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)