How to Win at Battleship

I used to play Battleship with my son, but he doesn't want to play with me any more. He's often wondered how I can consistently win the game. He assumes (and he's right) that, since I'm a game theorist, I've probably figured out some sort of mind-reading trick to be able to intuit where his ships are located. Apart from mind reading, I also rely on an optimal search strategy. Anyway, here's an amusing piece in Slate about a Microsoft employee who has taken this idea to its logical extreme.

http://www.slate.com/blogs/browbeat/2012/05/16/_battleship_how_to_win_the_classic_board_game_every_time.html

Happy Summer

Something to remember the class by. This photo courtesy of Alper.

Have a happy summer and a great career gamers. Please stay in touch and feel free to visit the game theory website and blog for a refresh of key learnings from the class. Also, if you find a need for more game theory in your organization, please reach out. In the past, I've done custom sessions at several companies looking for more outward thinking. Many of these requests came from Game Theory alumni.

Keep using your outward thinking and empathy to build mental models and figure out what course of action to take. Previous game theory alums have said that the tools in the class were essential to career management and successfully leading teams.

Judo in Action: The Pebble Watch

Ran across this piece speculating about the lack of VC support for the Pebble, which is basically a limited version of an iPhone packed into a wristwatch. 

http://battellemedia.com/archives/2012/04/does-the-pebble-cause-a-ripple-in-apples-waters.php

Now this seems like a classic judo. The gizmo itself is underpowered compared to the iPhone, the form factor obviously limits its appeal somewhat. And thus we come to the key question--how should Apple respond? 

Is the Pebble really committed to staying small? How large is the potential consumer base for such a device? Since you need an iPhone to run the thing, is it really a threat to Apple? Of course, Apple can kill it by producing their own Pebble, or they can let the thing go. 

My own guess is that this requires no response from Apple since the iPhone is essential for the thing to work. Apple has, in the past, tolerated thrid party offerings that change the form factor of iPod, such as the many speakers, clock radios, etc. produced for it. These have not hurt iPod at all. I expect that they'll reason analogously in this case. 

Your thoughts?

Classes #25 and 26 Highlights

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.

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
Gameblers	Nashty Equilibrium
Swimsocks	Pokerface
4 Young Men	JM Hypnotherapist
Wysiwyg	Beautiful Minds
YMCA^2	4 Men & a Baby Mama

Value of Education Results

 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.

http://www.youtube.com/watch?v=S0qjK3TWZE8&feature=player_embedded

Penalty Kicks

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

http://www.freakonomics.com/2010/06/10/freakonomics-radio-world-cup-edition/

How to Make a Good Final Project

 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

E-Retail Results

The results from the e-retail game are now posted. Check them out here:

E-retail results

Goodies

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."

http://www.fastcompany.com/most-innovative-companies/2012/red-bull-media-house

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

 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:

	Open	Closed
1st Price	Dutch	Yankee
2nd Price	English	Vickrey

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.

Bidding
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.

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

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.

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

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.

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:
http://www.christopherxjjensen.com/2012/03/05/evolutionary-games-infographic-project-first-sequence-images/

Conceptual Graphics depicting the Prisoner’s Dilemma, Stag Hunt, and Hawk-Dove games:
http://www.christopherxjjensen.com/2012/02/06/evolutionary-games-infographic-project-new-conceptual-images/

Conceptual Graphics depicting the Ultimatum game:
http://www.christopherxjjensen.com/2012/03/15/evolutionary-games-infographic-project-ultimatum-game-conceptual-images/

“Realistic/applied” Example Graphics depicting the Prisoner’s Dilemma, Stag Hunt, and Hawk-Dove games:
http://www.christopherxjjensen.com/2011/11/21/evolutionary-games-infographic-project-first-examples-matrices/

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.

Problem Set Answers

By popular demand, now up in the handouts section of the course website are some answers to the problem sets. These include supplemental notes for problem set 2 showing how to solve lobbying games in general. More importantly, the model problem set solution offered by the Latin Gambits for PS3 is also posted. 

Enjoy

Sport Geenius Payouts

I've now computed the payouts for Sports Geenius. Check them out here:

Sports Geenius Payouts

If you are a lucky winner, please stop by the office of my assistant, Milton Fong (he is across the way from my office) and pick up your cash. Congratulations to the winners!

OPEC Final Results

Excellent discussion of what makes for effective trust and coordination. I thought the focus on communication and of appeals to non-economic motives was especially valuable. For your reference, below is a link to the spreadsheet with the final totals. Please input your earnings (where $1 million = 1 ecu) into the P&L spreadsheet. Thanks!

OPEC Final Results

OPEC Round 10

A: $86.88, 77,403

B: 83.23, 77,292

Cold fusion coin = heads. Cold fusion is invented. There is no round 11. 

OPEC Round 9 Results

Market A: $63.11, 78,287
Market B: $62.24, 75,318

The last embers of cooperation flicker out.

Cold fusion: Result = Tails, so cold fusion not invented. Round 10 due today, though I think I can guess what the production amounts will be.

OPEC Round 8 Results

Market A: Price = $101.75, Quantity = 73,458
Market B: Price = $84.02, Quantity = 77,308

Things are still holding together in market A. Market B is off the rails.

Cold fusion die = 4. Result: Cold fusion not invented so round 9 is on. Quantities due tonight at 1159.

OPEC Round 7 Results

Sorry for the delay. Out of town playing golf in Santa Barbara. Sandpiper is an awesome course.

Market A: Price = 101.76, Quantity = 71,115
Market B: Price = 65.45, Quantity = 74,488

Cooperation completely collapses in market B!

OPEC Round 6

The family is off to Santa Barbara, so no video for this one.

Market A: Price = $104.69, Quantity = 75,317
Market B: Price = 90.63, Quantity = 77,038

Some cracks in the armor??

OPEC Round 5 Results

Back on track...

Final Topics Clearinghouse

Some teams want to get a head start on the final project. Who am I to get in the way of this noble endeavor? So, by popular demand, I have now put up a final project topics clearinghouse. Same rules apply: first come, first served. Happy topicing!

Final Projects Topic Clearinghouse

Presentation Order

Mid-semester presentations are next week. The format is 10 minutes for presentation and up to 2 minutes for Q&A. Please submit your presentation files to me 2 hours in advance, so I can preload them on my laptop. This will minimize the transition times between presentations, which is essential given our tight schedule.

Here is the order for the presos. Note that you are free to swap times with another group if this is mutually agreeable.

Monday: 1. Good Swimmers, 2. Wysiwyg, 3. Nashty Equilibrium, 4. Pokerface, 5. YMCA^2, 6. JM Hypnotherapist

Wednesday: 1. Beautiful Minds, 2. 4 Young Men, 3. Latin Gamblers, 4. Swimsocks, 5. Gameblers, 6. 4 Men & a Baby Momma

OPEC Round 4 Results

Oil prices collapse in markets A and B.

OPEC Round 3 Results

Mid Semester Topics

To avoid topic duplication, I have now added a Topics Clearinghouse document to the course website. Each team should enter a topic on the sheet. The first entrant for a topic "owns" it. No other group can claim the same topic unless they have a radically different aspect of the topic that they are analyzing.

Claim your topics here: Topics Clearinghouse

Class #12 Highlights

In this class, we learned about the theory of achieving coordination in repeated games. The idea is to combine carrots (promises of rewards for good behavior) with sticks (threats of punishment for bad behavior) to obtain cooperation.

This required: 

1. A payoff difference from the future consequences of bad versus good behavior. 

We saw that, when the game is only repeated twice or a small number of times, it was not possible to make credible promises to reward niceness in the last round of the game. As a consequence, good behavior breaks down. The lesson is that, as the endgame draws near, cooperation fails. 

2. Timely detection of bad behavior

We saw that, when an individual could get away with bad behavior for a couple of periods, sustaining cooperation became much more difficult. Likewise, delaying punishment also makes cooperation more difficult.

3. Proportional/Credible Punishments

If a punishment is so outrageous that the individual won't follow through, then it serves no role in getting good behavior. It must be credible that the punishment will be meted out. 

4. Forgiveness

Mistakes happen. An unforgiving punishment scheme suffers from two problems. It is disproportionate, so has credibility problems. It is also problematic since it cannot recover from errors. 

Together, these four keys allow for leveraging the future to achieve cooperation.

Revised Schedule

We are now officially one full class behind schedule. Accordingly, I have updated the syllabus to reflect the amended schedule. One topic, Principles of Bargaining, has been deleted and Judo has been moved into its slot. Please check the course website for the amended schedule. In terms of the near term roadmap:

Monday: GE v Westinghouse + OPEC Summit
Wednesday: Browser Wars

Following week: Mid Semester projects

OPEC Round 2 - Do Over

Dear Gamers,

Here are the results for round 2 (the do-over):

Market A: Price = 98.47, Quantity = 74,255
Market B: Price = 99.62, Quantity = 75,272

Round 3 due by Friday Wednesday at 1159pm. (Thanks for Billy Hwan for the alert correction.)

Class #11 Highlights

In class #11, we talked about building mental models. The case offers several frameworks that build up to form the "right" game to analyze. The first step, of course, is to gather relevant data. This is data not just about the financial aspects of a decision, but about the behavior of rivals as well. Competitor Analysis takes this data and uses it to paint a "portrait" of the rival. Sketching out assumptions and goals helps to determine which aspects of the payoff matrix on which to place weight. For example, Jerry Yang's founder status indicated that he highly valued control of Yahoo over other financial considerations. By studying current strategy and capabilities, one obtains a list of possible responses to your actions. For instance, if you are a startup contemplating a business model is some aspect of the social/mobile space, understanding the capabilities of Facebook is obviously essential in developing a non-threatening business strategy where their large user base will not be deployed against you. 

After completing a competitor analysis, it is useful to undertake a behavioral analysis. Are there ways that you can change the frame of a negotiation to get what you want? How does the positioning of the status quo affect the reaction to various negotiated outcomes. It is also useful to apply this same analysis to yourself. Is your data gathering subject to confirmatory bias? Are you overconfident in determining the appropriate scenario analysis to perform?

These behavioral factors can influence the perception of payoffs as well as the types of strategies your rival is likely to pursue. This is critical to building a mental model. Finally, game theory puts all of these analyses together to formulate what game is being played, what strategies are available and how payoffs are evaluated. As we saw in the Coors case, sometimes it is enough to know the relative payoff rankings, and these analyses can be especially useful in informing this aspect of payoffs. 

Together, these steps constitute the basic framework for assessing a rival's response to a new product introduction, a change in positioning, a new pricing strategy, and so on.

OPEC Do-Over

Dear Gamers,

I found the error in the simulator. Basically, the sum of all the OPEC quantities was coded as fixed rather than as reflecting the actual sum.

Here is the proposed fix. Since round 1 numbers were submitted legitimately, I reran the simulator with those quantities. The revised price results are

Market A: Price = $92.31, Quantity = 71,525
Market B: Price = $95.66, Quantity = 70,393

We will redo round 2 tonight at midnight. All subsequent rounds are the usual Mon, Wed, Fri at midnight schedule.

Sorry for the confusion.

OPEC Round 2

Round 2 results:

Market A: Price = 160.68, Quantity = 61, 576
Market B: Price = 165.80, Quantity = 62, 712

Market B enjoys a boom in demand while amenic demand plagues market A. Round 3 due by Monday at 1159PM.

OPEC Round One

The round one results are now available.

Goals of OPEC

I've been asked in various ways what your goals should be in the OPEC game. Here's my view of "best practices" in regard to OPEC and all the games we do in the class:

Your objective should be to make as much money as possible using realistic strategies. In OPEC, that means coming up with creative solutions to cooperation that would be workable in the REAL WORLD context of international competition. Cheesy workarounds that violate the spirit but not the letter of the rules I set out may help you to achieve the monetary objective, but will not provide you with usable lessons in a business context.  

If you're uncertain about the legitimacy of a given practice, you should ask yourself whether whatever tactic you have in mind is at all sensible in the real world version of the environment being simulated. If it is not, then you should refrain from that practice.  While your narrow goal is to make money, the broader pedagogical goal of the experiments is to give you the opportunity to try out various tactics and hone skills useful in the real world. Tricks that take advantage of the fact that it is a simulation, rather than reality, may net you a short-run monetary gain don't help you a bit in becoming a better strategist/tactician/negotiator/leader in the real world. Presumably the reason you took the class is to become a better leader and not to learn how to "game" a simulation. 

OPEC Clarifications

Dear Gamers,

Two important clarifications for the OPEC game:




1.  Your colleague, Rodrigo Donoso, brought to my attention a critical typo in the OPEC Data sheet. The total reserves for each country is off by a factor of ten. In other words, the Saudi total reserves should be 528,000 rather than 52,800. I have now updated the spreadsheet to reflect this fact. 


In your calculations, the total reserves should not be binding unless the game lasts for a really long time. For instance, the Saudis will not run through their capacity, even if they are producing all out, in fewer than 44 turns. 


2. All production units are in 000s of barrels. Thus, if Saudi produces 12,000 in period 1 and the world oil price is $100, then it earns revenues of $1,092 million. 


Let me know if you have any additional questions. 

Class #6 Highlights

In class #6, we studied the question of how to value the assets of a company. This is a fundamental question. Indeed, acquisitions and divestments are the two most significant decisions any CEO can undertake in guiding firm strategy. Conventional inward thinking suggests that we study the cash flows generated by the asset, the sale value, the replacement cost, or other such metrics in valuing an asset. Our game theory approach was to apply the "it's a wonderful life" rule to determine the strategic value of an asset. 

Under this rule, we study the value of the company with an without the asset. In the case, we showed situations where this analysis leads to the conclusion that an asset can have a negative value. In the case, having excess capacity prevented the smaller firm from undertaking a price cutting strategy without provoking a price war. By shedding the asset, the smaller firm became less threatening and unilateral price cuts were more likely to be tolerated by the larger firm. So long as the small firm had enough remaining capacity to add share, these price cuts were, in fact, profitable. 

The shedding of assets to seem less threatening to a rival is called the puppy dog ploy. A key part of firm strategy is calculating where the breakeven point is in terms of share grabbing that avoids provoking a costly price war. Even though one might think that excess capacity provides option value, in some circumstances, it can actually reduce a firm's competitive options and thereby destroy value. 

Class 9 Highlights

In class #9, we concluded our unit on dominance with a couple of observations.

1. In auction settings, the only way to get truth-telling and efficiency in equilibrium is to apply Vickrey's Law. No other auctions will work. For example, If we use the rule that in the A,B setting, the winner of A simply pays the amount of the losing bid, then bidding above your value can be profitable. Likewise, in the multi-unit auction setting, using a uniform price auction will also not work in that a bidder's own bid can determine the price of units won. Therefore, bidders have an incentive to bid below their value for units further down the demand curve.

One practical implication of this second finding relates to auction IPOs. Most auction IPOs, such as those run through Hambrecht & Co. use the uniform price auction. For bidders seeking small numbers of shares, bidding is approximately truthful, but large institutional investors seeking many shares will have incentives to shade down bids. Thus, this auction does not completely do away with the "pop" on initial trading as the bid determining the price probably reflects a discount below fundamentals owing to these incentives.

The highlight of the second half of the class was a solution to the teams problem. We first noticed that, in a conventional teams problem, free-riding was an important consideration. In effect, the game was a prisoner's dilemma. Efficiency wages, i.e. paying wages above the market rate, can help to some extent by activating reciprocal motives on the part of employees. For years, this was IBM's strategy. It has also been routinely demonstrated in laboratory settings.

Incentives based solutions include profit sharing and bonus schemes. We saw that unless effort was extremely profitable relative to the personal cost to the employee, profit sharing schemes suffer from the same free rider problem as fixed wage schemes. Bonus schemes transform the problem into a stag hunt. The riskiness of the stag hunt depends on the aggressiveness of the target. The more aggressive the profit target, the more fragile the trust relationship and the less the likelihood of success. As a practical matter, a firm that strives to get more out of its employees may end up getting less than a firm that sets more modest goals. It is important to consider this tradeoff between trust and profits in determining appropriate incentives for a company.

As a practical example, some pundits have noted that the emphasis on "accountability" and ambitious short-term targets at Yahoo led to a culture where cooperation and trust across properties was diminished rather than strengthened. In stag hunt, one can think of the hare strategy as one of "silos" within an organization. Each group pursues its own goals rather than pursuing synergistic opportunities between groups. The lesson from game theory is that, accountability in the form of high powered incentives and severe punishments for missing targets creates exactly the conditions for silos to become the correct best response by managers in the firm. That is, we can use game theory to see how incentives can affect culture--sometimes in unexpected and undesirable ways.

Game Theory Class #5 Highlights

In this class, we studied the timing principle. In games where there is no private information about payoffs, a player moving first can always do at least as well as going at the same time. Moreover, in many situations, moving first can improve payoffs. The reason secrecy doesn't pay is that the only possible secret is your strategy. In equilibrium, individuals are engaging in mind reading, so even this is no longer a secret. When there are no real secrets, there is nothing to be gained by keeping moves hidden. Transparency, on the other hand, can shape the rival's strategic response. This option value is potentially useful. As we saw in the McCain-Schumer experiment, it was quite useful for the first mover. 

We also observed that the right first move depended on the competitive position of the first mover relative to the second mover. When an aggressive move from the first-mover provokes a retreat by the second, then being aggressive is optimal. On the other hand, when aggression is met with aggression (as in the case when the first mover has lower value than the second), then the right strategy is to ratchet down competition. This is referred to as the favorite and underdog effects, respectively. 

Class 7 and 8 Highlights

In these classes, we studied dominance. Recall that a dominated strategy is one where there is some other strategy that does at least as well (and sometimes strictly better) regardless of the strategy chosen by the rival. 

One can use this concept repeatedly to "dominance solve" some games, but each round of dominance requires ever greater levels of common knowledge of rationality. For instance, the equilibrium for the beauty contest can be solved using infinite rounds of iteration of dominated strategies. But, as you saw earlier, that prediction fares poorly. A good rule of thumb is the deletions up to about two rounds are same, but not thereafter. 

We then applied this concept to Vickrey auctions. These are auctions satisfying Vickrey's law: You pay the amount of the externality you inflict on others. This is a version of the It's a Wonderful Life Principle. First, compute the values to all other players if you were not present. Then compute their values when you are. If you pay this amount in winning an item or items, then it is a dominant strategy to bid truthfully. This is a powerful insight for designing proper incentives. 

In practice, there are two limitations: 1. It doesn't work well when there are a large number of options with synergies between them. 2. It doesn't work well when fairness is an important consideration. For instance, we saw how Vickrey auctions can lead to situations where the high bidder pays less (or even nothing) for an item while a lower bidder ends up paying more for the same item. 

Game Theory P&L

Please fill in your P&L from McCain-Schumer and Spectrum Auctions in the P&L Spreadsheet located on the Game Theory website. The results from both games are posted there as well next to the relevant experiment in the syllabus. In McCain-Schumer, your score in ecus is your raw score divided by 1 million. The same is true of spectrum. Thus, if you earned $110 million in Spectrum, this counts for 110 ecus.

Thanks!

Sports Geenius

Just a reminder to be a part of the experiments on the structure of incentives in tournaments. Please visit the site:

http://fantasyallnews.com/SportsGeenius/

and sign in using your email and the password I provided in class. This is a good chance to make decisions under contest incentives as well as to earn a little money. Any feedback you might have is also appreciated.

Please note: SportsGeenius is open Mon, Weds, and Fri. It is closed on other days. This is purely for testing purposes. The final product is intended to be open every day.

Class #3 Highlights

In class # 3, we talked about rationality. While caricatures of economics and game theory posit that rationality is the same thing as maximizing money, the reality is more nuanced. One needs to pay attention to non-pecuniary factors like fairness, identity, pride, altruism, spite, and so forth. The tools of game theory are flexible enough to handle these sorts of additions. Indeed, the art of successful "mind reading" is getting the game right in the sense of including all relevant factors determining a rival's payoffs.

We also talked about the fundamental rule of game theory: look forward, reason back. Through this rule, we discovered that the competition among teams for a player in the presence of a right of first refusal option was largely illusory. We also discovered that a press release designed to deter entry can only be successful to the extent that the threats and promises offered are credible.

Side notes: Results from McCain are due by midnight of 1/30/12. Also, I've fixed the calendar entries in the syllabus.

Class #1 and 2 Highlights

As I mentioned at the outset: The goal of this course is to change your mindset, to provide you with a new and useful lens through which to view the world. The shorthand for this is inside versus outside thinking. Inside thinking focuses on how to make optimizing decisions when faced with either a static setting or environmental risks. For instance, in marketing you identify the willingness to pay of key customer segments and then choose optimal prices for each.

Outside thinking deals with strategic risk--there are other players in the game besides yourself. These players have goals, ambitions, and strategies, and it is important to factor these in when making decisions. The metaphor for outside thinking is a chessboard. The "best" space on a chessboard depends on where all the other pieces are and, perhaps more importantly, depends on the anticipated moves by the other player.

We illustrated the difference through the Race for the GOP Nomination game. In that game, inside thinking assumed that all other players simply chose the candidate corresponding to the signal received and then optimized. Viewed in this light, later voters are very likely to make the correct decision since they have lots of data on which to base that decision. Outside thinking paid attention to the incentives of earlier voters to vote strategically, i.e. to vote against their own signal. Using outside thinking, we discovered that the primary race is very likely to produce a "cascade"---a run of decisions all favoring a single candidate. Indeed, we saw this behavior in the experiment as well. The key implication is that later voters do not have much data on which to base their decision and, in fact, information is not collected by voting in this fashion.

Why is this important? Under inside thinking, you would (correctly) conclude that voting sequentially is likely to produce the correct choice given enough voters. With outside thinking, you would realize that there is a serious strategic problem with sequential voting. It is quite likely to produce the wrong answer. In our setting, there was a 20% chance that voting would produce the wrong answer even if we had an infinite number of voters.

We might then compare this to another common system--everyone voting at the same time. In our game, this would produce the correct answer always. Indeed, using game theory, we can discover that there is a general result that if all voters have reasonably similar incentives (like choosing the more electable candidate in the primary), then a national primary will choose the correct voter with certainty as the number of voters gets large. Thus, by using outside thinking, we learn that there is a right way and a wrong way to use voting to make good decisions. Since voting is a common way to make decisions in business settings as well as political settings, this is quite important in developing effective ways of having your company make decisions.

Game Theory Teams

Building a Team

Here is the incomplete list of team members from emails received to date. If you are not on the list, please send me an email with your team members and team name.

Game Theory Teams                                                                                                Spring 2012

Gameblers: Maria Alejandra Gonzalez, Alper Batur, ismael ghozael, Fabio Povoa, Mohamed Shommo

Latin Gambits: Paul Kisiliuk, Rodrigo Donoso, Andres Pachano, Matias Bebin, Inaki (Jose Ignacio) Ruiz

Good Swimmers: Alden Woodrow, Patrick Flemming, Laura Bentzien, Kyle Bentzien, Dana Ledyard.

Pokerface: Gustavo Ribeiro, Jasmine Hellings, Javier Figueroa, Juan Manuel de los Rios Wakeham, Shannon Riley

Nash-ty equilibrium: Gene Boyle, Eamonn Courtney, Billy Hwan, Ella Yanai, Janice Yuen

4 Young Men: Aditya, Archit, German, Sue, Darren, 

SwimSocks: Caroline Mock, Oscar Salinas, Sam Mathias, Sam Wiggin, Patrick Mar
Beautiful Minds: Alex Chou, James Cook, Pei-fu Hsieh, Patrick Schneider, Derek Simmons and Jenni Tonti.
YMCA²: Yoichi Katayama, Matthias Egler, Carlos Facanha, Alexandre Montoro, Aaron Tang

4 Men and a Baby Mama: Rahul Bijor, Brandon Yahn, Laura Andron, Josh Mogabgab, Andrew Hamilton
JM Hypnotherapist: Rafa, Iris, Jeff Williamson, Juan Sanchez Morales, Dave Lewis

Wysiwyg: Phil Dawsey, Adam Boscoe, Sam Filer, Abhishek Singhal

The Race for the GOP Nomination

Choosing the Right Move

From the Game Theory in the Wild files comes this piece on the Colbert Report spotted by your colleague Dave Lewis. The piece is about the book The Dictator's Handbook, written by the NYU game theorist Bruce Bueno de Mesquita. The piece talks about how the professor uses game theory in a computer model to predict geopolitical events. Here's a useful tool for applying these ideas: The Predictioneer's Game.

Key highlight from the interview: A prediction on the GOP nomination. Enjoy!

http://www.colbertnation.com/the-colbert-report-videos/406665/january-23-2012/bruce-bueno-de-mesquita

Welcome to Game Theory

Welcome to the Spring 2012 edition of game theory. All of the assignments are available from the main game theory website. I'll use this blog to recap the key highlights from each class. It will also be used to make announcements about assignments and to offer takes on whatever I happen to be thinking of at the moment. You should check the blog regularly for announcements and results from the various games.

The blog is also an excuse to show off my photos. Unless otherwise credited, all the photos on the blog are done by me. Photography is a real passion of mine, and I especially enjoy sharing the images I create. Creativity is a major subtheme of the class.

I hope you enjoy the semester we'll have together!