# Avoiding Price Wars

September 2012

The negative impact on industry profits due to price compression from firms engaging in price wars can possibly be avoided by a better understanding of strategic games.  Observing competing firm’s historical behavior and current price announcements may offer valuable insights on future actions.  Modeling such strategies in a game theoretical scope allows for more informed pricing decisions and possible profit saving maneuvers.

Leveraging comparative positioning by price alone is not a sufficient means of product differentiation.  Even in highly commoditized industries other means of price promotions and market segmentation can alleviate the need to compete on price.  In most instances price wars are not a deliberate method of squeezing out competition and removing product capacity in markets.  Price wars tend to be quite costly for not only the initiating firm but for the entire market and seem to promise uncertain long-term gains.  Executives knowing the detrimental effects of price war engagement need to learn avoidance techniques to discourage such behavior by sometimes irrational firms.

The Bertrand duopoly model provides a baseline pricing game that explores firm interaction under simple assumptions of reality.  Basically two firms exist in a market, provide homogeneous goods, and choose prices according to profit maximization.  Notice the assumptions of this model describe a highly commoditized industry where price is the only determinant of competitive advantage.  The firm with the lowest price receives the entire market endowment of consumer demand.  Therefore firms have direct incentive to undercut the competing firm to a price that converges on the marginal cost.  This case is representative of the common prisoner’s dilemma game where opposing firms are coaxed to gain significant short-term profit by cutting price at the expense of long-term tighter margins.

Consider the following example:  Firm A and B compete in a homogenized market where product offerings from each firm are almost identical.  The only competing factor is price.  The following chart explains the price strategies, market segments, and unit contributions margins.  Assume market segment 2 will not buy the good when both firm’s maintain the price.

When both firms interact in a healthy market not existent of price wars each firm receives a profit of $250. When both firms choose to engage in a price war they realize a profit of$200 each.  When one firm chooses to maintain price and the other deviates unilaterally by cutting price, the lower priced firm receives $400 and the firm that maintained price receives$0.  The normal form game representation below shows the strategy space, payoffs, and players associated with this scenario.

Using the iteration process or basic common sense one can observe that the equilibrium of this specific game is where both firm A and B choose to cut price and end up in the lower right quadrant receiving $200 each. A market possessing seasoned managers and rational managers would realize the long-term benefits of maintaining the price. But without binding agreements or credible threats maintaining price is not achievable. Regardless the strategy space under the stated constraints, each firm has a best response of cutting price. Clearly all markets are not considered homogeneous in offerings, the number of competitors is likely more than two, and the managerial aptitude varies. Describing a more realistic view of markets in which firms operate provides a more useful method for interpreting pricing behavior and outcomes. Adding substitutability variables to account for heterogeneity, parameter representing market maturity levels, and adding n-players is a common method to bolster the model’s robustness. These techniques support diverging best response functions. Not only do firms choose their best response strategies according to price, they now also consider other important market characteristics. Understanding how each factor contributes to strategy choice involves mathematically derivation of imbedded best response functions. For simplicity sake, mature executives have implicit knowledge of historical behavior of other firms and know how their products are differentiated. A simple yet powerful example of how consumer loyalty and switching costs can mitigate the probability of price wars occurring helps demonstrate the power of non-price factors. What if we build on our original example and keep all variables constant but add customer loyalty segmentation into our mix. This comparative static will also include a measure for product differentiation. Assume 80% of market 1 will buy firm A’s product even if firm B cuts its price and 55% of market 1 will buy firm B’s product even if firm A chooses to cut price. How will this known metric affect our firm’s best response functions? Let’s see! If firm A and B maintain price they both achieve a payoff of$250.  If firm A and B choose to play the strategy “cut price” they both receive profit of $200. If firm A chooses to maintain price and firm B cuts price, firm A receives$400 ([0.8(100)($5)]) and firm B receives$240 ([(0.2(100)+100)($2)]). If firm B chooses to maintain price and firm A cuts price, firm B receives$275 ([0.55(100)($5)]) and firm A receives$290 ([(0.45(100)+100)(\$2)]).  The following normal form representation of the game shows the union of strategies and payoffs.

The equilibrium through iteration results in the outcome {(A,B): Cut Price, Maintain Price}.  This outcome is quite significant.  Under the same conditions where the prisoner’s dilemma was the default result but changing market dynamics, a new conclusion is established.  The best response function and dominate strategy of firm B is to maintain price regardless of what firm A chooses to do.  Firm B knowing how loyal customers are to firm A will never have incentive to cut prices because its result is an inferior outcome.  Firm A estimating the market profile and observing firm B’s strategy to always play “maintain price” will choose to offer a discounted price to augment profit.

Other types of analyses prove useful in interpreting the credibility of pricing threats brought on by competing firms.  Repeated games of complete and perfect information such as “tit-for-tat” help analyze the long-term effects of such price interaction in the market.  Other non-price dimensions such as industry maturity, substitutability, market presence, and even cost structures give interesting and non-anticipated outcomes in comparison to the base-line prisoner’s dilemma game.  Firms that realize price wars are only detrimental to firm and industry health fare better in the long-run.  Price by itself cannot establish a competitive advantage.