Managerial Game Theory

One of the first models covered in game theory is the Prisoner’s Dilemma. I’m sure you’ve heard of it or at least recognize it from episodes of Law and Order. Let’s look at the simple model with 2 individual players so we can eliminate mixed strategy equilibria and focus strictly on pure strategies.

The two strategies for each player are “productive” and “exploitive”. The payoffs for the two players can be summarized on the usual grid.


Productive Exploitive








One possible economic interpretation of this payoff structure is the ratio of compensation to work output. A ‘1’ represents compensation that accurately prices the employee’s output. A ‘2’ or a ‘0’ represent either excessive compensation for the same output or excessive output for the same compensation. Consistent with these payoffs, the manager prefers to get as much output as possible for as little compensation as possible while the employee prefers the opposite.

In a single period game, the dominant strategy of both players is to choose the exploitive relationship but if both players believe that they will repeat the game, the productive strategy produces the maximum utility for both players. It is fairly safe to assume that both players will begin with the productive strategy since they believe that the game will be played multiple times. The utility of one player starting off with an exploitive relationship and playing until time ‘t’ would be

U= Σ[2, 0/(1+r), 0/(1+r)2, 0/(1+r)3,…0/(1+r)t]

where r is the discount rate under which the player values the next period payoff in the current period. As we can see, the utility of this player is 2 so this player will only begin with an exploitive relationship if he/she believes that

2 > Σ[1, 1/(1+r), 1/(1+r)2, 1/(1+r)3, 0/(1+r)k…0/(1+r)t]

where k+1 is the number of times the game is played before the other player switches to an exploitive strategy. Without an extremely high discount rate ‘r’ the player needs to trust that the other will not switch strategies for relatively few game iterations. So few iterations are needed that I would say that any player with a rational discount rate would start with a productive relationship. Unfortunately, it does not follow that both players will continue to pursue a productive relationship beyond the first few iterations of the game.

The player with the higher discount rate will switch strategies first in order to realize a higher present value of the increased payoff of ‘2’. At this point, both players will pursue the exploitive relationship until the end of the game. Since the discount rate may be interpreted as a measure of risk aversion, the player with greater risk aversion will be the first to pursue an exploitive relationship.

While there are many real world complications with the enforcement of the payoff structure and possible reputational effects for future working relationships, it is important to understand the ease with which reputational effects may be mitigated through HR disclosure policies. Excessive faith in employee controls and risk management policies can lead to risk averse managers and employees both pursuing exploitive relationships. Employees and managers may want to engage in working relationships with riskier counterparties if they want to remain productive.

The Decreasing Marginal Utility of Donuts

This morning I ran through the Dunkin Donuts to pick up two donuts for me and two donuts for my wife. Four donuts cost $3.85 while 6 donuts cost a little over $4.00. The cashier tried to convince me that buying 6 donuts would be cheaper. Understandably, the cashier would not know that I was ordering for only two people or that we prefer not to stuff ourselves with more than two donuts each. Still, I feel like the cashier never quite believes that I understand the cost per donut is lower with an order of 6 versus 4 but that it is entirely rational to base decisions on total cost rather than unit cost.

Value Creation

I hear a lot of opinions on how economic value is created. Some of these opinions are supported by secondhand anecdotal evidence and most of them are used to support various political or social positions. Some of the most absurd theories on value creation even come from wealthy and/or successful people so someone without a business education may be forgiven for believing that this is a philosophical question that can only be answered through a belief in some set of principles. I would like to articulate why there is an objective reality to value creation. It has very little bearing on any political or social position and absolutely nothing to do with faith.

Value is created through the decision making process. This process need not be rational; the only thing that matters is success. As in warfare, winning by skill, preparation, accident, luck, or for the wrong reasons are all sufficient. Unfortunately, in this framework, there is an objective definition of success and it requires two ingredients. The first ingredient is an understanding of the money generated from a new venture and the second is understanding the price of the money necessary to start and maintain the project. Success is defined as a project that generates a rate of return greater than the cost of the money that is required for the project. That is it. Full stop.

While the concept is simple, there is also an objective methodology for calculating success. Future cash flows must be discounted at the cost of capital which is the rate at which you obtain the capital necessary to start and run the business. Oftentimes this rate is uncertain so the best estimate is used and the results are tested to see if changes in this rate affect the decision to go ahead with the project. The internal rate of return is the constant rate at which a series of positive and negative cash flows can be discounted such that the net present value of these cash flow are zero. This can also be described as the discount rate at which the manager is financially indifferent to taking on a new project. If that discount rate is greater than your cost of capital then you undertake the project.

Whether managers know this process or not, this is the only method of creating economic value. Improving on this process requires either lowering your cost of capital by getting money at a lower interest rate or by increasing the present value of the cash flows generated from the project. This can be achieved by reducing the investment in the project, getting the cash flows earlier, or increasing the growth rate in cash flows.

The Effects of Venture Capital Strategy


Highland Capital and Tallwood Venture Capital represent two strategies of venture capital investing. Highland represents the traditional diversified portfolio strategy where many unrelated investments are made and little operational support is provided by the investor. Tallwood represents the focused portfolio strategy where fewer investments are made in a specific industry and investors are able to provide a greater amount of time and operational support to their firms. Neither of these firms is absolute in their strategic focus. Highland provides some support to some of its investments in the form of office space and access to other industry leaders. Highland also has focused teams in specific industries and cannot simply invest in any firm. While I will discuss a hybrid approach later in the paper, the number of focused sectors and number of investments in each sector results in a strategy that is indistinguishable from a diversified strategy.

Tallwood only has two executives in residence to assist partners in providing technical advise for its portfolio. Clearly, this is insufficient to provide constant support to their firms however this paper will discuss relative differences in strategies rather than absolute examples of either strategy. I will explain why this difference matters to investors, how it affects investment selection within the firm, and the type of firms that are most likely to receive funding from each strategy. Given the extremely high exits necessary to compensate for a large number of losers, a diversified strategy is interested in funding companies that have a low probability of success and a high-expected growth rate. A high probability of success would not allow for a large enough equity stake given a limited amount of equity and a low growth rate does not provide a sufficiently high exit valuation. Increasing an investor’s focus on an industry allows for investing in ideas that may have a smaller market potential but greater probability of success.

Investor Motivation

From the investor’s point of view, venture capital should provide superior risk adjusted returns with a liquidity premium when compared with public markets. Without this return, there is no incentive to invest. The problem lies with describing risk in statistical terms in order to get a precise quantitative answer rather than business terms that usually results in a more qualitative answer.

Investing in a venture capital firm requires a lockup period where the investor cannot withdraw the investment or may withdraw but at a severe penalty. This is to protect other investors in the fund from being forced to contribute more capital than planned or to sell illiquid investments at a discount. As compensation for being unable to quickly withdraw their investment, an investor requires a liquidity premium. Without this liquidity premium, investors would be better off buying assets such as stocks with the same returns and no penalty for selling early. Endowments that have too much of their portfolios allocated to illiquid assets may not be able to support their liquidity needs when a financial crisis causes the value of their stocks and bonds to fall. When the liquidity risk is not considered, venture capital returns may be overstated.

While venture capital may be an unappealing investment based on overestimated returns and underestimated risk, there may be opportunities to make a rational investment by choosing a successful fund manager. If an investor will need to accept a lockup period of up to 10 years, the initial manager selection is critical. There is a substantial risk that one of the partners may retire or leave the firm and support staff typically has a higher turnover so the selection process will need to focus on strategy rather than personality. Knowing this, the question then becomes what strategy produces above average returns in the venture capital industry?

Venture Capital Industry Concerns 

According to Fred Wilson, venture firms need average exit multiples of three to meet the returns required by investors. The average industry exit multiple was 1.6 which is approximately a ten percent annual IRR. According to the article, another unnamed industry analyst estimated that venture capital would need to decrease by 50% in order to generate adequate risk adjusted returns before coming to the conclusion that the venture capital model doesn’t scale. This conclusion seems justified when we compare the expectation of a 10% return in 2010 with the expectation of a 25% to 35% return in 1998 and the realized return of 8.2% as of the third quarter of 2010 but does not take into account a strategy change in the venture capital industry.

Highland Capital represents the traditional diversified venture capital strategy. As Peter Bell noted in his presentation, the success of any investment is viewed as a random process and Highland’s partners are generalists that follow a top down approach to individual investments. The partner first determines an attractive industry; one that is in the growth period of the industry S-curve. High growth companies command higher valuations at exit and are easier to market to the public market or an acquirer. Since there is little disagreement in the industry on what the high growth industries will be, venture firms will tend to over invest in attractive industries.

According to Zider, a venture capital investment has an estimated 10% probability of success, which implies that the average venture capital firm has excess capital to allocate to investments. The exact proportion of the remaining 90% that is required to obtain the winning 10% cannot be determined with certainty without making some assumptions. In Highland Capital’s case, the assumption is that venture investors are not skilled in selecting investments. This assumption supports the diversification strategy also limiting the amount of time each partner can devote to an individual investment. A generalist who invests in a diversified portfolio has little incentive to choose the best firm in an attractive industry with time being a limited resource. This conclusion is based on the assumption of limited equity in quality firms seeking capital and limited time combined with excess funds with which to invest.

In Tallwood’s case, the firm has a focused portfolio strategy where the top down approach can only be applied in a limited manner. If investments are limited to the semiconductor industry and are smaller in number, Tallwood can pursue a bottom up investment strategy where more time is spent evaluating whether the particular investment is attractive as opposed to evaluating whether an industry is attractive. Time constraints become more relaxed relative to a diversified strategy since there are fewer investments to track. The focused portfolio strategy assumes that partners have some expertise in selecting investments and advising companies. Without this assumption, there would be no incentive to limit the number of investments or the industry in which to invest.

An alternative to the diversified and focused portfolio strategies is for a single venture capital firm to have multiple partners where each partner or team of partners is focused on a particular industry or technology. This hybrid strategy can mimic the results of either the diversified or focused portfolio depending on the number of investments made by each partner and the resources available for each partner or team to support their investments. A partner with few investments has an incentive to select best in class companies and provide operational support while a partner with many investments will provide little to no support and assume success is a random process. In the former example, the hybrid strategy will mimic a focused strategy while in the latter case; the strategy will be similar to a diversified strategy.

Financial Theory

The assumptions I have made regarding diversified and focused portfolio strategies in the venture capital industry are supported by the work of Fisher Black and Robert Litterman in their model of portfolio optimization. The Black Litterman model was original applied to currencies but it can be applied to any investment. The main idea of this model is to optimize a portfolio not just on expected return but also on the deviation between market expected returns and the investor’s expected return. In essence, invest more money when the investor believes that he/she has an edge over the market.

The diversified strategy is diversified because partners believe that they do not have more skill at selecting investments than the market. Under the Black Litterman model, we would expect these firms to exhibit “herding” behavior investing in the same firms and industries and, as Peter Bell confirmed, this is what we observe in the industry. Focused funds believe that they have an edge over other investors and overweight those firms as described by the model. This results in fewer investments and more resources to support each investment.

Returning to the argument of the amount of excess capital necessary to secure a 10% success rate, the focused fund must assume that either they have a higher success rate than diversified funds or they have higher returns from their winners. Without one or both of these assumptions, there would be no incentive to remain limited to a focused strategy. If we assume that one or both of these possibilities are true, a focused firm has the opportunity to invest in firms where the expected return is lower than that required of a diversified fund. This occurs because of the secondary weighting of the difference between investor expectations and market expectations described by the Black Litterman model. The two components of expected return, possible returns weighted by probabilities of success, have some interesting implications regarding the type of investments that each strategy will prefer.

Impact on Funded Companies

In the case of Highland, a diversified portfolio results in many companies receiving funding with each project receiving little to no operational guidance. Given the extremely high exits necessary to compensate for a large number of losers, the type of ideas that get funding are those that have a low probability of success, a high growth rate, and a high expected return. Knowing that there is excess capital when measured against the limited amount of quality equity for the reasons discussed above, only a low probability of success will guarantee a sufficient equity stake to compensate for the large number of losers in the diversified portfolio. A high probability of success would not allow for a large enough equity stake and would not provide sufficient returns for the diversified investor.

Increasing an investor’s focus on an industry allows for investing in ideas that may have a smaller market potential but greater probability of success. This type of investing serves several important purposes. First, it is obviously an efficient allocation of capital that produces economic growth. Second, it provides a form of financing that is less expensive than the most speculative angel investing but more expensive than traditional debt financing. Usury laws prohibit charging an appropriate interest rate for the amount of risk that investors are exposed to even when investing in a company with a greater probability of success. This is because many firms that fit this description may not have sufficient physical assets to post as collateral. Firms with a focused strategy ensure that companies that may not change the world but may create substantial economic value receive funding.

Recent data from the National Venture Capital Association suggests that investors are on average pursuing a diversified strategy. Despite low and even negative returns the number of deals remains high while the amount invested decreases. This would suggest that venture capital investors are making numerous small investments rather than a small number of large investments. The most recent data also suggest that investors continue to choose the same sectors in which to invest. Cambridge Associates reports that 75% of its venture capital benchmark is composed of healthcare, IT, and software and that these sectors outperform other venture capital investments. This would seem to support the idea that most investors do not deviate from market expectations and under the Black Litterman model, would be best served by pursuing the diversified portfolio strategy.

If most venture firms are investing in similar companies and the returns of the industry are declining, an investor may still be able to obtain above average risk adjusted returns. One method is by choosing a venture capital manager that has sufficient expertise to beat the average venture capital return through a focused strategy. One problem with this alternative is that managers have an incentive to limit the number of investors in order to reduce the risk of missing a capital call. Investing with a focused fund of sufficient quality may not be possible for an individual investor. An alternative is to choose a venture capital manager that has a strong enough reputation and network to ensure that they are able to invest in the best firms in an attractive industry. Since the amount of equity with a high probability of success is limited and there is an excess supply of capital, it is critical that a venture firm that pursues a diversified strategy be able to invest in the best firms. Without this network and reputation, investors should not expect above average risk adjusted returns.

Cambridge Associates Private Equity and Venture Capital Funds Closed out First Half of 2010 with 5th Consecutive Quarter of Positive Returns November 2010

Ghalbouni, Joseph and Rouziès, Dominique The VC Shakeout. Harvard Business Review, Jul/Aug 2010, Vol. 88, Issue 7/8

Zider, Bob How Venture Capital Works. Harvard Business Review, Nov/Dec 1998

The Economist: Status Displays

The Economist recently reported on a study conducted by Rob Nelissen and Marijn Meijers from Tilburg University in the Netherlands on how brands change our personal interactions. Through a series of experiments, the researchers showed that a well-known designer brand alone confers a higher perceived status and wealth on the wearer that alters how others interact with him or her.

The positive effect from the label allowed a subject to get more people to take a survey, solicit donations, obtain a job, and receive a higher salary. In a game where participants were asked to risk giving money to a stranger with the possibility of losing the money or doubling it based on whether the stranger was trustworthy, people were willing to risk 36% more money with a stranger wearing designer clothes as opposed to the same clothes without a label.

While other studies have shown that people respond to brands, this study implies that the reason is biological rather than cultural. The author compares the brand to the tail of a peacock in that both the brand and the label signal superior quality although the peacock’s traits are intrinsic while the quality of the label is transferred to the wearer.

With such a clear economic effect, particularly a 9% higher salary offer to the wearer of a well-known brand, it is surprising that more sales programs do not include particular wardrobe requirements. A business with no links to consumer clothing might benefit from studies on the particular brand preferences of their target market and require their sales force to dress appropriately. Job seekers would benefit from access to similar studies on the preferences of the hiring managers in their industry and the article suggests that anything less than 9% of a year’s salary would be an appropriate price to pay while still benefiting the job seeker.

What is most interesting about this study is not what it suggests about brand names; it is what it suggests about human behavior. In order for the brand to affect behavior, most people would need to behave according to a few assumptions. The first assumption is that all people value different brands in the same manner. This requires a long term disciplined marketing effort that defines the brand in a manner that is easily understood by everyone, not just the target market.

The second assumption is that the qualities such as wealth or taste that permit a person to select and purchase the clothes are the best indications of the attribute that we are trying to judge such as skill or trustworthiness. This assumption is troublesome because it implies that we may be cognitive misers more than we would care to admit. Since transference seems to occur so easily, a marketing message can focus on one or two positive attributes and, if successful, the brand can represent all that is good in the world.

The third assumption is that people are generally not concerned with a fake signal. This explains why when a brand may have so much influence over behavior, people are still willing to buy counterfeit goods with a fake brand even when the imitation is of poor quality. People do not respond to the brand if the wearer received the clothing from someone else so what appears to be important is the ability to select and obtain the brand rather than having access to it.

Social Business Models

In operations management, co-production is the use of a business’ customers to assist in creating a good or service. Obvious examples are assembling Ikea furniture, self checkout, and using an ATM. Social media is also co-production. The value of Facebook, Twitter, or the rest is not the platform; it is the network and content that we create using the tools provided by the company. Unlike assembling furniture or replacing people with machines, the majority of social media’s value is created through co-production while in our other examples, co-production represents a small portion of the total value.

Imagine that the Internet consisted only of institutions such as businesses, governments, universities, etc… These institutions have little need of social networks among themselves but maintain a presence on social networks in order to communicate with various stakeholders. In this simplified world, social networks would be nearly worthless while web search would maintain its usefulness simply as a way to access information posted by institutions.

A natural reaction to this scenario is to point out that the Internet is in fact dominated by people rather than institutions but that does not diminish the usefulness of the simple model. Any web application or service that relies on co-production also requires maintaining the attention of a large user base. This is different from previous software models where the user base only needed to pay attention at the time of purchase and is easily demonstrated by imagining how the business model will provide value without constant attention.

Attention, by itself, is not a competitive advantage because it is easily replicated and has never been maintained for very long. Business models that rely on co-production must build both a competitive advantage as well as convincing investors that their offering will draw constant attention year after year. Buying this sort of business model is akin to investing in a television show that you believe will never be cancelled.

This is not to suggest that social networks have no commercial value. Clearly, companies can make good money on advertising or charging access fees. The main point is that when someone talks about how the new social website is going to change the world to remember that attention spans are short and all shows get canceled.

I’m about to make a trip to Seattle, San Francisco, and Palo Alto to visit some tech companies and VC firms. I’m hoping to get some feedback on building long term value versus building temporary value but I am skeptical about receiving straight forward answers. Hopefully, I will be proven wrong.

Faith-Based Tax Policy

The justification behind tax cuts as stimulus is derived from the laissez faire argument and the Laffer curve. While the Laffer curve was made popular by Arthur Laffer on the Reagan administration Economic Policy Advisory Board, it was first described by 14th century Muslim intellectual Ibn Khaldoun. The idea of tax cuts as stimulus was also proposed by John Maynard Keynes though its current proponents appear to be unwilling to associate themselves with Keynesians.

The laissez faire argument states that any transfer of wealth from the state to the people is positive for economic growth since government is always detrimental to the economy. This is a philosophical belief that does not take into account the current state of the world and the limits of short-term change. In the short and medium term, the size of government will not be changed substantially due to the checks and balances that exist in government. Unless there is a national consensus on what must be done, the conflict in competing political interests will prevent large changes from occurring quickly. As this pertains to tax policy and the size of government, unless proponents of smaller government can match tax cuts with spending cuts, government debt will increase creating a larger tax burden on the future economy.

Proponents of tax cuts counter that the Laffer curve proves that tax cuts will not produce deficits because the economic growth produced by the tax cuts will increase total tax revenues. In order for this tax elasticity effect to occur, the current tax rate must be above the rate at which taxes are a disincentive to productivity. Since there is little empirical evidence to support an objective tipping point, the effectiveness of the Laffer curve is dependent on the subjective assessment of whether current taxes are too high. As tax policy is linked to philosophical arguments on the proper size of government, those who believe in smaller government will likely use the Laffer curve to justify lowering taxes without consequence relative to any given rate.

Risk Aversion and Job Creation

The current consensus view is that the economy will remain weak until consumers start spending again. In the near-term, consumers will increase spending as they become more confident about their job situation and in the long-term, they will need to repair their balance sheets before returning to the level of spending we were accustomed to. This is what many people refer to as “New Normal” since consumers are unlikely to be capable of returning to the old level of spending without another debt bubble. Many people believe that jobs will be created as economic activity increases but this circular argument is being refuted as the largest public companies accumulate cash and continue to grow profits. This is where politics complicates the narrative as analysts attribute the lack of job creation to uncertainty about taxes, healthcare or some other partisan issue. The bottom line is that we still live in a capitalist system regardless of the marginal tax rate or the method of healthcare care administration and business is only rewarded for successfully taking on risk.

Business risk is largely borne by small business since large company employees are rewarded for maintaining the status quo in order to protect their existing competitive advantage. (When you make buggy whips, it doesn’t matter if you’re a fox or a hedgehog and every business eventually enters the buggy whip stage.) As more of our economic activity is dominated by large companies, there is a decreasing impact from real entrepreneurs that are willing to take risk and we should not be surprised when the risk aversion of the entire economy increases. While tax cuts certainly increase profits, there is no direct connection to wealth creation as opposed to wealth transfer. Jobs will be created when businesses are willing to show some leadership and take on risk. Everything else is just politics.

Reflections on the 2008 CES

This was my first visit to the Consumer Electronics Show in Las Vegas, NV. I spent everyday wandering through the endless displays of gadgetry goodness but was hard pressed to find any truly innovative products. I found the presentations to be the most useful for understanding how the industry thinks and what they can realistically deliver. Paul Otellini’s presentation was a good show but couldn’t deliver details on how or when the translation and GPS capabilities could be incorporated into real products because the whole thing was a simulation run on servers located backstage. Jerry Yang’s keynote was exciting but I doubt that the full platform will be released on time as presented. After a depressing presentation by several private equity investors, I realized that no one is interested in building a consumer centric company which is why Apple will probably continue to succeed in the consumer electronics space despite their rushed product life cycles and lack of respect for early adopters. It seems that consumer electronics firms succeed more on marketing and management capability than technological innovation.