Download presentation
1
Game Theory Topic 2 Simultaneous Games “Loretta’s driving because I’m drinking and I’m drinking because she’s driving.” - The Lockhorns
2
Review Understanding the game Noting if the rules are flexible
Anticipating our opponents’ reactions Thinking one step ahead Where does this lead us? We’ve defined the “game” but not the outcome Mike Shor
3
Equilibrium The likely outcome of a game when rational, strategic agents interact Each player is playing his or her best strategy given the strategy choices of all other players No player has incentive to change his or her action unilaterally Outline: Model interactions as games Identify the equilibria Decide when they are likely to occur Mike Shor
4
Cigarette Advertising on TV
All US tobacco companies advertised heavily on TV Surgeon General issues official warning Cigarette smoking may be hazardous Cigarette companies fear lawsuits Government may recover healthcare costs Companies strike agreement Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits. 1964 1970 Mike Shor
5
Strategic Interaction
Players: Reynolds and Philip Morris Strategies: Advertise or Not Advertise Payoffs: Companies’ Profits Environment: Each firm earns $50 million from its customers Advertising costs a firm $20 million Advertising captures $30 million from competitor How to represent this game? Mike Shor
6
Strategic Form of a Game
PLAYERS Philip Morris No Ad Ad Reynolds 50 , 50 20 , 60 60 , 20 30 , 30 STRATEGIES PAYOFFS Mike Shor
7
What to Do? Philip Morris No Ad Ad Reynolds 50 , 50 20 , 60 60 , 20 30 , 30 If you are advising Reynolds, what strategy do you recommend? Mike Shor
8
Best Replies A strategy is a best reply to some opponents’ strategy if it does at least as well as any other strategy si is a best reply to s-i if for every si’ Not necessarily unique Mike Shor
9
Solving the Game Best reply for Reynolds: Philip Morris No Ad Ad
50 , 50 20 , 60 60 , 20 30 , 30 Best reply for Reynolds: If Philip Morris advertises: If Philip Morris does not advertise: Mike Shor
10
Dominance A strategy is dominant if it outperforms all other strategies no matter what opposing players do Games with dominant strategies are easy to solve No need for “what if …” thinking Mike Shor
11
Dominance si strictly dominates si’ if for every s-i
(the payoff is strictly higher for every strategy of the other players) si weakly dominates si’ if for every s-i, and for some s-i Mike Shor
12
Dominance A strategy si is strictly dominant if it strictly dominates all other strategies for that player A strategy si is weakly dominant if it weakly dominates all other strategies for that player Mike Shor
13
Dominance Example 1 A strictly dominates B & A strictly dominates C
Therefore A is strictly dominant X Y Z A 10 20 30 B 8 18 25 C 5 Mike Shor
14
Dominance Example 2 A strictly dominates B & A weakly dominates C’
Therefore A is weakly dominant X Y Z A 10 20 30 B 8 18 25 C’ Mike Shor
15
Dominance Example 3 A strictly dominates B & A does not dominate C’’
Therefore A is not dominant X Y Z A 10 20 30 B 8 18 25 C’’ Mike Shor
16
Dominance If you have a dominant strategy use it.
(and no ability to agree on an alternate course of action) use it. If your opponent has a dominant strategy then expect her to play it. Mike Shor
17
Prisoner’s Dilemma Both players have a dominant strategy
Optimal No Ad Ad 50 , 50 20 , 60 60 , 20 30 , 30 Equilibrium Both players have a dominant strategy The equilibrium results in lower payoffs for each player Mike Shor
18
Prisoner’s Dilemma Both players have a dominant strategy (s1,s1)
u11 , u11 u12 , π21 u21 , u12 u22 , π22 Both players have a dominant strategy (s1,s1) u11 > u21 u12 > u22 The equilibrium results in lower payoffs for each player u22 > u11 The above two statements imply: u12 > u22 > u11 > u21 Mike Shor
19
Cigarette Advertising
After the 1970 agreement: Cigarette advertising decreased by $63 million Industry Profits rose by $91 million Mike Shor
20
Prisoner’s Dilemma The dominant strategy will be played Mike Shor
21
Social Behavior in Pigs
Baldwin and Meese (1979), “Social Behavior in Pigs Studied by Means of Operant Conditioning,” Animal Behavior Two small pigs: First pig gets 8 units of food, second gets 2 If simultaneous, each gets 5 Pushing the lever costs 1 One small, one big: If big pig is first, eats all of the food If small pig is first, it gets 6 units of food If simultaneous, big pig gets 7 Mike Shor
22
Prisoner’s Dilemma The dominant strategy will be played
An equilibrium is NOT necessarily efficient Players can be forced to accept mutually bad outcomes Bad to be playing a prisoner’s dilemma, but good to make others play Mike Shor
23
How to Win a Bidding War by Bidding Less?
The battle for Federated (1988) Parent of Bloomingdales Current share price ≈ $60 Expected post-takeover share price ≈ $60 Macy’s offers $70/share contingent on receiving 50% of the shares Do you tender your shares to Macy’s? Mike Shor
24
How to Win a Bidding War (continued)
Robert Campeau bids $74 per share not contingent on amount acquired Campeau’s Mixed Scheme: If less than 50% tender their shares, each receives: $74 per share If X>50% tender, each receives: Mike Shor
25
The Federated Game To whom do you tender your shares?
Majority of Others Macy’s Campeau You $70 $60 $74 $67+ To whom do you tender your shares? Mike Shor
26
How to Win a Bidding War Each player has a dominant strategy: Tender shares to Campeau Resulting Price: (½ x 74) + (½ x 60) = $67 BUT: Macy’s offered $70 ! Mike Shor
27
“ The biggest, looniest deal ever. ”
Dominant Strategies “ The biggest, looniest deal ever. ” – Fortune Magazine, July 1988 on Campeau’s acquisition of Federated Stores Mike Shor
28
Prisoner’s Dilemma Examples
Pricing by Firms High or low prices? Value menus and loyalty programs Divorce Hire attorneys or proceed amicably? Nuclear Weapons Build or don’t build weapons? State governments Inducements to attract business to a state Mike Shor
29
Dominated Strategies Two restaurants compete
Can charge price of $30, $50, or $60 Customer base consists of tourists and natives 600 tourists pick randomly 400 natives select the lowest price Marginal costs are $10 Mike Shor
30
Tourists & Natives Example scenario:
Restaurant 1: $50, Restaurant 2: $60 Restaurant 1 gets: 300 tourists natives = 700 customers x ($50-$10) = $28K Restaurant 2 gets: 300 tourists + 0 natives = 300 customers x ($60-$10) = $15K Mike Shor
31
Tourists & Natives R. 2 $30 $50 $60 R. 1 10 , 10 14 , 12 14 , 15
12 , 14 20 , 20 28 , 15 15 , 14 15 , 28 25 , 25 in thousands of dollars Mike Shor
32
Dominance A strategy si is strictly dominated if some strategy si’ strictly dominates it A strategy si is weakly dominated if some strategy si’ weakly dominates it Mike Shor
33
Iterated Deletion of Strictly Dominated Strategies
Does any player have a (strictly) dominated strategy? Eliminate the strictly dominated strategy Reduce the size of the game Repeat: Iterate the above procedure Mike Shor
34
Iterated Deletion of Dominated Strategies
$30 $50 $60 R. 1 10 , 10 14 , 12 14 , 15 12 , 14 20 , 20 28 , 15 15 , 14 15 , 28 25 , 25 Mike Shor
35
No Dominated Strategies
Often there are no dominated strategies Some games may have multiple equilibria Equilibrium selection becomes an issue Method: For each player, find the best response to every strategy of the other player Mike Shor
36
Equilibrium An outcome in which every player is playing a best response to the strategies of all other players. An equilibrium is a strategy profile s such that si is a best reply to s-i for all i. Mike Shor
37
Equilibrium Illustration
The Lockhorns Mike Shor
38
Games of Coordination Complements & technology adoption
Two complementing firms Must use same technology, but each firm has a preferred technology Equilibrium does not offer a unique prediction Commit (or go first) to win! Firm 2 A B Firm 1 100 , 50 0 , 0 0 , 0 50 , 100 Mike Shor
39
Games of Assurance Joint research ventures
Each firm may invest $50,000 into an R&D project Project succeeds only if both invest If successful, each nets $75,000 Firm 2 $50K $0 Firm 1 75 , 75 -50 , 0 0 , -50 0 , 0 Mike Shor
40
Games of Chicken Entry into small markets Firm 2 Stay Swerve Firm 1
-50 , -50 100 , 0 0 , 100 50 , 50 Mike Shor
41
The Right Game to Play Why do we “solve” games?
To know which one to play! How do internal corporate changes impact the outcome of strategic interaction? Some games are better than others Mike Shor
42
Capacity Constraints Can decreasing others’ added value increase our profits? Can decreasing total industry value increase our profits? Mike Shor
43
Multiple Equilibria What is the predictive power of game theory when there are multiple equilibria? Sometimes nothing ? Refinements Focal points Efficiency Evolutionary stability Fairness Risk dominance Mike Shor
44
Summary Games have predictable outcomes Select the right game to play
Notice dominant & dominated strategies Select the right game to play Looking ahead: Sequential Games: How do games unfold over time? Mike Shor
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.