Abstract
Existing research has identified different firm characteristics that determine an incumbent’s reaction toward market entrants. This study widens the perspective from a firm’s absolute attributes to its relative positioning within its competitive environment. The hypotheses for the empirical analysis are derived from game theoretic models with either vertical or horizontal product differentiation. In each of the two theoretical models two incumbents initially choose very different quality and variety levels, respectively, and move closer to the center when faced by entry of a competitor. From the vertical differentiation model we predict a stronger price reduction by high-quality firms. In our empirical analysis we are using a novel dataset of the high-quality restaurant market in Germany to test the theoretical findings. While the hypotheses with respect to adjustments of prices and varieties are supported, we do not find empirical evidence for the predicted quality adjustment.
Similar content being viewed by others
Notes
In the high-quality restaurant market, reputation commits restaurants to their attribute choices. If a restaurant cheats, it will suffer a loss in reputation. This argument applies to the incumbents as well as the entrant (Snyder and Cotter 1998). A similar result could be obtained by expanding the models to include positioning-related adjustment costs.
Because quality \(q_B\) is restricted to \(q_B\le 1\), the three-firm case requires \( \frac{13}{36}<\alpha \). See Appendix B for details.
See Lancaster (1990) in regard to modeling product variety.
As above, offering a medium variety level is indeed optimal for the entrant.
Considering this yields \(p_{A}^{*}-p_{A}^{**}=\frac{917}{2160} <p_{B}^{*}-p_{B}^{**}= \frac{1605}{2160}\) for \(\alpha =\frac{5}{9}\).
For \(\alpha =\frac{5}{9}\) we obtain \(q_{A}^{*}-q_{A}^{**}=-\frac{5}{20} <q_{B}^{*}-q_{B}^{**}=\frac{7}{20}\).
Even though ratings might differ between Michelin and Schlemmer critics, it should not be a problem to combine both data sources since we consider changes in ratings rather than absolute values.
This is a realistic case because the variable relative variety ranges between 0.24 and 1.61.
References
Aoki, R., & Prusa, T. J. (1997). Sequential versus simultaneous choice with endogenous quality. International Journal of Industrial Organization, 15(1), 103–121.
Arend, R. J. (2009). Defending against rival innovation. Small Business Economics, 33(2), 189–206.
Barney, J. (1991). Firm resources and sustained competitive advantage. Journal of Management, 17(1), 99–120.
Brekke, K. R., Nuscheler, R., & Rune Straume, O. (2006). Quality and location choices under price regulation. Journal of Economics & Management Strategy, 15(1), 207–227.
Brenner, S. (2005). Hotelling games with three, four, and more players. Journal of Regional Science, 45(4), 851–864.
Caves, R. E. (1998). Industrial organization and new findings on the turnover and mobility of firms. Journal of Economic Literature, 36(4), 1947–1982.
Chamberlin, E. H. (1933). The Theory of Monopolistic Competition. Boston: Harvard University Press.
Choi, C. J. & Shin, H. S. (1992). A comment on a model of vertical product differentiation. The Journal of Industrial Economics, 229–231.
Cremer, H. & Thisse J.-F. (1994). Commodity taxation in a differentiated oligopoly. International Economic Review, 613–633.
Cummings, P. (2009). Methods for estimating adjusted risk ratios. Stata Journal, 9(2), 175.
Dalbor, M. C., & Sullivan, M. J. (2005). The initial public offerings of restaurant firms: The case of industry-specific micromarket capitalization offerings. Journal of Small Business Management, 43(3), 226–241.
d’Aspremont, C., Gabszewicz, J. J., & Thisse, J.-F. (1979). On hotelling’s stability in competition. Econometrica, 47(5), 1145–1150.
Degryse, H. (1996). On the interaction between vertical and horizontal product differentiation: An application to banking. The Journal of Industrial Economics, 169–186.
Donnenfeld, S., & Weber, S. (1992). Vertical product differentiation with entry. International Journal of Industrial Organization, 10(3), 449–472.
Donnenfeld, S. & Weber, S. (1995). Limit qualities and entry deterrence. The RAND Journal of Economics, 113–130.
Durand, R., Rao, H., & Monin, P. (2007). Code and conduct in French cuisine: Impact of code changes on external evaluations. Strategic Management Journal, 28(5), 455–472.
Economides, N. (1989). Quality variations and maximal variety differentiation. Regional Science and Urban Economics, 19(1), 21–29.
Economides, N. (1993). Hotelling’s ’main street’ with more than two competitors. Journal of Regional Science, 33(3), 303–319.
Falck, O., Heblich, S., & Kipar, S. (2011). Incumbent innovation and domestic entry. Small Business Economics, 36(3), 271–279.
Fogarty, J. J. (2012). Expert opinion and cuisine reputation in the market for restaurant meals. Applied Economics, 44(31), 4115–4123.
Frank, R. G., & Salkever, D. S. (1997). Generic entry and the pricing of pharmaceuticals. Journal of Economics & Management Strategy, 6(1), 75–90.
Frick, B., Gergaud, O., & Matic, P. (2013). It pays to be different: Strategy choice and firm performance in the restaurant industry. Discussion paper 13–10, discussion paper series in economics and management of the German Economic Association of Business Administration (GEABA).
Gabszewicz, J. J., & Thisse, J.-F. (1979). Price competition, quality and income disparities. Journal of Economic Theory, 20(3), 340–359.
Geroski, P. A. (1995). What do we know about entry? International Journal of Industrial Organization, 13(4), 421–440.
Hotelling, H. (1929). Stability in competition. The Economic Journal, 39(153), 41–57.
Huang, K. G., & Murray, F. E. (2010). Entrepreneurial experiments in science policy: Analyzing the Human Genome Project. Research Policy, 39(5), 567–582.
Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, 221–233.
Hug, S. (1995). Third parties in equilibrium. Public Choice, 82(1–2), 159–180.
Hung, N. M., & Schmitt, N. (1988). Quality competition and threat of entry in duopoly. Economics Letters, 27(3), 287–292.
Hung, N. M., & Schmitt, N. (1992). Vertical product differentiation, threat of entry, and quality changes. In J. M. A. Gee & G. Norman (Eds.), Market Strategy and Structure (pp. 289–307). New York: Harvester Wheatshearf.
Johnson, C., Surlemont, B., Nicod, P., & Revaz, F. (2005). Behind the stars. A concise typology of Michelin restaurants in Europe. Cornell Hotel and Restaurant Administration Quarterly, 46(2), 170–187.
Jonkers, K., & Cruz-Castro, L. (2013). Research upon return: The effect of international mobility on scientific ties, production and impact. Research Policy, 42(8), 1366–1377.
Joskow, A. S., Werden, G. J., & Johnson, R. L. (1994). Entry, exit, and performance in airline markets. International Journal of Industrial Organization, 12(4), 457–471.
Karakaya, F., & Yannopoulos, P. (2011). Impact of market entrant characteristics on incumbent reactions to market entry. Journal of Strategic Marketing, 19(02), 171–185.
Lancaster, K. (1990). The economics of product variety: A survey. Marketing Science, 9(3), 189–206.
Lane, C. (2010). The Michelin-starred restaurant sector as a cultural industry: A cross-national comparison of restaurants in the UK and Germany. Food, Culture and Society: An International Journal of Multidisciplinary Research, 13(4), 493–519.
Lehmann-Grube, U. (1997). Strategic choice of quality when quality is costly: The persistence of the high-quality advantage. The RAND Journal of Economics, 372–384.
Lerner, A. P., & Singer, H. W. (1937). Some notes on duopoly and spatial competition. The Journal of Political Economy, 45(2), 145–186.
Linnemer, L. (1998). Entry deterrence, product quality: Price and advertising as signals. Journal of Economics & Management Strategy, 7(4), 615–645.
Loginova, O., & Wang, X. H. (2011). Customization with vertically differentiated products. Journal of Economics & Management Strategy, 20(2), 475–515.
Lutz, S. (1997). Vertical product differentiation and entry deterrence. Journal of Economics, 65(1), 79–102.
Makadok, R. (1998). Can first-mover and early-mover advantages be sustained in an industry with low barriers to entry/imitation? Strategic Management Journal, 19(7), 683–696.
Marion, B. W. (1998). Competition in grocery retailing: The impact of a new strategic group on BLS price increases. Review of Industrial Organization, 13(4), 381–399.
McCann, B. T., & Vroom, G. (2010). Pricing response to entry and agglomeration effects. Strategic Management Journal, 31(3), 284–305.
Motta, M. (1993). Endogenous quality choice: price vs. quantity competition. The Journal of Industrial Economics, 113–131.
Mussa, M., & Rosen, S. (1978). Monopoly and product quality. Journal of Economic Theory, 18(2), 301–317.
Neven, D., & Thisse, J. F. (1990). On quality and variety competition. In J.-F. R. J. J. Gabszewicz & L. A. Wolsey (Eds.), Economic decision making: Games, econometrics and optimization (pp. 175–199). Amsterdam: North-Holland.
Neven, D. J. (1987). Endogenous sequential entry in a spatial model. International Journal of Industrial Organization, 5(4), 419–434.
Noh, Y.-H., & Moschini, G. (2006). Vertical product differentiation, entry-deterrence strategies, and entry qualities. Review of Industrial Organization, 29(3), 227–252.
Novshek, W. (1980). Equilibrium in simple spatial (or differentiated product) models. Journal of Economic Theory, 22(2), 313–326.
Palfrey, T. R. (1984). Spatial equilibrium with entry. The Review of Economic Studies, 51(1), 139–156.
Porter, M. E. (1985). Competitive advantage: Creating and sustaining superior performance. New York: Free press.
Prescott, E. C. & Visscher, M. (1977). Sequential location among firms with foresight. The Bell Journal of Economics, 378–393.
Shaked, A. (1982). Existence and computation of mixed strategy Nash equilibrium for 3-firms location problem. The Journal of Industrial Economics, 93–96.
Shaked, A. & Sutton, J. (1982). “Relaxing price competition through product differentiation”, The Review of Economic Studies, pp. 3–13.
Shaked, A. & Sutton, J. (1983). Natural oligopolies. Econometrica: Journal of the Econometric Society, 1469–1483.
Simon, D. (2005). Incumbent pricing responses to entry. Strategic Management Journal, 26(13), 1229–1248.
Singh, S., Utton, M., & Waterson, M. (1998). Strategic behaviour of incumbent firms in the UK. International Journal of Industrial Organization, 16(2), 229–251.
Smith, S. W., & Shah, S. K. (2013). Do innovative users generate more useful insights? An analysis of corporate venture capital investments in the medical device industry. Strategic Entrepreneurship Journal, 7(2), 151–167.
Snyder, W., & Cotter, M. (1998). The Michelin Guide and restaurant pricing strategies. Journal of Restaurant & Foodservice Marketing, 3(1), 51–67.
Stuart, T. E., & Podolny, J. M. (1996). Local search and the evolution of technological capabilities. Strategic Management Journal, 17(S1), 21–38.
Suchman, M. C. (1995). Managing legitimacy: Strategic and institutional approaches. Academy of Management Review, 20(3), 571–610.
Surlemont, B., Chantrain, D., Nlemvo, F., & Johnson, C. (2005). Revenue models in haute cuisine: An exploratory analysis. International Journal of Contemporary Hospitality Management, 17(4), 286–301.
Tabuchi, T. (1994). Two-stage two-dimensional spatial competition between two firms. Regional Science and Urban Economics, 24(2), 207–227.
Tan, D., & Meyer, K. E. (2011). Country-of-origin and industry FDI agglomeration of foreign investors in an emerging economy. Journal of International Business Studies, 42(4), 504–520.
Thomas, L., & Weigelt, K. (2000). Product location choice and firm capabilities: Evidence from the US automobile industry. Strategic Management Journal, 21(9), 897–909.
Thomas, L. A. (1999). Incumbent firms’ response to entry: Price, advertising, and new product introduction. International Journal of Industrial Organization, 17(4), 527–555.
Utaka, A. (2008). Pricing strategy, quality signaling, and entry deterrence. International Journal of Industrial Organization, 26(4), 878–888.
White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50(1), 1–25.
Acknowledgments
We would like to express our thanks to the editor, Erik E. Lehmann, and two anonymous referees who helped to improve the manuscript tremendously. Further, we want to thank Markus Reisinger for invaluable comments and suggestions as well as Christoph Starke and discussants at the 14th Annual Meeting of the German Economic Association of Business Administration in Magdeburg, Germany.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1: Quality and price: two-firm case
Solving the game using backward induction implies maximization of profits given by Eq. (3) with respect to prices. The first-order conditions lead to the best price responses
and equilibrium prices, given the quality levels \(\left( q_{A},q_{B}\right) \) are
Substituting these expressions into the firms’ profits gives
At the first stage of the game, firms maximize these profits with respect to quality. This yields first order conditions for an interior solution
and best responses
Because qualities are restricted to a non-negative number on the quality scale \(0\le q_A<1\), we can rule out \(q_A(q_B) = \frac{-1 - q_B \alpha }{\alpha }\). Solving the best response equation system for qualities \(q_A\) and \(q_B\) yields two solutions
Again, because \(q_A\ge 0\), we can rule out solution 1. The second solution constitutes a minimum for firm \(B\) as \(\frac{\partial ^2 \pi _B}{\partial q_B^2} >0\). Hence, there is no interior equilibrium.
Because our quality scale is given by \([0,1]\), there might be solutions where only one or both qualities are chosen at an end of the scale:
-
Case 1: \(q_A>0\) and \(q_B=1\)
-
Case 2: \(q_A=0\) and \(q_B<1\)
-
Case 3: \(q_A=0\) and \(q_B=1\)
Next, we analyse whether these corner solutions constitute equilibria.
1.1 Case 1: \( q_A>0\) and \( q_B=1\)
If firm B locates at the higher end of the quality scale, \(A\)’s best response simplifies to
As above, we can rule out the first solution because qualities have to be non-negative. For \(\alpha \le 1\), the same applies to the second solution. If, however, \(\alpha >1\), \(A\)’s best response is \( q_A(q_B= 1)=\frac{-1+\alpha }{ 3\alpha }\). Given this, \(B\)’s best response is
that is, for \(\alpha >4\), \(q_B(q_A)=\frac{7-\alpha }{3\alpha }\) denotes \(B\)’s best response, and for \(0<\alpha <4\) it is \(q_B(q_A)=\frac{5+\alpha }{9\alpha }\). In neither of the two preceding cases, \(q_B=1\) is a solution because \(\frac{7-\alpha }{3\alpha }\ne 1\) and \(\frac{5+\alpha }{9\alpha } \ne 1\). As a consequence, \(B\) has an incentive to deviate from \(q_B=1\).
Thus, there is no equilibrium with \(q_A>0\) and \(q_B=1\).
1.2 Case 2: \( q_A=0\) and \( q_B<1\)
If firm A locates at the lower end of the quality scale, \(B\)’s best response is
The second solution can be ruled out because it constitutes a minimum. As \(B\)’s quality is restricted to \(q_B\le 1\), the first solution is \(B\)’s best response for \(\alpha >\frac{2}{3}\). Is there an incentive for \(B\) to deviate from the underlying quality choice to the corner solution \(q_B=1\)? For \(\frac{2}{3}<\alpha <\frac{8}{3}\), there is no incentive to deviate from the proposed equilibrium because \(\pi _B(q_B=\frac{2}{3\alpha })>\pi _B(q_B=1)\).
Furthermore, firm \(A\)’s best response to \(B\)’s choice is \( q_A(q_B= \frac{2}{3 \alpha })=0\) as \(\frac{\partial \pi _A}{\partial q_A}<0\) for \(\frac{2}{3}<\alpha <\frac{8}{3}\).
Hence, for \(\frac{2}{3}<\alpha <\frac{8}{3}\), \(\left( q_{A}^{*},q_{B}^{*}\right) =(0,\frac{2}{3 \alpha })\) constitutes an equilibrium.
1.3 Case 3: \(\ q_A=0\) and \(\ q_B=1\)
We know from case 1, that \(A\) chooses \( q_A(q_B= 1)=\frac{-1+\alpha }{ 3\alpha }>0\) if \(\alpha >1\). Therefore, we restrict case 3, where we look for a corner solution, implying \(q_A=0\), to \(\alpha \le 1\).
In case 3, firm \(A\)’s optimal quality choice is to position itself at the lower end of the scale \(q_A(q_B=1)=0\) because \(\frac{\partial \pi _A}{\partial q_A}<0\).
From case 2, we know that \(B\) chooses best response \( q_B(q_A= 0)=\frac{2}{3 \alpha }\) if \(\alpha >\frac{2}{3}\) because this generates higher profits than \(q_B=1\). Based on this finding, we further restrict our attention to \(\alpha <\frac{2}{3}\). Here, \(B\) chooses \(q_B(q_A=0)=1\) because \(\frac{\partial \pi _B}{\partial q_B}>0\).
Hence, for \(\alpha <\frac{2}{3}\), \(\left( q_{A}^{*},q_{B}^{*}\right) =(0,1)\) constitutes an equilibrium. \(\square \)
Appendix 2: Quality and price: three-firm case
Using expressions \(\hat{t}_{AE}\) and \(\hat{t}_{EB}\) for the indifferent consumers, firms’ profits read as
Solving the game using backward induction implies maximizing profits with respect to prices. The best responses are
This system leads to the following equilibrium prices for given qualities \( \left( q_{A},q_{E},q_{B}\right) \)
with the second-order conditions being satisfied. Substituting these prices in firms’ profits gives
Maximizing the entrant’s profits with respect to \(q_{E}\) for given qualities \(\left( q_{A},q_{B}\right) \) of the incumbent firms then gives the first-order condition
with \(\frac{\partial ^2 \pi _E}{\partial q_E^2}<0\). Hence
Substituting this best response of the entrant firm \(E\) into the incumbents’ profits gives
The incumbent’s optimal qualities are then given by the first-order conditions
with \(\frac{\partial ^2 \pi _A}{\partial q_A^2}<0\) and \(\frac{\partial ^2 \pi _B}{\partial q_B^2}<0\). The only positive solution to these equations that implies profit maxima is \(\left( q_{A}^{**},q_{B}^{**}\right) =\left( \frac{5}{36\alpha },\frac{13}{ 36\alpha }\right) ,\) leading to \(q_{E}^{**}=\frac{9}{36\alpha }\) and equilibrium prices \(\left( p_{A}^{**},p_{E}^{**},p_{B}^{**}\right) =\left( \frac{203}{3888\alpha },\frac{331}{3888\alpha },\frac{ 635}{3888\alpha }\right) .\) Because quality \(q_B\) is restricted to \(q_B\le 1\), \(\alpha >\frac{13}{36}\) must hold. \(\square \)
Appendix 3: Positioning choice of the entrant
We next analyze whether the entrant has an incentive to deviate from the proposed three-firm case equilibrium by choosing a position on the quality scale different from \(q_A<q_E<q_B\) given that \(q_A=q_A^{**}\) and \(q_B=q_B^{**}\). We restrict our attention to the cases \(q_E=0\) and \(q_E=1\). Any other deviation (i.e., \(0<q_E<q_A\) or \(q_B<q_E<1\)) would lead to strictly lower profits than the extreme positions \(q_E=0\) and \(q_E=1\).
1.1 Case 1: \( 0= q_E<q_A<q_B\)
Inserting the expressions for the indifferent consumers \(\hat{t}_{AE}\) and \(\hat{t}_{AB}\), causes firms’ profits to read as
Solving the game using backward induction leads to the following equilibrium prices for given qualities \(\left( q_{A},q_{E},q_{B}\right) \)
with the second-order conditions being satisfied. Substituting these prices together with \(q_E=0\) into \(E\)’s profits gives
For \(q_A=\frac{5}{36 \alpha }\) and \(q_B=\frac{13}{36 \alpha }\), the entrant’s profit simplifies to
For any \(\alpha \), \(\pi _{E}(q_E=\frac{9}{36 \alpha })=\frac{121}{13122 \alpha }>\pi _{E}(q_E=0)=\frac{1722845}{283855104 \alpha }\). Hence, \(E\) has no incentive to deviate from \(q_E=\frac{9}{36 \alpha }\).
1.2 Case 2: \( q_A<q_B<q_E=1\)
Inserting the expressions for the indifferent consumers \(\hat{t}_{AE}\) and \(\hat{t}_{AB}\), causes firms’ profits to read as
Solving the game using backward induction leads to the following equilibrium prices for given qualities \(\left( q_{A},q_{E},q_{B}\right) \)
with the second-order conditions being satisfied. Substituting these prices together with \(q_E=1\) into \(E\)’s profits gives
For \(q_A=\frac{5}{36 \alpha }\), \(q_B=\frac{13}{36 \alpha }\), the entrant’s profit simplifies to
Respective demand is given by
and requires \(\left. 0<\alpha <\frac{1}{108} \left( 46-5 \sqrt{73}\right) \vee \frac{5}{36}<\alpha <\frac{1}{108} \left( 46+5 \sqrt{73}\right) \right) \) so that \(x_E\ge 0\). For these \(\alpha \), \(\pi _{E}(q_E=\frac{9}{36 \alpha })=\frac{121}{13122 \alpha }>\pi _{E}(q_E=1)=\frac{(36 \alpha -13) \left( 97-3312 \alpha +3888 \alpha ^2\right) ^2}{1679616 (5-36 \alpha )^2 \alpha }\). Hence, \(E\) has no incentive to deviate from \(q_E=\frac{9}{36 \alpha }\). \(\square \)
Appendix 4: Variety: two-firm case
We solve the game using backward induction. Using the firms’ profits (6), the first-order conditions lead to the following second stage best price responses:
This system has the following solution in equilibrium prices given varieties \(\left( v_{A},v_{B}\right) ,\)
Substituting these expressions into the firms’ profits and maximizing with respect to a firm’s variety shows that marginal profits are
because \(0\le v_{A}<v_{B}\le 1.\) Hence, the optimal positioning in variety \(\left( v_{A}^{*},v_{B}^{*}\right) =\left( 0,1\right) \,\)and equilibrium prices are \(\left( p_{A}^{*},p_{B}^{*}\right) =\left( c+1,c+1\right) .\) \(\square \)
Appendix 5: Variety: three-firm case
Using expressions \(\hat{s}_{AE}\) and \(\hat{s}_{EB}\) for the indifferent consumers, profits read as
Solving the game using backward induction first implies maximizing profits with respect to prices. Second stage best responses are
Given varieties \(\left( v_{A},v_{E},v_{B}\right) \), this system of equations results in equilibrium prices
Substituting these equilibrium prices into the entrant’s profit function gives us
Given the varieties \(\left( v_{A},v_{B}\right) \) of the incumbent firms, the entrant’s optimal positioning with respect to \(v_{E}\) results from the first-order condition
Because for extreme positions \(v_{E}=v_{A}\) or \(v_{E}=v_{B}\), the second order condition is positive
the only solution is
Substituting this best response of the entrant firm \(E\) into the incumbents’ profits gives
Maximizing with respect to firms’ variety gives the following first-order conditions
The first equation is satisfied for \(v_{A}=\frac{1}{2}\left( v_{B}-\frac{1}{6 }\right) \), implying that the second equation has two solutions, \(v_{B}=\frac{ 13}{18}\) and \(v_{B}=\frac{43}{30}.\) The second solution, however, turns out to be a minimum so that profits are maximized for \(\left( v_{A}^{**},v_{B}^{**}\right) =\left( \frac{5}{18},\frac{13}{18}\right) .\) This implies a best response \(v_{E}^{**}=\frac{1}{2}\) and equilibrium prices \(\left( p_{A}^{**},p_{E}^{**},p_{B}^{**}\right) =\left( c+\frac{32}{243},c+\frac{22}{243},c+\frac{32}{243} \right) \). \(\square \)
Rights and permissions
About this article
Cite this article
Jost, PJ., Schubert, S. & Zschoche, M. Incumbent positioning as a determinant of strategic response to entry. Small Bus Econ 44, 577–596 (2015). https://doi.org/10.1007/s11187-014-9609-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11187-014-9609-x