Pricing and the "Beautiful Mind"

At the time of this writing, we received the sadly news of the death of John Nash, the brilliant mathematician and Nobel prize winner whose Nash Equilibrium theory is perhaps one of the biggest contribution in the behavioral sciences.

Nash Equilibrium is a set of strategies; “one for each of the n players of a game, that has the property that each player’s choice is his best response to the choices of the n-1 other players.” (Holt & Roth, 2004: 3999). This theory has many applications in economics, negotiations, behavioral sciences and many others.

A perfect Bayesian Nash Equilibrium in a dynamic market shows that consumers’ search activities increase or lower in response to sellers’ adjustment in prices as result of changes in product costs. This is explained as an effect of consumers’ price expectations on seller’s dynamic pricing strategies (Yuan & Han, 2011).

More, the Nash Equilibrium has been applied to airline’s dynamic pricing (Collins & Thomas, 2012), dynamic pricing with inventory control and uncertain demand (Adida & Perakis, 2010), pricing, allocation and overbooking with uncertain demand (Mookherjee & Friesz, 2008) and dynamic pricing of perishable assets (Gallego & Ming, 2008), among many others works in dynamic pricing.

Furthermore, Nash Equilibrium has been applied to retail prices (Kopalle et al., 1996), sales promotions (Richards & Patterson, 2005) and shelf-space allocation (Leng & Zhang, 2013) with many more areas of application within retail pricing. As an example, Nash Equilibrium can enhance in-store promotions, store layouts, product assortments, and couponing and holiday promotions.

Likewise, the area of price and revenue optimization already has used Nash Equilibrium in multi-product price optimization (Gallego & Ruxian, 2014), optimization of substitute products (Levis & Papageorgiou, 2007) and bids and auctions (Smith & Case, 1975).

Today, the world has lost a “Beautiful Mind” but his legacy will endure and will continue bringing more advances in the pricing field.

References:

Nash, J 1950, “Equilibrium points in n-person games”, PNAS, 36 (1) 48-49

Smith, B, & Case, J 1975, 'Nash Equilibria in a Sealed Bid Auction”, Management Science, 22, 4, pp. 487-497

Kopalle, P, Rao, A, & Assun?ao, J 1996, 'Asymmetric Reference Price Effects and Dynamic Pricing Policies', Marketing Science, 15, 1, p. 60,

Holt, C, Roth, A 2004, “The Nash Equilibrium: A perspective”, PNAS, 101(12), 3999-4002

Richards, T, & Patterson, P 2005, 'Sales Promotion and Cooperative Retail Pricing Strategies', Review Of Industrial Organization, 26, 4, pp. 391-413,

Levis, A, & Papageorgiou, L 2007, 'Active demand management for substitute products through price optimisation', OR Spectrum, 29, 4, pp. 551-577

Gallego, G, & Ming, H 2008, 'Dynamic Pricing of Perishable Assets under Competition', Working Papers -- University Of Toronto Rotman School Of Management, p. 1

Mookherjee, R, & Friesz, T 2008, 'Pricing, Allocation, and Overbooking in Dynamic Service Network Competition When Demand Is Uncertain', Production And Operations Management, 17, 4, pp. 455-474

Adida, E, & Perakis, G 2010, 'Dynamic Pricing and Inventory Control: Uncertainty and Competition', Operations Research, 58, 2, pp. 289-302

Yuan, H, & Han, S 2011, 'The Effects of Consumers' Price Expectations on Sellers' Dynamic Pricing Strategies', Journal Of Marketing Research (JMR), 48, 1, pp. 48-61,

Collins, A, & Thomas, L 2012, 'Comparing reinforcement learning approaches for solving game theoretic models: a dynamic airline pricing game example', Journal Of The Operational Research Society, 63, 8, pp. 1165-1173,

Leng, M, Parlar, M, & Zhang, D 2013, 'The Retail Space-Exchange Problem with Pricing and Space Allocation Decisions', Production & Operations Management, 22, 1, pp. 189-202

Gallego, G, & Ruxian, W 2014, 'Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities', Operations Research, 62, 2, pp. 450-461