Research Themes Optimization and game theory in economics
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Research Themes Optimization and game theory in economics Amit Mehra Assistant Professor, Information Systems Indian School of Business, Hyderabad Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Software Upgrades with Price Competition Amit Mehra, ISB Ram Bala, ISB Ramesh Sankaranarayanan, Univ. of Connecticut To cite this paper, please use the following: Mehra, Amit, Bala, Ram and Sankaranarayanan, Ramesh. “Software Upgrades with Price Competition. ” Working Paper, Indian School of Business, 2007. Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Background • Upgrades are endemic to the software industry • So is competition… • What is the nature of upgrade policy under competition? Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Relevant Literature • Pricing under monopoly • Bhargava and Chaudhary (2001) and (2007) • Sundararajan (2004) • Monopoly upgrades – Upgrade policies related to pricing • • Dhebar (1994) Fudenberg & Tirole (1998) Kornish (2001) Ghose, Huang and Sundararajan (2006) • Pricing under Competition without upgrades • Moorthy (1988) • Jing (2006) and (2007) • Fudenberg & Tirole (2000) • Impact of switching costs on competition • Viswanathan (2005) • Klemperer (1987) • Farrell & Shapiro (1988) • Our work – Upgrades under competition for software – Impact of switching costs on upgrade policy Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Pricing with upgrades under competition • Price Discrimination Not Possible – Same price for all customers (old and new) • Price Discrimination Possible – Who gets the discount? • Existing customers of the firm’s product? • New customers to be acquired from the competitor? – Based on “proof of purchase” Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Setting and Questions • Setting: Incumbent and a later competitor • What is the nature of the equilibria? – Pricing and market shares – Which of them is the optimal one for a first mover? • What can the first mover do to attain the optimal equilibrium? – Can some parameter values like switching costs be tweaked for this purpose? Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Model – Period 1 Incumbent introduces a product f I Utility for customer f–td • f > d, so that product has positive value for all customers • Customer’s choice • Buy from I => Utility: f – t d –p 1 • Do not Buy => Utility: 0 t • Customers horizontally differentiated with respect to their tastes • Are uniformly distributed between 0 and 1 on this “taste dimension” => Customer with index 0<= t <= 1 suffers fit cost t d • Incumbent introduces a product at the left end of the market Copyright Prof. Amit Mehra Indian School of Business, • Product utility in one period is f Hyderabad 500032 • Sets a price p 1 Amit_Mehra@isb. edu
Model – Period 2 Incumbent and entrant simultaneously introduce upgrade fu > f fu I fu E t 1 -t CUSTOMERS • Incumbent’s period 1 customers incur switching cost “s” if they buy entrant’s product • Options for period 1 customers • Use period 1 product: f – t d • Buy from incumbent: fu – t d – pu • Buy from entrant: fu –(1 - t) d – pd - s • Options for new customers • Do not buy: 0 • Buy from incumbent: fu – t d – pi • Buy from entrant: fu – (1 -t) d – pe FIRMS • Incumbent’s pricing • For customers of period 1: pu • For new customers: pi • Entrant’s pricing • For incumbent’s customers of period 1: pd • For new customer’s: pe • Constraint on prices: pu < pi ; pd < pe Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Forward Looking customers anticipate future benefits before taking first period actions • Buy from Incumbent in period I – Use period 1 product in period 2 • 2 f – 2 t d – p 1 – Buy upgrade from incumbent in period 2 • f + fu – 2 t d – p 1 - pu (A) – Buy upgrade from entrant in period 2 • f + fu – t d – (1 -t) d – p 1 - pd (C) • Do not buy in period 1 The segments must be ordered as A, B, C, D – Buy from incumbent in period 2 • fu - t d – pi (B) – Buy from entrant in period 2 • fu – (1 - t) d – pe (D) – Do not Buy in period 2 • 0 Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Ordering of segments: A, B, C, D (D) fu – (1 - t) d – pe Customer Surplus (A) f + fu – 2 t d – p 1 - pu t Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Possible market structure in equilibrium • 4 segments in order (A, B, C and D) – In an equilibrium a particular segment may/ may not exist => 15 equilibria ignoring the one in which there are no customers • Plausible equilibria – Some of incumbent’s customers upgrade + some new customers buy from entrant => Segment A and D exist – Thus 4 possibilities • • All A, B, C, D exist A, C, D A, B, D A: Buy I + Upgrade to I B: Do not buy + Buy from I C: Buy I + Upgrade to E D: Do Copyright Prof. Amit Mehra Business, not. Indian buy School + Buyoffrom E Hyderabad 500032 Amit_Mehra@isb. edu
Incumbent Profits • Incumbent profits – Are maximum in equilibrium with competitive upgrade discounts • Exists only if • Are decreasing in switching costs – In the other two equilibria • Profits are increasing with switching costs • Profits are independent of switching costs Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Prescription for the first mover • For given f and fu – increase switching costs => Conditions for A, C, D (high profit) equilibrium are satisfied • Once this condition is satisfied, avoid further increase in switching costs Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Entrant’s Profits in the optimal equilibrium • Are sometimes increasing in switching costs – When and – Opposite to impact on incumbent – Thus while • Incumbent would like to check switching costs • Entrant would like to increase switching costs Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
Contributions • Upgrades under competition are marked with multiple plausible equilibria • The highest profit equilibrium for the incumbent is the one in which incumbent cedes market share to the entrant – And there the entrant uses a competitive upgrade discount price • Attaining this equilibrium requires a minimum threshold switching cost – However, further increases in switching costs must be avoided Copyright Prof. Amit Mehra Indian School of Business, Hyderabad 500032 Amit_Mehra@isb. edu
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