3.1.4 types of games. strategic behavior in business and econ outline 3.1. what is a game ? 3.1.1....
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3.1.4 Types of Games
Strategic Behavior in Business and Econ
Outline
3.1. What is a Game ?3.1.1. The elements of a Game3.1.2 The Rules of the Game: Example3.1.3. Examples of Game Situations3.1.4 Types of Games: Complete and Incomplete Information
3.2. Solution Concepts3.2.1. Static Games of complete information: Dominant
Strategies and Nash Equilibrium in pure and mixed strategies3.2.2. Dynamic Games of complete information: Backward
Induction and Subgame perfection
Strategic Behavior in Business and Econ
Games can be classified into different categories according to different criteria:
Number of players Number of strategies Simultaneous moves or sequential moves Zero-sum games or not Informational structure Nature of the game: conflict, coordination, . . . etc
Strategic Behavior in Business and Econ
From a practical point of view, a meaningful classification is based on:
Number of players Number of strategies Simultaneous moves or sequential moves Zero-sum games or not Informational structure Nature of the game: conflict, coordination, . . . Etc
They determine the analysis tools (techniques) to use
Strategic Behavior in Business and Econ
In this sense we can find, basically, four different types of games
Complet e Inf ormat ion Incomplet e Inf ormat ion
S t at ic
Dynamic
Player s have all r elevant
inf ormat ion, and move
simulat enously
Not all player s have all t he
r elevant inf ormat ion, and
move simulat enously
Player s have all r elevant
inf ormat ion, and move
sequent ially
Not all player s have all t he
r elevant inf ormat ion, and
move sequent ially
All games in a given category are represented and solved alike
Strategic Behavior in Business and Econ
Examples:
Complet e Inf ormat ion Incomplet e Inf ormat ion
S t at ic
Dynamic
Pr isoner s' Dilemma,
S ummer pr icing
FCC auct ions
(sealed- bid auct ion)
Chess,
Market E nt r y
Collect ibles auct ions
(E nglish auct ions)
Strategic Behavior in Business and Econ
Static Games of Complete Information
They are, in general, the most simple games. Their main featuresare:
All the players choose their strategies simultaneously. This does not mean “at the same time” but “without knowing the choice of others”
Because of this simultaneity they can be represented by means of a table (payoff matrix)
They are “one-shot games”, that is, they are played only once All the players have all the information regarding who are the other
players, what are the own strategies and the strategies of the others, what are the own payoffs and the payoffs of the others, and what are the rules of the game
Strategic Behavior in Business and Econ
Static Games of Incomplete Information
They are like the previous ones, only that the informational structureis different
Not all the players have all the information regarding who are the other players, what are the strategies of the others, or what are the payoffs of the others.
The typical case is when the players don't know the payoffs of the other players
Example: Sealed-bid Auctions: You don't know what is the value of the item to other players
Strategic Behavior in Business and Econ
Dynamic Games of Complete Information
Their main features are:
Players choose their strategies sequentially, one after the other This means some players take actions knowing what other have done
Because of this sequentiality they must represented using trees They are also “one-shot games”, that is, they are played only once Nevertheless, some special dynamic games consist of the repetition
of a one-shot game played several times All the players have all the information regarding who are the other
players, what are the own strategies and the strategies of the others, what are the own payoffs and the payoffs of the others, and what are the rules of the game
Strategic Behavior in Business and Econ
Dynamic Games of Incomplete Information
Again, they are like the previous ones, only that the informational structure is different
Not all the players have all the information regarding who are the other players, what are the strategies of the others, or what are the payoffs of the others.
The typical case is when the players don't know the payoffs of the other players
Example: English Auctions: You don't know what is the value of the item to other players
3.2 Solution Concepts
Strategic Behavior in Business and Econ
Outline
3.1. What is a Game ?3.1.1. The elements of a Game3.1.2 The Rules of the Game: Example3.1.3. Examples of Game Situations3.1.4 Types of Games
3.2. Solution Concepts3.2.1. Static Games of complete information: Dominant
Strategies and Nash Equilibrium in pure and mixed strategies3.2.2. Dynamic Games of complete information: Backward
Induction and Subgame perfection
Strategic Behavior in Business and Econ
Solution Concepts
A solution to a game consists of a prediction of whatwill be the logical outcome of the game (what will be thestrategies chosen by the players and the correspondingpayoffs) based on the rationality and common knowledgeassumptions of Game Theory
Depending on the type of the game, the representationwill be different and hence the analysis and the method tofind the solution (the solution concept) won't be the same.
Strategic Behavior in Business and Econ
Solution Concepts
Complet e Inf ormat ion Incomplet e Inf ormat ion
S t at ic Bayesian Nash E quilibr ium
Dynamic
E quilibr ium in Dominant S t rat egies,
E liminat ion of Dominat ed S t rat s.
Nash E quilibr ium
Nash E quilibr ium,
Backward Induct ion,
S ubgame Per f ect E quilibr ium
Bayesian Per f ect Nash E quilibr ium,
S equent ial E qulibr ium
A solution of a game is called an Equilibrium of the game
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Equilibrium
The basic idea behind any equilibrium concept is that itcorresponds to an outcome of the game (a choice of strategies by all the players) that is stable, in the sense that
Given what the other players are doing, nobody has any reason to change his or her own strategy
Therefore, since an equilibrium describes a choice ofstrategies for the players that nobody wants to change, itseems logical to think that it is a “good” prediction.
(Basic) Game Theory, though, does not explain how this equilibrium is reached
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$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Suppose that Bar 1 chooses $5 and Bar 2 chooses $4
Strategic Behavior in Business and Econ
$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Suppose that Bar 1 chooses $5 and Bar 2 chooses $4Then, the payoffs are: 15 to Bar 1
28 to Bar 2
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$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Suppose that Bar 1 chooses $5 and Bar 2 chooses $4Then, the payoffs are: 15 to Bar 1
28 to Bar 2But if Bar 2 is charging $4 then Bar 1 wants to charge $4(to earn a payoff to 20 instead of 15)
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$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Hence, Bar 1 choosing $5 and Bar 2 choosing $4 is NOTstable, is NOT an equilibrium
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$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Consider Bar 1 charging $4 and Bar 2 charging $4 instead
Strategic Behavior in Business and Econ
$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Consider Bar 1 charging $4 and Bar 2 charging $4Now the payoffs is 20 to each Bar
Strategic Behavior in Business and Econ
$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Consider Bar 1 charging $4 and Bar 2 charging $4Now the payoff is 20 to each Bar Do they want to change the strategy ?
Strategic Behavior in Business and Econ
$2 $4 $5
Bar 1$2 10 , 10 14 , 12 14 , 15$4 12 , 14 20, 20 28 , 15$5 15 , 14 15 , 28 25, 25
Bar 2
Example: Summer Pricing
Consider Bar 1 charging $4 and Bar 2 charging $4Now the payoff is 20 to each Bar Do they want to change the strategy ?
NO !Bar 1 charging $4 and Bar 2 charging $4 is stable, is an Equilibrium of the game
Strategic Behavior in Business and Econ
Good news !
The equilibrium tells us what seems to be the logical (stable)outcome of the game
Bad news !
Game Theory does not tell us how the equilibrium is reached,how players “discover” that they should be playing the equilibriumstrategies. This is specially important when there is more thanone equilibrium (Ex: Antena 3 vs. Telecinco)
(Learning ?, Trial-and-error ?, Evolution ?, Hint ?)
Strategic Behavior in Business and Econ
Example: The Driving Game
Paul and Mary are driving in opposite directions on a twolane road.What should they do when they cross ?
Drive on the right lane ?Drive on the left lane ?
Strategic Behavior in Business and Econ
Mary
Right Left
PaulRight 0 , 0 -50 , -50
Left -50 , -50 0 , 0
Example: The Driving Game
If both drive on “their” right, then there is no accident If they drive on different lanes, then there is an accident
that has a cost of -$50,000 to each of them
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Mary
Right Left
PaulRight 0 , 0 -50 , -50
Left -50 , -50 0 , 0
Example: The Driving Game
There are 2 equilibrium:Both players driving on the rightBoth players driving on the left
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Mary
Right Left
PaulRight 0 , 0 -50 , -50
Left -50 , -50 0 , 0
Example: The Driving Game
There are countries stabilized on the Drive on the right equilibriumThere are countries stabilized on the Drive on the left equilibriumThe question is: How did they reach one or the other ?
Strategic Behavior in Business and Econ
Best Reply
All the solution methods that we are going to study arebased on the prior concept of Best Reply
For each player, a best reply to the strategy(ies) chosen bythe other player(s) is, simply, the strategy that gives the highest payoff
In all the previous examples, and all the examples to come, the red circles indicate the best replies in each case
Strategic Behavior in Business and Econ
Documentary
Match
Antena 3(player 1)
Telecinco (player 2)
1, 1
DocumentaryMatch
2, 1.5
0.75, 0.751.5, 2
Example: The Battle for TV share
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For Antena 3,
If Telecinco chooses Match, my Best Reply is Documentary• If Telecinco chooses Documentary, my Best Reply is Match
For Telecinco,
If Antena 3 chooses Match, my Best Reply is Documentary• If Antena 3 chooses Documentary, my Best Reply is Match
Strategic Behavior in Business and Econ
Employees can work hard or shirk
Salary: $100K unless caught shirking
Cost of effort: $50K
Managers can monitor or not
Value of employee output: $200K
Profit if employee doesn’t work: $0
Cost of monitoring: $10K( Monitoring will catch a shirking worker for sure)
Example: A (simple) Principal-Agent game
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ManagerMonitor No Monitor
EmployeeWork 50 , 90 50 , 100
Shirk 0 , -10 150 , -100
Example: A (simple) Principal-Agent game
What are the Best Replies ? (The Red Circles)
Strategic Behavior in Business and Econ
ManagerMonitor No Monitor
EmployeeWork 50 , 90 50 , 100
Shirk 0 , -10 150 , -100
Example: A (simple) Principal-Agent game
Notice that there is no equilibrium !!