Courtesy of Matt Sauer, MFSWNBInvestments:


  • Amazon and retailing.
  • Economic models of retailing.
  • Disruption in the business models.

What Game are You Playing?

Game theory is often introduced to future decision makers at a young age through tic-tac-toe then continues with chess strategy and sunsets with a few examples in business school. The influence of game theory is integrated into our lives in many disciplines including biology, computer science, business and economics. Understanding what game we are playing and whether it is zero-sum or non-zero-sum, cooperative or non-cooperative or single round or repeating is necessary to make the best decision.

Antoine Augustin Cournot was the first to use game theory analysis to solve for production of goods in a market. He solved for an equilibrium that concluded that a duopoly creates more output than a monopoly but sells at a lower price. We will begin with the Cournot model and compare it to Bertrand’s model before analyzing some well-known simple models. It is from these models that we can analyze how disruptive innovations can be modeled to solve for an equilibrium if it exists.

Price and Quantity

Bertrand and Cournot are contrasting economic models for market participants and differ in the input variable. Bertrand assumes that price is set, and quantity is solved for while Cournot assumes that production is set based on competitors’ output and the market clearing price is obtained. There was no integration of the two theses until Nash equilibriums were used to solve for the best solution for both participants in the duopoly.

The formation of a market such as retail may utilize either model at a given time based on a participant’s perceived strengths. If capacity and output are hard to change then Cournot is the better model, if output and capacity are easily changed then Bertrand is the better model. In the Bertrand model a duopoly is all that is required to induce perfect competition while that is not the case in the Cournot model until the number of firms heads towards infinity.

The chart above demonstrates the difference between a disruptive technology and a competitor with comparable capabilities. On the Cournot side, a disruptor does not have similar sunk costs or inventory costs while it may not function at capacity or be at equilibrium. Models such as Dollar Shave Club continue to reorganize share in once glacial moving categories. The absence of inventory at the retailer and the disinterest on the production output of the incumbents allow them to lower the category profit pool while building their share.

Market participants would prefer to be operating in a Cournot model rather than a Bertrand model because the former can maintain the price above marginal cost. A disruptive innovation forces the incumbent into playing a game of prisoner’s dilemma regarding pricing but then drives the market into a Bertrand model. It is at this point that the incumbent is compromised because their cost structure is higher than the new entrant, but the disruptor usually does not settle at the equilibrium presented by the cost structure of the incumbent known as limit pricing.


Students of game theory recognize Prisoner’s Dilemma as a common non- zero-sum game thought experiment. In the game the two participants can try to get out of prison by choosing whether to cooperate with the jailors or not. If only one cooperates then that prisoner is worse off while the other goes free. Both cooperating has a penalty while both defecting has a larger penalty.

Corporate management experiences this problem consistently. Ownership of a product that has good economics, a brand and hard-fought market share can be threatened by new competitors utilizing new technologies. The first industries to have gone through the shake out created by the internet are now becoming part of history. When a new technology that can disrupt an industry is presented, management is instantly engaged in a prisoner’s dilemma. The new entrant will make the choice whether to lower the price of the product, the incumbent can lower the price or maintain. If they both lower the price there is a temporary equilibrium that makes them both worse off than the optimal strategy for industry profits. If they maintain they are temporarily better off and if only one lowers the price that entity will gain share.

The real-world application of this problem becomes stickier. The game never ends. The disruptive innovation always has the decision rights and can make the first move. The disruptive company can begin a spiraling down of price with the incumbent’s economic situation continuing to worsen. Wal-Mart was a disruptive innovation in the retail industry that created a slow marching down of the profit pool of retailing on a per household basis in a given geography. Meanwhile the internet eliminated the pricing in classified advertising immediately and did not intend on playing many rounds of the prisoner’s dilemma.

Although it looks as if the prisoner’s dilemma is a zero-sum game it is an example of a non-zero-sum game where there is a solution where both parties are better off if it is only played for one round. In multiple round scenarios there are other issues such as retaliation by the last round’s loser. Interestingly enough the definition of a zero-sum game with n participants becomes a non-zero-sum game with n+1 participants with the surplus becoming a global gain.

Competition has always been with us, so what is new? The difference between a disruptive technology versus a me-too competitor is substantial. The best response for both parties in the traditional me-too world is to maintain price and cooperate with the leader maintaining a price umbrella. Usually the cost structures are comparable and function in a linear equation. This is the Cournot model with no price leadership or the Stackelberg model with price leadership.

The disruptive company has a lower cost structure if not a substantially lower price structure. This entrant is not driven by maintaining the price umbrella, the goal is market share. Cooperation does not work. One of the underlying assumptions in the prisoner’s dilemma is that both parties have the same structural characteristics. However, a disruptive technology often has a very different marginal utility function. This entrant may not view capital returns in the short run with the same discipline as the incumbent.

When we extend our economic models to have differentiated products then we will begin to have premium and value products. Disruptive technologies may not have to select a value/price proposition such as a me-too competitor. In the latter the new entrant must select a segment of the market such as value or premium. The chart below was meant to describe the general case of a disruptive technology, yet it is the Apple iPod and iPhone story. The iPod bottom fed in music and the incremental innovations recreated the cell phone category.

If the entrant can take advantage of the networking effect as a strategy as Apple did, the prisoner’s dilemma game is over. Clayton Christensen has pointed out that disruptive innovation does not necessarily mean a better product, it only means a product with the ability to take share away from the incumbents and grow at their expense. A product like the iPhone that is revolutionary in its performance is not required but it sure is nice. The mantra of the 1990’s was better-faster-cheaper, Apple was able to avoid the attribute of cheaper because of superior overall product value.

What models should incumbents use to decide if a currently inferior product is going to disrupt their business? Let’s go back to the beginning.


Let’s study the duopoly model brought forth by Hotelling in 1929. It can be easily summarized by imagining pushcarts on a crowded beach. If they sell undifferentiated products, then the proper location for them is opposite ends of the breach as rational customers will bisect the beach and walk towards the nearest pushcart. This easy to recognize solution is the Nash equilibrium of profits for the duopoly. As one of the pushcart owners decides to cheat in order to capture more customers, the result is that they both will until they are next to each other in the middle. Selling homogenous products next to one another will result in a price war that will dampen industry profits.

A company’s physical location can lead to excess profits in an otherwise homogenous market. In retailing Wal-Mart originally used small town locations as a differentiation factor in order to increase the profit pool. This allowed the company to have lower cost tangible assets such as real estate and lower cost intangible assets such as managerial salary and customer service. Recently, the internet has accentuated the advantages of location (or no location) while it inverts retailing’s profit maximizing algorithms.

The historic physical node relationship was paramount for retailers to minimize cost by exploiting the minimum travel time and cost between the stores (or in mathematical terms “nodes”). The internet delivery model inverses the model by using centralized distribution to send product through a third-party logistics-based distribution model. The customer acquisition costs in the physical world in Hotellings model were based on location with no network effect while the internet retailer customer acquisition costs are search based costs with a network effect. Hotelling’s duopoly model had customer acquisition costs comparable except for the customer’s travel cost. In the extrapolation of the pushcart on the beach example, once the pushcarts are next to each other and there is no differentiation then price competition evolves. The internet creates a series of pushcarts next to one another all competing on price with the cost differential related to customer acquisition costs. Thus, the retailing model is a new paradigm with little resemblance to the Hotelling model.

If the classical retailing models ignore customer acquisition costs while their importance is paramount, what model should be used?

The Hotelling model has been the underlying model of a significant amount of academic research regarding retailing competition. The model has been tweaked to allow for more variables that resemble reality. Competition based on price which was first modeled by Bertrand is an obvious extension of Hotelling’s model and is used to solve for a Bertrand-Nash equilibrium which is considered to be a weak equilibrium because it does not have the optimal outcome because of the reduction of price as a competitive move. Economides proved the Bertrand-Nash equilibrium for a series of distribution points lined up continuously and symmetrical.

The solution to a problem with multiple nodes that are not equal distance and have different target sales values is obviously difficult. The models that we are discussing so far are simply economists solving for equilibrium rather than the real world operational issues faced by real management teams.

Back to Bertrand

The simplification of Bertrand’s retail model is that the firms set price and then sell into the demand created by the price. If their price remains the lowest then all of the demand will come to them, if their price is matched then the demand is split by the other’s who match price. One simplification we can utilize is that we can imagine the retail world into two competitors consisting of Amazon and the rest of the field. In Hotelling’s model, Amazon is now snuggled up next to their competitor so price is the sole competitive move, This simplification allows us to think about retailing and the impact Amazon has on the field without getting into a model that is overbearing.

Amazon now has the luxury of choosing the market, understanding the model in place and transforming it over time. In markets where there is no product differentiation, Amazon can become the low price leader and utilize the Bertrand model. In a market without limited capacity, Amazon can supply quantity to meet the demand at a set price. However for the other competitors amazon is not one competitor because it can reproduce copies of itself and itself act as if it were a number of new competitors and drive the Cournot models back to Bertrand. Amazon’s stock has continuosly priced in its engulfing of an industry’s profit pool as it has entered different industries. Economic game theory suggests that the market is right.

As Hotelling was thinking about his beach it probably never occurred to him that there would one day be a competitor that owned the beach. Through Amazon Web Services that is becoming the reality for Amazon.


Economic models have been studied for upwards of 200 years and have become increasingly complex with multivariate equations used to solve to make the models more similar to the marketplace. Market positioning, price leadership, distribution costs and capital capacity have all been modeled to provide an answer regarding the equilibrium of the market. Amazon is using sophisticated analytics and artificial intelligence to drive the economic models to simplicity. As this occurs the profitability looks more like the Bertrand winner take all more and more. The market is returning to the genesis of Game theory and the impact has yet to be felt.

--Matt Sauer, MWSWNB Investments. Originally published here.