MKTG 555: Marketing Models

Transcription

1 MKTG 555: Marketing Models A Brief Introduction to Game Theory for Marketing February 14-21,

2 Basic Definitions Game: A situation or context in which players (e.g., consumers, firms) make strategic decisions that take into account each other s actions and responses. Strategy: A rule or plan of action for playing a game. Each player has a strategy s i. Strategy profile/vector: A rule or plan of action for all players in the game (s 1, s 2, s 3, s i,..s N ). Payoff: The value (e.g., utility, dollars) associated with a possible outcome in the game. Each player (i) has his/her own payoff in a game. Optimal strategy: For each player, the strategy (s i ) that maximizes that player s expected payoff. 2

3 Some Types of Non-Cooperative Games Static Games with Complete Information Dynamic Games with Complete Information Static Games with Incomplete (Private) Information Simple Dynamic Games with Incomplete Information (Signaling Games) 3

4 Some Types of Non-Cooperative Games Static Games with Complete Information Dynamic Games with Complete Information Static Games with Incomplete (Private) Information Simple Dynamic Games with Incomplete Information (Signaling Games) 4

5 Concept of Dominant Strategy Payoff Matrix for an Advertising Game Firm B Advertise Don t Advertise Firm A Advertise (10, 6) (15, 1) Don t Advertise (7, 8) (10, 3) Dominant Strategy for firm A: Advertise Dominant Strategy for firm B: Advertise 5

6 Nash Equilibrium Firm A Payoff Matrix for a Second Advertising Game Firm B Advertise Don t Advertise Advertise (10, 6) (15, 1) Don t Advertise (7, 3) (20, 8) A strategy profile (s 1, s 2,., s n ) is a Nash equilibrium, if for each player i, his choice s i is the best response to the other players choices, s i. Strategy for firm A:? Strategy for firm B:? 6

7 Nash Equilibrium Payoff Matrix for a Third Advertising Game Firm B Advertise Don t Advertise Firm A Advertise (10, 10) (2, 15) Don t Advertise (15, 2) (6, 6) Strategy for firm A:? Strategy for firm B:? 7

8 Nash Equilibrium Payoff Matrix for a Fourth Advertising Game Firm B Advertise Don t Advertise Firm A Advertise (10, 10) (0, 0) Don t Advertise (0, 0) (6, 6) Strategy for firm A:? Strategy for firm B:? 8

9 Nash Equilibrium Payoff Matrix for a Fifth Advertising Game Firm B Advertise Don t Advertise Firm A Advertise (10, 6) (0, 0) Don t Advertise (0, 0) (6, 10) Strategy for firm A:? Strategy for firm B:? 9

10 Some Types of Non-Cooperative Games Static Games with Complete Information Dynamic Games with Complete Information Static Games with Incomplete (Private) Information Simple Dynamic Games with Incomplete Information (Signaling Games) 10

11 Subgame-Perfect Nash Equilibrium (from Gibbons 1997) A Game that Relies on a Noncredible Threat (Gibbons) L R L (1, 2) (1, 2) R (0, 0) (2, 1) Two potential Nash equilibria: (L, L ) and (R, R ). Which one will be played? 11

12 Cournot Duopoly Players: 2 firms selling identical products Strategies: Quantities produced of identical products (substitutes) are q i and q i. Players make their moves simultaneously. Payoffs: Cost of production is c per unit Price: p = a b q i + q i Profit i (q i, q i ) = (p c)q i Profit i (q i, q i ) = (p c)q i 12

13 Basic Econ a Marginal revenue curve for Monopolist (slope -2b) p M Demand curve (slope b) c q M q C q M : Quantity produced by a monopolist q C : Quantity produced under perfect competition 13

14 Cournot Duopoly q i a c b BR i q i = a c q i 2b 2 a c 2b Cournot-Nash Equilibrium Quantities that produce monopoly profits BR i 1 (q i ) = a c q i 2b 2 q M = a c 2b q C = a c b q i 14

15 Economic Implications of Different Market Structures q i a c b Marginal revenue curve for Monopolist (slope -2b) BR i q i = a c q i 2b 2 Demand curve (slope b) Cournot-Nash Equilibrium q M q i = q i = < q i + q i a c 3b < q C a c 2b q i c BR i 1 q i = a c q i 2b 2 q i q M q C q i 15

16 Stackelberg Duopoly Players: 2 firms selling identical products Strategies: Quantities produced of identical products (substitutes) are q i and q i. Player 1 makes the first move, and player 2 then follows (Leader-Follower game) Payoffs: Cost of production is c per unit Price: p = a b q i + q i Profit i (q i, q i ) = (p c)q i Profit i (q i, q i ) = (p c)q i 16

17 Dynamic Game Backward Induction q i Cournot-Nash Equilibrium Will the Stackelberg Nash equilibrium be the same as the Cournot equilibrium? Will q i here be higher than in the Cournot equilibrium? a c 2b BR i 1 q i = a c q i 2b 2 q M = a c 2b q C = a c b q i 17

18 Bertrand Competition Players: 2 (or more) firms selling identical products Strategies: Price charged p i and p i. Payoffs: Cost of production is c per unit p; p α, p > 0 Demand Q = 0 p > α where: p = Min(p i, p i ) Profit i = p i p i c if p i < p i (α p) 0 2 p c if p i = p i = p otherwise 18

19 Reaction Functions in Bertrand Price Competition p i p H p M : Monopoly price p H : Highest feasible price c: Unit cost p M Bertrand Nash equilibrium c p M p H = p i 19

20 Imperfect Vs. Incomplete Games In an imperfect information game, the players are unaware of the actions chosen by other players. However they know who the other players are, what their possible strategies/actions are, and their preferences/payoffs, i.e., information about the other players in imperfect information is complete. In incomplete information games, players may or may not know some information about the other players, e.g., their type, their strategies, payoffs or their preferences. 20

21 Balasubramanian Equilibrium Results (N Retailers + 1 Direct Marketer) 21

22 Balasubramanian Equilibrium Results (N Retailers + 1 Direct Marketer) 22

23 Equilibrium Results for Two-Stage Game Coverage ( ) + Price Competition 23

24 Equilibrium Results for Two-Stage Game Coverage ( ) + Price Competition 24