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.