Game Theory Fundamentals: Strategies, Equilibrium, and Market Models

Game Theory Fundamentals

Game Theory is a simplified model approach used to formalize conflict in terms of a game. It formalizes conflict situations between two parties, taking into account their actions and reactions. It offers a promising approach to analyze competitive situations that can be formally translated into the categories of this theory.

Core Components of a Game

The games consist of:

• A set of players.
• A set of strategies.
• The payoffs to each player for every possible combination of their strategy choices.

Both players typically make their decisions simultaneously, without knowing the other player's decision.

Key Equilibrium Concepts

Dominant Strategy and Pareto Efficiency

A dominant strategy is the best possible payoff for a player, no matter which strategy the other player chooses. The game's equilibrium resulting from dominant strategies is often not efficient according to the Pareto criterion.

The Nash Equilibrium

The Nash Equilibrium is the best possible payoff for the players. It is the set of strategies that represent the best responses to each other for all players. A game with a finite number of players, each with a finite number of strategies, has at least one Nash equilibrium.

Zero-Sum Games

A zero-sum game is one in which the sum of all positive and negative payoffs is constant. Examples include price or quantity choices in oligopolistic markets or the Prisoner's Dilemma game.

Five Duopolistic Market Situations

Game theory provides models for analyzing competition in duopolistic markets:

1. Cournot-Nash Game: Firms simultaneously decide on output levels.
2. Von Stackelberg Game: Sequential decision-making regarding output.
3. Bertrand Game: Firms simultaneously decide on prices.
4. Price-Leadership Game: One firm sets the price, and others follow.
5. Collusion (Cartel): Results in a cartel where the aggregated profit of both firms is maximized. A collusion cartel is a formal type of cooperation referring to parameters such as price setting, output levels produced, or market shares.

Cournot Quantity Competition

This model involves simultaneous quantity strategies. A Nash equilibrium is reached when each firm's output level is the best response to the other firm's output level.

Credible Threat and Plausible Threat

A credible threat implies that an action, such as a price war, no longer makes sense as soon as market entry has taken place. Conversely, the text defines a plausible threat as a credible threat where the retaliatory action (a war) begins automatically after market entry.