1 / 35

3.1.4 Types of Games

3.1.4 Types of Games. Outline. 3.1. What is a Game ? 3.1.1. The elements of a Game 3.1.2 The Rules of the Game: Example 3.1.3. Examples of Game Situations 3.1.4 Types of Games: Complete and Incomplete Information 3.2. Solution Concepts

charlesmoore
Download Presentation

3.1.4 Types of Games

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3.1.4 Types of Games

  2. Strategic Behavior in Business and Econ Outline 3.1. What is a Game ? 3.1.1. The elements of a Game 3.1.2 The Rules of the Game: Example 3.1.3. Examples of Game Situations 3.1.4 Types of Games: Complete and Incomplete Information 3.2. Solution Concepts 3.2.1. Static Games of complete information: Dominant Strategies and Nash Equilibrium in pure and mixed strategies 3.2.2. Dynamic Games of complete information: Backward Induction and Subgame perfection

  3. 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

  4. 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

  5. Strategic Behavior in Business and Econ In this sense we can find, basically, four different types of games All games in a given category are represented and solved alike

  6. Strategic Behavior in Business and Econ Examples:

  7. Strategic Behavior in Business and Econ • Static Games of Complete Information • They are, in general, the most simple games. Their main features • are: • 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

  8. Strategic Behavior in Business and Econ • Static Games of Incomplete Information • 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: Sealed-bid Auctions: You don't know what is the value of the item to other players

  9. 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

  10. 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

  11. 3.2 Solution Concepts

  12. Strategic Behavior in Business and Econ Outline 3.1. What is a Game ? 3.1.1. The elements of a Game 3.1.2 The Rules of the Game: Example 3.1.3. Examples of Game Situations 3.1.4 Types of Games 3.2. Solution Concepts 3.2.1. Static Games of complete information: Dominant Strategies and Nash Equilibrium in pure and mixed strategies 3.2.2. Dynamic Games of complete information: Backward Induction and Subgame perfection

  13. Strategic Behavior in Business and Econ Solution Concepts A solution to a game consists of a prediction of what will be the logical outcome of the game (what will be the strategies chosen by the players and the corresponding payoffs) based on the rationality and common knowledge assumptions of Game Theory Depending on the type of the game, the representation will be different and hence the analysis and the method to find the solution (the solution concept) won't be the same.

  14. Strategic Behavior in Business and Econ Solution Concepts A solution of a game is called an Equilibrium of the game

  15. Strategic Behavior in Business and Econ Equilibrium The basic idea behind any equilibrium concept is that it corresponds 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 of strategies for the players that nobody wants to change, it seems logical to think that it is a “good” prediction. (Basic) Game Theory, though, does not explain how this equilibrium is reached

  16. 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 Example: Summer Pricing Bar 2 Suppose that Bar 1 chooses $5 and Bar 2 chooses $4

  17. 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 Example: Summer Pricing Bar 2 Suppose that Bar 1 chooses $5 and Bar 2 chooses $4 Then, the payoffs are: 15 to Bar 1 28 to Bar 2

  18. 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 Example: Summer Pricing Bar 2 Suppose that Bar 1 chooses $5 and Bar 2 chooses $4 Then, the payoffs are: 15 to Bar 1 28to Bar 2 But if Bar 2 is charging $4 then Bar 1 wants to charge $4 (to earn a payoff to 20 instead of 15)

  19. 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 Example: Summer Pricing Bar 2 Hence, Bar 1 choosing $5 and Bar 2 choosing $4 is NOT stable, is NOT an equilibrium

  20. 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 Example: Summer Pricing Bar 2 Consider Bar 1 charging $4 and Bar 2 charging $4 instead

  21. 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 Example: Summer Pricing Bar 2 Consider Bar 1 charging $4 and Bar 2 charging $4 Now the payoffs is 20 to each Bar

  22. 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 Example: Summer Pricing Bar 2 Consider Bar 1 charging $4 and Bar 2 charging $4 Now the payoff is 20 to each Bar Do they want to change the strategy ?

  23. 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 Example: Summer Pricing Bar 2 Consider Bar 1 charging $4 and Bar 2 charging $4 Now 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

  24. 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 equilibrium strategies. This is specially important when there is more than one equilibrium (Ex: Antena 3 vs. Telecinco) (Learning ?, Trial-and-error ?, Evolution ?, Hint ?)

  25. Strategic Behavior in Business and Econ Example: The Driving Game • Paul and Mary are driving in opposite directions on a two • lane road. • What should they do when they cross ? • Drive on the right lane ? • Drive on the left lane ?

  26. Strategic Behavior in Business and Econ Right Left Paul Right 0 , 0 -50 , -50 Left -50 , -50 0 , 0 Example: The Driving Game Mary • 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

  27. Strategic Behavior in Business and Econ Right Left Paul Right 0 , 0 -50 , -50 Left -50 , -50 0 , 0 Example: The Driving Game Mary • There are 2 equilibrium: • Both players driving on the right • Both players driving on the left

  28. Strategic Behavior in Business and Econ Right Left Paul Right 0 , 0 -50 , -50 Left -50 , -50 0 , 0 Example: The Driving Game Mary There are countries stabilized on the Drive on the right equilibrium There are countries stabilized on the Drive on the left equilibrium The question is: How did they reach one or the other ?

  29. Strategic Behavior in Business and Econ Best Reply All the solution methods that we are going to study are based on the prior concept of Best Reply For each player, a best reply to the strategy(ies) chosen by the 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

  30. Strategic Behavior in Business and Econ Example: The Battle for TV share Telecinco (player 2) Documentary Match 1, 1 2, 1.5 Match Antena 3 (player 1) 1.5, 2 0.75, 0.75 Documentary

  31. Strategic Behavior in Business and Econ • 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

  32. Strategic Behavior in Business and Econ Example: A (simple) Principal-Agent game • 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)

  33. Strategic Behavior in Business and Econ Monitor No Monitor Employee Work 50 , 90 50 , 100 Shirk 0 , -10 150 , -100 Example: A (simple) Principal-Agent game Manager What are the BestReplies ? (The Red Circles)

  34. Strategic Behavior in Business and Econ Monitor No Monitor Employee Work 50 , 90 50 , 100 Shirk 0 , -10 150 , -100 Example: A (simple) Principal-Agent game Manager Notice that there is no equilibrium !!

More Related