that committing to charge a negative price is difficult. Microsoft solved this problem through bundling. By putting its browser together with the OS, in effect, it sold the browser at a negative price as our analysis showed. Now, a user's choice was no longer Netscape or Explorer it was Explorer versus Netscape and Explorer. This drastically changed Netscape's value proposition and allowed Microsoft to quickly gain share. Through network effects, these share gains then changed the equation for developers too and tipped the market away from Netscape.

Of course, this might have been a Pyrrhic victory for Microsoft as it unleashed years of antitrust hell that continue to this day. With the benefit of hindsight, we can see that the threat of browsers to discomfit the OS was significantly overblown. Microsoft might have been better served to have lost this battle thus avoiding antitrust scrutiny and the loss of focus that this entailed.

Key Takeaways

  • Commitment strategies can fundamentally change the game--even in markets with strong network effects.
  • Microsoft's commitment was to charge a negative price for its browser.
  • Anticipating commitment strategies is critical for rivals. Netscape might have foreseen this possibility and pre-empted it through FTC decrees and the like.

Class #13 Highlights

In this class, we studied how to avoid price wars and, more generally, how to achieve tacit cooperation. The setting was the steam turbine business with competitors GE and Westinghouse. The industry structure was only moderately attractive. While there were few competitors and barriers to entry were high, at the same time the good was undifferentiated and there was excess capacity in the market.

A key feature of the business landscape was that negotiations were conducted in secret. This seems natural--secrecy is a standard tool for maintaining one's bargaining power in the face of tough and concentrated downstream buyers. But secrecy causes problems for maintaining price discipline.

GE solved the problem by recognizing the four keys to successful cooperation:
1. Transparency
2. Credibility and speed of punishment.
3. Proportionality
4. Forgiveness

The transparency problem was solved through a simplified price book, no negotiations from listed prices, publishing quotes and orders, and making all this information available via audit to any downstream party requesting it. The other aspects were solved through the use of a multiplier on listed prices, which could be quickly adjusted and then reset to turn on and off punishments.

On the one hand, this solution surrenders some bargaining power to buyers; however, by removing the latitude of its sales staff to negotiate deals, GE arguably reclaimed some of this bargaining power through commitment.

GE also did one other clever thing--they reduced their own temptation to cheat through price protection guarantees to buyers. These guarantees meant that future price reductions would be less profitable for GE and hence there would be less incentive to renege on the agreement.

Key Takeaways

  • Clarity, transparency, credibility, and forgiveness are all essential to successful coordination.
  • Reducing the profits from cheating also makes agreement easier
  • Achieving these objectives may require sacrificing bargaining power elsewhere.

Monday, April 2, 2012

Game Theory Infographics

Chris Jensen, a colleague at Pratt Institute, is developing infographics for archetypal games. He is looking for feedback, so if you have any, send it to me and I'll pass it along to him. Personally, I'm not sure how useful these infographics are, but they certainly are cute and attractive, so I thought I'd pass them along.

Sequence Graphics depicting the Prisoner’s Dilemma, Stag Hunt, Hawk-Dove, and Ultimatum games:

Conceptual Graphics depicting the Prisoner’s Dilemma, Stag Hunt, and Hawk-Dove games:

Conceptual Graphics depicting the Ultimatum game:

“Realistic/applied” Example Graphics depicting the Prisoner’s Dilemma, Stag Hunt, and Hawk-Dove games:

Judo Results

Your colleague Inaki Ruiz was kind enough to prepare a spreadsheet with the results from the Judo game. You can find it here:

Judo Results

Please input the profits from this game as well as those of earlier games into the Profit and Loss spreadsheet. For this game, ECUs = Profits/100.