Resultados en relación a los objetivos específicos

Price randomization could be explained in the literature by either a limited capacity story or a limited information story. As part of each of these classes of models, there is a multiplicative term that enters the model that involves capacity or the amount of information that consumers are receiving. A two-firm symmetric model has been

developed that takes in account both elements – capacity limitations and information limitations – that leads to price randomization. Adding both features together in the model enhances the ability of the higher priced firm to capture more customers than either model would produce alone – the remainder of the customers that the other firm could not serve due to capacity limitations plus the loyal customers that see only one price. The result of this type of model is that there is a semi-multiplicative term of capacity and information within the distribution calculation.

There are a number of extensions with this model. The model can also be simplified down to a straight limited capacity model by allowing all consumers to be informed about both firms prices or setting α2 = 1. The model can be generalized to a closed solution where there more than two firms so long as all firms sell out to capacity

except for one firm. Finally, the two-firm model can be carried over into asymmetric situations where capacity of one firm is greater than the other firm. In that case and if

total capacity of both firms is not too large, (ie smaller than

n n n 2 2 2 1 2

α

α

α

be an atom in the probability distribution of the smaller firm at the highest price. If total

capacity of both firms is larger than

n n n 2 2 2 1 2

α

α

α

and smaller than

α

α

the largest firm has the atom in its pricing distribution. If the firms play a Kreps and Scheinkman two-stage game of building capacity first before selling to customers, there will be a symmetric solution to the game at the lowest possible level of capacity.

3: Equilibrium Price Randomization with Asymmetric Customer Loyalty

3-1. Introduction

Loyal or business travelers are important to an airline’s business. These travelers are generally a small portion of the overall customer base yet make a larger portion of the annual airline trips than the average public. These customers generate large revenue for airlines as they take more trips and generally pay higher fares than the average fare paid by the public. Airlines go to great length to court these travelers with their frequent flier programs rewarding repeat business with these travelers. With frequent flier programs and airlines having a presence in important hub cities, frequent travelers are often loyal with their business to one airline. The size of the loyal customer base can help determine an airline’s fortune.

Leisure or not so loyal travelers are another group of customers that an airline serves. These customers search from airline to airline for the lowest price. These travelers do not make as many trips as the loyal travelers and are generally not as

important to an airline’s business. Airlines will offer these customers system-wide sales, weekly email specials, coupons, and last-minute specials to entice these travelers to book with them. Customers will then face prices that fluctuate.

These two qualitative features of airline travel – a small group of loyal travelers and fluctuating prices fit as great examples from the literature of incomplete information and random pricing. Varian (1980), for instance, uses a model of sales where there is a

group of uninformed customers on price and informed group of customers on price. Varian assumes in his model that firms have the same proportion of uninformed, or customers seeing only one price, divided evenly between firms. Firms will want to charge these customers the monopoly price. This group of customers that see only one price is not large enough that firms could concentrate selling to these customers. The other group of customers, those that can see all prices, shop at the firm that offers that offers the lowest price. To win these customers, firms will have to offer the lowest price. Firms can only offer one price, so they have problem – how do they serve both groups of customers? Firms randomize their prices in an interval to capture as much expected revenue from the uninformed types and expected revenue from the informed types.

Varian assumes that the proportion of loyal customers is the same for each firm. This is not a realistic assumption in today’s economy with so many different sized firms. If this assumption is relaxed, how do the results change? What will the probability distribution for the firms look like? Will there still be sales? How will the size of the firm influence the results?

As the model will show firms still randomize over an interval of prices. Unlike Varian (1980), the largest firm now has an atom of probability at the monopoly price. Increasing the largest firm’s loyal customers causes all firms to discount less. Increasing the smaller firm(s)’ loyal customers causes only the largest firm to discount more.

Increasing the shoppers causes the smaller firm(s) to discount more; the largest firm has a more complicated reaction. Increasing the number of firms causes all firms to discount

less. A statistic showing the probability of at least one firm having the lowest price can be created.