Download presentation

Presentation is loading. Please wait.

Published byTurner Saunders Modified over 2 years ago

1
Introduction to Microeconomics Game theory Chapter 9

2
Basic elements – The players. – The strategies. – The payoffs. Payoff matrix – A table that describes the payoffs in a game for each possible combination of strategies. LO1: Basic Elements of A Game Elements of a Game © 2012 McGraw-Hill Ryerson Limited Ch9 -2

3
Strategy Dominant strategy – One that yields the highest payoff no matter what the other players in the game choose Dominated strategy – Any other strategy available to a player that has a dominant strategy

4
The Prisoner’s Dilemma – A classic example of potential conflict between the narrow self-interest of individuals and the broader interest of larger communities. The Prisoner’s Dilemma – Each player has a dominant strategy. – The dilemma is: Payoffs are smaller than they would be if each player had played a dominated strategy. Lo4: The Effect of Dominant Strategy Prisoner’s Dilemma © 2012 McGraw-Hill Ryerson Limited Ch9 -4

5
Will the prisoners confess? – Two prisoners, Horace and Jasper, are being held in separate cells for a serious crime that they did in fact commit. – The prosecutor, has only enough hard evidence to convict them of a minor offence. The Payoff Matrix for the original Prisoner’s Dilemma © 2012 McGraw-Hill Ryerson Limited Ch9 -5 Lo4: The Effect of Dominant Strategy

6
Example 9.3: Will the prisoners confess? – The dominant strategy for each prisoner is to confess. Table 9.3: The Payoff Matrix for the original Prisoner’s Dilemma © 2012 McGraw-Hill Ryerson Limited Ch9 -6 √ √ Dominate strategy Lo4: The Effect of Dominant Strategy

7
Will the prisoners confess? – The dominant strategy for each prisoner is to confess. The Payoff Matrix for the original Prisoner’s Dilemma © 2012 McGraw-Hill Ryerson Limited Ch9 -7 √√ Dominate strategy Lo4: The Effect of Dominant Strategy

8
Will the prisoners confess? – When each follows his dominant strategy and confesses, both will do worse than if each had shown restraint. Table 9.3: The Payoff Matrix for the original Prisoner’s Dilemma © 2012 McGraw-Hill Ryerson Limited Ch9 -8 Nash Equilibrium Nash Equilibrium Better Outcome Lo4: The Effect of Dominant Strategy

9
..\..\..\..\..\..\Users\gmason.PRAINC\Documen ts\Pavtube\youtube_converter\Nash Equilibrium - YouTube.mp4..\..\..\..\..\..\Users\gmason.PRAINC\Documen ts\Pavtube\youtube_converter\Nash Equilibrium - YouTube.mp4

10
Terminology When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. The result of the comparison is one of: B dominates A: choosing B always gives as good as or a better outcome than choosing A. There are 2 possibilities: – B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other player(s) do. – B weakly dominates A: There is at least one set of opponents' action for which B is superior, and all other sets of opponents' actions give B at least the same payoff as A. B and A are intransitive: B neither dominates, nor is dominated by, A. Choosing A is better in some cases, while choosing B is better in other cases, depending on exactly how the opponent chooses to play. For example, B is "throw rock" while A is "throw scissors" in Rock, Paper, Scissors.Rock, Paper, Scissors B is dominated by A: choosing B never gives a better outcome than choosing A, no matter what the other player(s) do. There are 2 possibilities: – B is weakly dominated by A: There is at least one set of opponents' actions for which B gives a worse outcome than A, while all other sets of opponents' actions give A at least the same payoff as B. (Strategy A weakly dominates B). – B is strictly dominated by A: choosing B always gives a worse outcome than choosing A, no matter what the other player(s) do. (Strategy A strictly dominates B). This notion can be generalized beyond the comparison of two strategies. – Strategy B is strictly dominant if strategy B strictly dominates every other possible strategy. – Strategy B is weakly dominant if strategy B dominates all other strategies, but some are only weakly dominated. – Strategy B is strictly dominated if some other strategy exists that strictly dominates B. – Strategy B is weakly dominated if some other strategy exists that weakly dominates B. Source: Wikipedia

11
ThePrisonersDilemma.cdf

12
Imagine that Pepsi and Coca Cola are the only makers of cola drinks. Both are earning economic profits of $6000/day. Assume the following: – If Pepsi increases its advertising expenditures by $1000/day and Coca Cola spends no more on advertising, Pepsi’s profit will increase to $8000/day and Coca Cola’s will decrease to $2000. – If both spend $1000 on advertising, each will earn an economic profit of $5500/day. – If Pepsi stands pat while Coca Cola increases its spending by $1000, Pepsi’s economic profit will fall to $2000/day, and Coca Cola’s will increase to $8000. – The payoffs are symmetric. Will Pepsi spend more money on advertising? LO1: Basic Elements of A Game Ch9 -12 © 2012 McGraw-Hill Ryerson Limited

13
The Payoff Matrix for an Advertising Game © 2012 McGraw-Hill Ryerson Limited Ch9 -13 LO1: Basic Elements of A Game

14
Table 9.1: The Payoff Matrix for an Advertising Game © 2012 McGraw-Hill Ryerson Limited Ch9 -14 Suppose Coca Cola assumes that Pepsi will raise its spending on advertising, in that case, Coca Cola’s best option would be to follow suit. Payoff is higher LO1: Basic Elements of A Game

15
Table 9.1: The Payoff Matrix for an Advertising Game © 2012 McGraw-Hill Ryerson Limited Ch9 -15 Suppose Coca Cola assumes that Pepsi will do nothing, in that case, Coca Cola’s best option would be to raise its spending on advertisements. Payoff is higher LO1: Basic Elements of A Game

16
Table 9.1: The Payoff Matrix for an Advertising Game © 2012 McGraw-Hill Ryerson Limited Ch9 -16 No matter which strategy Pepsi chooses, Coca Cola will earn a higher economic profit by increasing its spending on advertising. Nash equilibrium Nash equilibrium Since this game is perfectly symmetric, a similar conclusion holds for Pepsi: No matter which strategy Coca Cola chooses, Pepsi will do better by increasing its spending on advertisements. Dominate strategy LO2: Identifying Dominant Strategy LO3: Find an Equilibrium for a Game

17
Dominant strategy: – A strategy that yields a higher payoff no matter what the other players in a game choose. Dominated strategy: – Any other strategy available to a player who has a dominant strategy. Nash Equilibrium: – Any combination of strategies in which each player’s strategy is his best choice, given the other players’ strategies. LO2: Identifying Dominant Strategy Strategies © 2012 McGraw-Hill Ryerson Limited Ch9 -17

18
Example 9.2: The Payoff Matrix for an Advertising Game When One Player Lacks a Dominant Strategy © 2012 McGraw-Hill Ryerson Limited Ch9 -18 No matter what Pepsi does, Coca Cola will do better to increase its advertising, so raising the advertising budget is a dominant strategy for Coca Cola. Payoff is higher Dominate strategy LO3: Find an Equilibrium for a Game

19
Example 9.2: The Payoff Matrix for an Advertising Game When One Player Lacks a Dominant Strategy © 2012 McGraw-Hill Ryerson Limited Ch9 -19 Pepsi does not have a dominate strategy in this game. Payoff is higher Payoff is higher LO3: Find an Equilibrium for a Game

20
Example 9.2: The Payoff Matrix for an Advertising Game When One Player Lacks a Dominant Strategy © 2012 McGraw-Hill Ryerson Limited Ch9 -20 Nash equilibrium: If Pepsi believes that Coca Cola will spend more on advertisements, Pepsi’s best strategy is to keep its own spending constant. Dominate strategy Nash Equilibrium Nash Equilibrium LO3: Find an Equilibrium for a Game

21
Cartel: – A coalition of firms that agree to restrict output for the purpose of earning an economic (excess) profit. – Normally cartels involve several firms. This makes retaliation against a dissenter difficult. – Agreements are not legally enforceable and hence may be unstable. – Constant temptation for each participant to cheat on the agreement. Example: OPEC oil cartel production quotas. – Economic naturalist 9.1: Why might cartel agreements be unstable? LO5: Games with Equilibrium Like Prisoner’s Dilemma Cartels © 2012 McGraw-Hill Ryerson Limited Ch9 -21

22
– Faced with the demand curve shown, a monopolist with zero marginal cost would produce 1000 bottles/day (the quantity at which marginal revenue equals zero) and sell them at a price of $1.00/bottle. FIGURE 9.1: The Market Demand for Mineral Water D MR © 2012 McGraw-Hill Ryerson Limited Ch9 -22 LO5: Games with Equilibrium Like Prisoner’s Dilemma

23
– By cutting its price from $1/bottle to $0.90/bottle, Aquapure can sell the entire market quantity demanded at that price, 1100 bottles/day, rather than half the monopoly quantity of 1000 bottles/day. FIGURE 9.2: The Temptation to Violate a Cartel Agreement D MR 0.90 1100 © 2012 McGraw-Hill Ryerson Limited Ch9 -23 LO5: Games with Equilibrium Like Prisoner’s Dilemma

24
– Each firm’s dominant strategy is to sell at the lower price, yet in following that strategy, each earns a lower profit than if each had sold at the higher price. TABLE 9.4: The Payoff Matrix for a Cartel Agreement © 2012 McGraw-Hill Ryerson Limited Ch9 -24 Nash Equilibrium Nash Equilibrium LO5: Games with Equilibrium Like Prisoner’s Dilemma

25
..\..\..\..\..\..\Users\gmason.PRAINC\Documen ts\Pavtube\youtube_converter\Game Theory 101 What Is a Nash Equilibrium (Stoplight Game) - YouTube_0.mp4..\..\..\..\..\..\Users\gmason.PRAINC\Documen ts\Pavtube\youtube_converter\Game Theory 101 What Is a Nash Equilibrium (Stoplight Game) - YouTube_0.mp4

Similar presentations

OK

Objectives © Pearson Education, 2005 Oligopoly LUBS1940: Topic 7.

Objectives © Pearson Education, 2005 Oligopoly LUBS1940: Topic 7.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on camera technology Ppt on digital media piracy control Ppt on recycling of waste management Ppt on business model of e-commerce Ppt on leverages Ppt on introduction to brand management Ppt on nuclear family and joint family images Ppt on adivasis of india Ppt on current account deficit usa Ppt on advance payment of tax