Price Discrimination and Game Theory

Price Discrimination

When two or more similar goods are sold at prices that are in different ratios to marginal costs

Ex. Charging different prices to different consumers (if the costs are the same)

Ex. Charging the same price to different consumers (if costs are different)

Conditions for Price Discrimination

Market Power- typically monopoly and oligopoly markets

Some information about customers- Awareness of different groups willing to pay different prices

Prevention of Resale (No arbitrage(])- Otherwise low price so numbers become competitors; Modifications, transportation costs, contracts

First-Degree Price Discrimination (Perfect Price Discrimination)

When the seller charges a different price to each consumer equal to each individual’s willingness to pay for the product

Challenges of First-Degree Price Discrimination

Requires commitment by the seller

Difficult to know this much information

Two-Part-Tariffs

Pricing schemes i which involve a fixed fee to consume any amount of good, and then a variable fee based on usage

One example of multi-part pricing

Examples of Two-Part Tariffs

Membership fees, entry fees, cell phone services (limited plans)

Outcome of Two-Part Tariffs

Charge a per-unit price that maximized total surplus and charge an entry fee that extracts all consumer surplus

Second-Degree Price Discrimination

Occurs when a seller charges different prices such that consumers from different groups select into those prices. The seller can distinguish between consumer groups, but the seller does not know which consumers belongs to which group

Examples of Second-Degree Price Discrimination

Coupons, quantity discounts, rewards programs

Third-Degree Price Discrimination

Occurs when a seller charges different prices to different consumer groups. The seller must be able to determine which consumers belong to which groups.

Note- can combined with two-part tariff

Examples of Third-Degree Price Discrimination

Student discounts, military discounts, age discounts

Bundling

Seeking two or more goods in a package

Pure Bundling

The goods are only available in the package

Examples Pure Bundling

Season tickets, cable television

Mixed Bundling

The goods can be purchased separately

Examples of Mixed Bundling

Fast Food combos, all-inclusive vacations

When is bundling most effective?

When there is a negative correlation between the consumers’ values for the goods. For example, Consumer A values ABC more than Consumer B, but values ESPN less than Consumer B

Price discrimination results in more:

Producer surplus overall

Game Theory

A branch of mathematics that economists use to analyze the strategic behavior of decision-makers

Games

Formula descriptions of strategic settings

Components of a Game

Players, Actions that each player can take, Description of the knowledge each player has, Outcomes (typically payoffs), player preferences over outcomes

Utility

An abstract representation of value

Payoffs = utility

Assumption:

Players are rational and there is common knowledge

Rational

If a player chooses between an option that gives x utils and an options that gives y utils x > y, then that player always chooses the option that gives them x utils

Common Knowledge

Every player knows all aspects (players, actions, payoffs), of a game

How do we make predictions?

In order to make predictions about player behavior, we need a systematic way of describing which actions players will take.

There are many notions of equilibrium that we can choose.

This equilibrium notion might depend on the type of game, and the assumptions we’re willing to make about how players reason.

List the players in extensive form:

Firm 1 is analyzing a market that Firm 2 is in and must decide whether to enter (E) the market or to not enter (NE). If Firm 1 does not enter,, Firm 1 gets payoff of 0 while Firm 2 gets a payoff of 3. If Firm 1 Enters, Firm 2 can either fight (F) or do nothing (DN). If Firm 2 fights after Firm 1 enters, both firms get a payoff of -1. If Firm 2 does nothing after Firm 1 enters, both firms get a payoff of 2.

Players: {Firm 1, Firm 2}

List the actions in extensive form:

Firm 1 is analyzing a market that Firm 2 is in and must decide whether to enter (E) the market or to not enter (NE). If Firm 1 does not enter,, Firm 1 gets payoff of 0 while Firm 2 gets a payoff of 3. If Firm 1 Enters, Firm 2 can either fight (F) or do nothing (DN). If Firm 2 fights after Firm 1 enters, both firms get a payoff of -1. If Firm 2 does nothing after Firm 1 enters, both firms get a payoff of 2.

A1: {E,NE}

A2: {F,DN}

Backwards Induction Equilibrium (BIE)

Where, starting at the end of the game and going backwards, we eliminate actions that are not optimal

Only useful in extensive form games

Nash Equilibrium

Of a two player game is any outcome such that neither player can deviation from the outcome and be better off.

Fix the choices of one player and see whether the other player can profitably deviation

Normal Form

Lists the actions each player can take, but loses the sequential structure

Commitment Problems

A class of games in which players cannot achieve a mutually beneficial outcome due to inability to commit or make credible threats/problems

Examples of commitment problems

The hold-up problem

A buyer commissions a painting from an artist. The artist anticipates that the buyer will try to renegotiate and chooses not to paint

Bertrand Competition

A type of oligopoly competition in which firms compete in prices

Outcome of Bertrand Competition

Firms attract more customers by lowering their prices just below those of their competitors. Competitors have the same incentive, so prices are driven down

Coordination Games

Equilibria arise in which players prefer to coordinate their actions

Coordination Trap

There is some mutually preferred outcome that players fail to attain because they coordinated on a worse outcome

Breakdown of collusion

In oligopoly markets, firms may collude with one another to monopolize the market. However, firms have incentives to cheat on their agreements and charge slightly lower prices in order to monopolize the market on their own. This is why it is difficult to sustain without contracts or mergers

Product Differentiation

In some markets, we see firms with similar product qualities. However, in some markets, strategic forces drive firms to maximally differentiate their products to avoid close competition which drives down prices

Principle of Minimum Differentiation (Hotelling’s Law)

Businesses or products cluster near one another

Reputation

In the real world, many consumers and firms interact over long periods of time. Therefore, a firm’s reputation may factor into their strategic interaction with consumers. For example, in a one period interaction, firms may have an incentive to reduce quality. However, in multi-period interactions, firms have an incentive to keep quality high so that the consumer returns. Furthermore, collusion between firms can be sustained in repeated interactions.