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# Game Theory

Game theory looks at how strategic decisions are formed and how they are implemented. It is the study of conflict and cooperation. Economists use it to understand oligopolies, which is a market with few producers whose actions impact price and their competitors. It is described as the act of looking ahead, to predict what other competitors will do, and reasoning backward, to determine what you should do in relation to the actions of othersÂ¹. The major contributors to the development of economic game theory include John Nash, Selten, and HarsanyiÂ².

This topic includes the study of externality issues and economics of information. As a decision-maker, game theory uses mathematical methodoogy to efficiently structure and analyze problems. For example, firms use game theory to make decisions about pricing and production levels. Game theory is also applied in economics in areas such as bargaining, merger pricing, voting systems, and many other fields. Economic theory has three other branches, along with game theory, which include decision theory, general equiliubrium theory, and mechanism design theory.

Nash Equilibrium is a concept in game theory that describes a situation where all participants are trying to determine the best strategy given the strategies of the other participantsÂ². In a Nash equilibrium, none of the participating players have any incentive to deviate from their chosen strategy. In general, game theory is based on the pay-offs that come from the different decisions and strategies.

References:

### Dominant Strategy, Nash Equilibrium, and prisoners' dilemma

Every year management and labor renegotiate a new employment contract by sending their pro-posals to an arbitrator who chooses the best pro-posal ( effectively giving one side or the other \$ 1 million). Each side can choose to hire, or not hire, an expensive labor lawyer ( at a cost of \$ 200,000) who is effective at preparing t

### Game Theory for Payoff Tables

The Tampa Tribune and the St. Petersburg Times compete for readers in the Tampa Bay market for newspapers. Recently, both newspapers considered changing the prices they charge for their Sunday editions. Suppose they considered the following payoff table for making a simultaneous decision to charge either a low price of \$0.50 or

### Business Game Theory: Opening New Stores

In a big city, two companies X and Y are competing for business. They have one store each. Under current conditions they share the total sales of \$800,000 equally. Company X is planning to open one or two more stores, or may continue with the existing store (no new stores). Company Y can open only one additional store, or may co

### Nash Equilibrium with AMD and Intel

Below is a payoff matrix for Intel and AMD for PC microprocessors. The first number per cell is AMD's profit while the second is Intel's. Intel Lower Price Same Price Higher Price AMD Lower Price -15,-15 2,6

### Nash Equilibrium / Sequential GamesSequential move games

15-4. Salary Negotiation The following represents the potential outcomes of your first salary negotiation after graduation: Assuming this is a Sequential Move Game with the employer moving first, indicate the most likely outcome. Does the ability to move first give the employer an advantage? If so, how? As the employee, i

### Answers to three common Microeconomics review questions. The topics covered are: 1. Payoff Matrix and Dominant Strategy 2. Nash Equilibrium 3. Pricing Decisions

Question 5 The figure shows the payoff matrix for two producers of bottled water, Blue Spring and Purple Rain. Each has two strategies available to it: a high price and a low price. The dominant strategy for Purple Rain is to ... a) always charge a low price. b) always charge a high price. c) always adopt the same strate

### Economic Analysis: Supply and Demand, Nash Equilibrium

Question 1 The market for olive oil in new York City is controlled by two families, the Sopranos and the Contraltos. both families will ruthlessly eliminate any other family that attempts to enter the New York City olive oil market. The marginal cost of producing oil is constant and equal to \$40 per gallon in either family. Th

### Managerial Economics: Game Theory, Dominant Strategy, and Nash Equilibrium

Please help with the following problem. Two players, Ben and Diana, can choose strategy X or strategy Y. If both Ben and Diana choose strategy X, each earns a payoff of \$1000. If both players choose strategy Y, each earns a payoff of \$200. If Ben chooses strategy X and Diana chooses strategy Y, then Ben earns \$0 and Diana ea

### Solution contains explanation of Nash Equilibrium in pure strategy, Prisoner's Dilemma and interrelation between both of them through an example.

Below is a payoff matrix for Intel and AMD. In each cell, the first number refers to AMD's profit, while the second is Intel's. a. Is there a Nash Equilibrium(s)? Why or why not? b. Is this an example of the Prisoner's Dilemma? Why or why not? Intel AMD Lower Price Same Price Higher Price Lower Price

### Does player A have a dominant strategy?

Consider the following payoff matrix: Player B Strategy Player A \$ 1,000 - \$ 2,000 Strategy \$ 2,000 - \$ 1,000 - \$ 1,000

### Nash Equilibrium: Coke and Pepsi Advertising Strategy

1. Find the solution to the following advertising decision game between Coke and Pepsi, assuming the firms act independently. Pepsi's budget Low Medium High Low 400; 400 320; 720 560; 600 Cok

### Game Theory: Do Price-matching Offers Discourage Price Cuts?

Please help with the following problem in around 200 words. Company X announces that if it reduces its price subsequent to a purchase, the early customer will get a rebate so that he or she will pay no more than those buying after the price reduction. A. If Company X has only one rival, and if its rival too makes such a

### Coke and Pepsi's advertising war

Please help with the following problem. Both firms have 2 strategies available: continue the advertising war (W) or reduce their advertising budget (R). The payoffs for each strategy combination are given in the following payoff matrix. Pepsi Coke W

### A managerial economics problem

Suppose there is a circle with numbered locations from 0-60 (with 0/60 at the top; like a clock in minutes). Customers are evenly distributed at locations around the circle. Three firms will locate at locations in order, so that firm F knows where previous firms located (i.e. 1 goes first, then 2 knowing what 1 did, then 3 knowi

### When McDonald's Corp. reduced the price of its Big Mac by 75 percent if customers also purchased french fries and a soft drink, The Wall Street Journal reported that the company was hoping the novel promotion would revive its U.S. sales growth. It didn't. Within two weeks sales had fallen. Using your knowledge of game theory, what do you think disrupted McDonald's plans?

When McDonald's Corp. reduced the price of its Big Mac by 75 percent if customers also purchased french fries and a soft drink, The Wall Street Journal reported that the company was hoping the novel promotion would revive its U.S. sales growth. It didn't. Within two weeks sales had fallen. Using your knowledge of game theory, wh

### Dominant Strategy, Nash Equilibrium

Dominant Strategy/Nash Equilibrium Firm 2 Firm 1 Price High Price Low Price High 400, 350 -80, 800 Price Low 800, -100 200,200 a) Does either firm have a dominant strategy, and if so, what it

### Given the following payoff matrix, determine whether a new firm should enter the coffee market and whether the dominant firm should charge a high or low price.

Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: Big Brew High Pr

### Should you work hard on a joint project? Use game theory to predict the answer.

You and a classmate are assigned a project on which you will receive one combined grade. You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation: If both of you work hard, you both get an A, which gives each of you 40 units of happiness. If only one of you works hard

### What is a Nash equilibrium? Find the Nash equilibrium for US-Mexico trade.

1. Consider trade relations between the US and Mexico. Assume that leaders of the two countries believe the payoffs to alternative trade policies are as follows: US' policy Low Tariffs High Tariffs Low Tariffs US gains \$25b US gains \$30b Mex gains \$25b M

### Payoff Matrix Explained

5. From the following payoff matrix, where the payoffs (negative values) are the years of possible imprisonment of individuals A and B, determine (a) whether individual A has a dominant strategy, (b) whether individual B has a dominant strategy, (c) the optimal strategy for each individual. (d) Do individuals A and B face a pri

### What McDonald's Corp. reduced the price of its Big Mac by 75 percent if customers also purchased French fries and a soft drink, The Wall Street Journal reported that the company was hoping the novel promotion would revive its U.S sales growth. It didn't. Within two weeks sales had fallen. Using your knowledge of game theory, what do you think disrupted McDonald's plans?

What McDonald's Corp. reduced the price of its Big Mac by 75 percent if customers also purchased French fries and a soft drink, The Wall Street Journal reported that the company was hoping the novel promotion would revive its U.S sales growth. It didn't. Within two weeks sales had fallen. Using your knowledge of game theory, wha

### FIFA case is examined.

You have been hired by FIFA to advise on the pricing of tickets for the World Cup Final on 11th July 2010 to be played at Soccer City Johannesburg, a stadium with seating capacity of 88,460. You have been told that the objective is to set a ticket price that will maximise total revenue, given that the marginal cost of an extra s

### Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 25, 15 4, 20 16, 14 28, 12 B 10, 10 5, 15 8, 6 18, 13 a. What is player 1's optimal strategy? Why? b. Determine player 1's equilibrium payoff. Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives \$0 and player 2 receives \$15. If both players move left, player 1 receives - \$10 and player 2 receives \$8. If player 1 moves left and player 2 moves right, player 1 receives 10 and player 2 receives \$10. a. Write the above game in extensive form. b. Find the ash equilibrium outcomes to this game. c. Which of the equilibrium outcomes is most reasonable? Explain.

Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 25, 15 4, 20 16, 14 28, 12 B 10, 10 5, 15 8, 6 18, 13 a. What is player 1's optimal strategy? Why? b. Determine player 1's equilibrium payoff. Consider a two-player, sequentia

### game theory: airbags

According to a recent article in The Wall Street Journal, side-impact crashes are among the deadliest, accounting for nearly 10,000 deaths per year. Child safety concerns have kept auto manufacturers from making side-impact airbags standard equipment, though they are optional on most middle- to highermarket automobiles. Openly c

### Strategic decision making is assessed.

Think of a time when you were involved in strategic decision making. This could be a business situation or a personal situation. It could be anything from purchasing inputs for a manufacturing firm, to dividing up household chores, to deciding whether we should we punt or go for the first down or kick a field goal? a. Discuss

### Assume for simplicity that a monopolist has no costs of production (MC=0) and faces a demand curve given by Q = 150-P. a) Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profit. b) Suppose instead that there are two firms in the market facing the demand and cost conditions just described for their identical products. Firms choose quantities simultaneously as in the Cournot model. Compute the outputs in the Nash equilibrium. Also compute market output, price and firm profits. c) Suppose the two firms choose prices simultaneously as in the Bertrand model. Compute the prices in the Nash equilibrium. Also compute firm output and profit as well as market output. 2 d) Graph the demand curve and indicate where the market price-quantity combination from parts (a)-(c) appear on the curve.

Assume for simplicity that a monopolist has no costs of production (MC=0) and faces a demand curve given by Q = 150-P. a) Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profit. b) Suppose instead that there are two firms in the market facing the demand and cos

### Finding the best strategy in game theory

Stategy D E F A 100, 125 300,250 200 ,100 B 250, 0 500 ,500 750 , 400 C 0, -200 400, 300 -100, 350 Please explain what the dominant strategy is . Does each player have a secure strategy? What is the

### Economics: Nash Equilibrium and Game Theory

Scenario A Consider the following game: Payoffs are in millions of dollars. Camden Inc. Put Poison Pill In Turbo Tech Dump Cash Assets

### Game Theory: Nash Equilibrium Problem

1. In a Nash equilibrium, each player has a dominant strategy. no players have a dominant strategy. at least one player has a dominant strategy players may or may not have dominant strategies. the player with the dominant strategy will win. 2. Nash equilibria are stable because,