Part 3. Oligopoly pricing Game theory 1 Classic models of oligopoly Game theory 2 Dynamic models of oligopoly Product differentiation Identifying and measuring market power
Part 3. Oligopoly pricing Game theory 1 Classic models of oligopoly Game theory 2 Dynamic models of oligopoly Product differentiation Identifying and measuring market power
Game theory 1 Why game theory Foundations and principles Static games of complete information Summary
Game theory 1 • Why game theory • Foundations and principles • Static games of complete information • Summary
Why game theory? Game-theoretic situation payoff interdependency or strategic Interdependency Payoff interdependency exists when the optimal choice by an agent depends on the actions of others The mutual dependency of payoffs on the actions by all players defines a game-theoretic situation. In contrast, decision theoretic situations are when there is no recognized payoff interdependence: the payoffs or profits of an action are determined without considering the choices of others EXamples of decision-theoretic and game-theoretic situations Noncooperative game theory is a set of tools that is used model the behavior or choices of players when the payoffs of a choice depends on the choice of other players Recognized payoff interdependency gives rise to interdependent decision making. The optimal choice of a player will depend on her expectation of the choices of others playing the same game
Why game theory? • Game-theoretic situation: payoff interdependency or strategic interdependency. • Payoff interdependency exists when the optimal choice by an agent depends on the actions of others. • The mutual dependency of payoffs on the actions by all players defines a game-theoretic situation. In contrast, decisiontheoretic situations are when there is no recognized payoff interdependence: the payoffs or profits of an action are determined without considering the choices of others. • Examples of decision-theoretic and game-theoretic situations • Noncooperative game theory is a set of tools that is used to model the behavior or choices of players when the payoffs of a choice depends on the choice of other players. • Recognized payoff interdependency gives rise to interdependent decision making. The optimal choice of a player will depend on her expectation of the choices of others playing the same game
Foundations and principles The basic elements of a game Any game has 4 elements which define the structure of of the game 1. players: the identity of those playing the game 2. rules: the rules of the game specify three things:(a) the timing of all players moves; (b) the actions available to a player at each of her moves; and ( c) the information that a player has at each move 3. outcomes: the outcome of a game depends on what each player does when it is her turn to move. The set of outcomes is determined by all of the possible combinations of actions taken by players 4. payoffs the payoffs of the game represent the players preferences over the outcomes of the game
Foundations and principles • The basic elements of a game • Any game has 4 elements which define the structure of of the game. • 1. players: the identity of those playing the game. • 2. rules: the rules of the game specify three things: (a) the timing of all players’ moves; (b) the actions available to a player at each of her moves; and (c) the information that a player has at each move. • 3. outcomes: the outcome of a game depends on what each player does when it is her turn to move. The set of outcomes is determined by all of the possible combinations of actions taken by players. • 4. payoffs: the payoffs of the game represent the players’ preferences over the outcomes of the game
Types of games(1) Classify games on the basis of (a the timing of moves and(b) uncertainty about the payoffs of rivals Static game: each player moves once, and when a player moves she does so not knowing the action of her rivals. Such a game is sometimes called a strategic game Dynamic game: players move sequentially and have some idea, perhaps imperfect, about what their rivals have done; that is, players are at least partially aware of the actions taken by others so far Such games are often called extensive games
Types of games(1) • Classify games on the basis of (a) the timing of moves and (b) uncertainty about the payoffs of rivals. • Static game: each player moves once, and when a player moves she does so not knowing the action of her rivals. Such a game is sometimes called a strategic game. • Dynamic game: players move sequentially and have some idea, perhaps imperfect, about what their rivals have done; that is, players are at least partially aware of the actions taken by others so far. Such games are often called extensive games
Types of games(2 In dynamic games we can distinguish between games of perfect information, where all players know the entire history of the game when it is their turn to move, and games of imperfect information in which at least some players have only a partial idea of the history of the game When it is their turn to move In a game of complete information, players know not only their own payoffs, but also the payoffs of all the other players. In a game of incomplete information, players know their own payoffs but there are some players who do not know the payoffs of some of the other players We can distinguish between 4 types of games: (a)static games of complete information; (b )dynamic games of complete information; (c) static games of incomplete information; (d )dynamic games of incomplete information
Types of games(2) • In dynamic games we can distinguish between games of perfect information, where all players know the entire history of the game when it is their turn to move, and games of imperfect information in which at least some players have only a partial idea of the history of the game when it is their turn to move. • In a game of complete information, players know not only their own payoffs, but also the payoffs of all the other players. In a game of incomplete information, players know their own payoffs, but there are some players who do not know the payoffs of some of the other players. • We can distinguish between 4 types of games: (a) static games of complete information; (b) dynamic games of complete information; (c) static games of incomplete information; (d) dynamic games of incomplete information
Equilibrium concepts The equilibrium concept identifies, out of the set of all possible strategies the strategies that players are actually likely to play Solving for an equilibrium is similar to making a prediction about how the game will be played
Equilibrium concepts • The equilibrium concept identifies, out of the set of all possible strategies, the strategies that players are actually likely to play. • Solving for an equilibrium is similar to making a prediction about how the game will be played
Fundamental assumptions Game-theoretic analysis is built on 2 fundamental assumptions 1. rationality: players are interested in maximizing their payoffs 2. common knowledge: all players know the structure of the game and that their opponents are rational, that all players know that all players know the structure of the game and that their opponents are rational, and so on
Fundamental assumptions • Game-theoretic analysis is built on 2 fundamental assumptions: • 1. rationality: players are interested in maximizing their payoffs. • 2. common knowledge: all players know the structure of the game and that their opponents are rational, that all players know that all players know the structure of the game and that their opponents are rational, and so on
Static game of complete information Static games of complete information have 2 distinguishing characteristics Complete information means that players know the payoffs of their opponents Static means that players have a single move and that when a player moves, she does not know the action taken by her rivals. This may be because players move simultaneously
Static game of complete information • Static games of complete information have 2 distinguishing characteristics. Complete information means that players know the payoffs of their opponents. Static means that players have a single move and that when a player moves, she does not know the action taken by her rivals. This may be because players move simultaneously
Normal form representation The normal form representation of a static game of complete information is given by: (a) a set of players identified by number (1, 2, ...,I], where I is the number of players; (b) a set of actions or strategies for each player i denoted S. This is simple the list of permissible actions player i can take; (c)a payoff function for each player Ti( s), which gives player is payoff for each strategy profile or play of the game, s=(S, S2,. s), where s, is the action taken by player i. The strategy taken by player must be allowed this means that it must be from the set or list of permissible actions, S form can be represented using a payoff matrix. The al For 2-player games with finite strategy sets, the nor convention is that the first number is the payoff to player 1 the row player) and the second number is the payoff from that strategy profile for player 2( the column player)
Normal form representation • The normal form representation of a static game of complete information is given by: (a) a set of players, identified by number {1, 2, …, I}, where I is the number of players; (b) a set of actions or strategies for each player i, denoted Si . This is simple the list of permissible actions player i can take; (c) a payoff function for each player i, πi (s), which gives player i’s payoff for each strategy profile or play of the game, s=(s1 , s2 , …, sI ), where si is the action taken by player i. The strategy taken by player i must be allowed; this means that it must be from the set or list of permissible actions, Si . • For 2-player games with finite strategy sets, the normal form can be represented using a payoff matrix. The convention is that the first number is the payoff to player 1 (the row player) and the second number is the payoff from that strategy profile for player 2 (the column player)
