Microeconomics

SEMESTER 1: MICROECONOMICS

CLASS 4 & 5

Lecture 4 & 5 Competition as a Game

GAME THEORY

Game theory = Study of human behavior and strategic decisions. Used to solve some of the hardest problems in economics. There are different solutions concepts.

-A game: at least 2 players

-Payoffs: what the player wins or lose: value associated with a possible outcome

-Rules

-strategy= rule or plan of action for playing a game

-optimal strategy= strategy that maximizes a player’s expected payoff. .

PAYOFF MATRIX

Payoff matrix = Table showing profit (or payoff) to each firm given its decision and the decision of its competitor.

 [pic 1]

Dominant strategy = strategy that is optimal no matter what an opponent (the other player) does

Weakly/ strictly dominant strategy =

Game equilibrium = Outcome of a game ?

DOMINANT STRATEGY EQUILIBRIUM

Dominant strategy equilibrium/ Equilibrium in dominant strategies = More basic solution concept. Outcome of a game in which each firm is doing the best it can regardless of what its competitors are doing.

[pic 2][pic 3]

We have a dominant strategy equilibrium when all players play a strictly dominant strategy. Here, we have a dominant strategy equilibrium when player 1 plays strategy A and player 2 plays strategy D. → (A;D)

In the example: [pic 4]

-Both players have a strictly dominant strategy: Payoff(S1) > Payoff(S2) whatever does the other player.

-Thus, this game admits a dominant strategy equilibrium, (S1, S1) with payoffs zeros.

This is an important result: under perfect competition or a price war situation, profits are zero.

CASE OF A COOPERATIVE GAME

Cooperative game = Game in which participants can negotiate binding contracts that allow them to plan joint strategies.

Noncooperative game = Game in which negotiation and enforcement of binding contracts are not possible

[pic 5]

 If the game were a cooperative game, i.e. if firms could legally sign binding contracts about price agreements, they would probably agree on creating a cartel and thus choose strategy S2:

➔ (S2; S2) would be the cooperative game equilibrium.

Cooperative game equilibrium = (S2;S2)

NASH EQUILIBRIUM

Nash equilibrium = A set of strategies, one for each player, in which no player wishes to change his behavior (strategy choice) of his oponents.

→ I’m doing the best I can given what you are doing

→ You’re doing the best you can given what I am doing.

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