Market Structure and Game Theory:

Foundations and Principles:

1) Basic Elements of a Game:

• Players: the identity of those playing the game, N ≥ 2

• Rules: the timing of all players’ move the actions accessible to a player at each of her moves the information that a player has at each move.

• Outcomes- It depends on what each player does when it is her turn to move. The set of results is determined by all of the possible combinations of actions taken by players.

• Payoffs- It represents the players’ liking over the outcomes of the game.

2) Types of Games:

• Static (strategic) games of complete information
• Dynamic games of complete information
• Static (strategic) games of incomplete information
• Dynamic games of imperfect information

3) Equilibrium Concepts:

We desire to focus on how to solve games. An equilibrium concept is a resolution to a game. By this we imply that the equilibrium concept identifies out of the set of all possible strategies the strategies that players are actually likely to play. Resolving for equilibrium is similar to making a prediction about how the game will be played. The focus is on defining commonly utilized equilibrium concepts and illustrating how to find strategies consistent with each concept.

4) Fundamental Assumptions:

• Rationality- Players are engrossed in maximizing their payoffs.

• Common Knowledge- Every player knows 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 Games of Complete Information:

“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 for the reason that players move simultaneously. ‘Complete information’ denotes that players know the payoffs of their opponents.

5) Normal Form Representation:

• A set of players, identified by number: {1, 2,...., I}
• A set of actions or strategies for each player i , denoted Si . This is the “list” of permissible actions player i can take.
• A payoff function for each player i , π_i s ( ) , where  s = (s₁, s₂ ,...., s_I) and s_i ∈S_i (strategy vector).
• In addition, the descriptions of some games require delineation of who knows what, when, and order of play, etc.

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