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 theitem 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 theitem 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

17. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing Suppose that Bar 1 chooses $5 and Bar 2 chooses $4

18. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing Suppose that Bar 1 chooses $5 and Bar 2 chooses $4 Then, the payoffs are: 15 to Bar 1 28 to Bar 2

19. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing Suppose that Bar 1 chooses $5 and Bar 2 chooses $4 Then, the payoffs are: 15 to Bar 1 28 to 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)

20. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing Hence, Bar 1 choosing $5 and Bar 2 choosing $4 is NOT stable, is NOT an equilibrium

21. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing Consider Bar 1 charging $4 and Bar 2 charging $4 instead

22. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing Consider Bar 1 charging $4 and Bar 2 charging $4 Now the payoffs is 20 to each Bar

23. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing 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 ?

24. Strategic Behavior in Business and Econ $2$4$5 Bar 1 $210, 1014, 1214, 15 $4 12, 1420, 2028, 15 $5 15, 1415, 2825, 25 Bar 2 Example: Summer Pricing 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

25. 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 ?)

26. 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 ?

27. Strategic Behavior in Business and Econ Mary RightLeft Paul Right 0, 0 -50, -50 Left -50, -500, 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

28. Strategic Behavior in Business and Econ Mary RightLeft Paul Right 0, 0 -50, -50 Left -50, -500, 0 Example: The Driving Game There are 2 equilibrium: Both players driving on the right Both players driving on the left

29. Strategic Behavior in Business and Econ Mary RightLeft Paul Right 0, 0 -50, -50 Left -50, -500, 0 Example: The Driving Game 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 ?

30. 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

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

32. 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

33. 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

34. Strategic Behavior in Business and Econ Manager MonitorNo Monitor Employee Work 50, 90 50, 100 Shirk 0, -10150, -100 Example: A (simple) Principal-Agent game What are the Best Replies ? (The Red Circles)

35. Strategic Behavior in Business and Econ Manager MonitorNo Monitor Employee Work 50, 90 50, 100 Shirk 0, -10150, -100 Example: A (simple) Principal-Agent game Notice that there is no equilibrium !!