# Wal-Marts Dilemma

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### Wal-Mart’s Dilemma :

Game theory decision Savings catcher program Small Group Wal-Mart’s Dilemma

### The People of Small Group:

The People of Small Group Steven Tharp

### Background:

Background Within game theory, the Nash equilibrium was created by John Nash as a way to solve games that involve multiple non-cooperative players

### Nash Equilibrium:

Nash Equilibrium The most popular example of the Nash equilibrium is the prisoners dilemma Simultaneous game Both prisoners making a decision without knowledge of the others choice If 1 and 2 each betray the other, each of them serves 8 years in prison If 1 betrays 2 but 2 remains silent, 1 will be set free and 2 will serve 10 years in prison (and vice versa) If 1 and 2 both remain silent, both of them will only serve 1 year in prison

### Nash Equilibrium :

Nash Equilibrium Wal-Marts’ dilemma is a sequential game, where competitors will be able to react to Wal-Mart’s decision to either implement the savings catcher program or not.

### Wal-Mart’s Savings Catcher:

Wal-Mart’s Savings Catcher “At Wal-Mart we have low prices everyday on everything. If a local competitor offers a lower advertised price on an eligible item you purchase at Wal-Mart, we have a program called Savings Catcher that allows you to get back the difference on a Wal-Mart Rewards eGift Car or a Bluebird by American Express Card. Amounts credited to these cards can be used to make purchases exclusively in-store at Wal-Mart or online at Walmart.com.” Enter receipt number into savingscatcher.walmart.com or in the Wal-Mart mobile app or scan the code at the bottom of the receipt using the Wal-Mart mobile app

### Savings Catcher Decision :

Savings Catcher Decision Assumptions: Quantity: 200 Units of a Good being Sold Price: \$1 Per Unit at Status Quo Business: Split 50/50 at Status Quo Pricing

### Decisions:

Decisions Savings Catcher and Amazon Lower Prices Wal-Mart implements the Savings Catcher Program and Amazon lowers prices by 10% on products. There are no changes in Quantity Both Wal-Mart and Amazon sell 100 units at \$0.90 per unit

### Decisions:

Decisions 2. Wal-Mart Status Quo and Amazon Lower Prices Amazon lowers prices by 10% Wal-Mart does nothing and loses 20% of it’s business Amazon: 120 Units * \$0.90 Wal-Mart: 80 Units * \$ 1.00

### Decisions :

Decisions 3. Savings Catcher and Amazon Status Quo Wal-Mart implements savings catcher and receives 20% of Amazon’s business with advertising and marketing Amazon doesn’t adjust prices at all Wal-Mart: 120 Units * \$ 1.00 Amazon: 80 Units * \$ 1.00

### Decisions :

Decisions Wal-Mart Status Quo and Amazon Status Quo Neither parties adjust pricing and split units equally Wal-Mart: 100 Units * \$ 1.00 Amazon: 100 Units * \$ 1.00

### Simultaneous Equilibrium :

Simultaneous Equilibrium The Simultaneous Equilibrium has a payout of 100 to each party; this situation is a sequential game though

Sequential Game

### Amazon’s Decision:

Amazon’s Decision

### Wal-Mart’s Decision:

Wal-Mart’s Decision