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

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.

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… •

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) •

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

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

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

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

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

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

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

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

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

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

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 –

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

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