Game Theory and Strategic Behavior

Game theory and strategic behavior

Game theory is a mathematical apparatus for analyzing strategic interaction. When the outcome depends on the actions of several players, game theory helps to predict results and understand strategies.

Basic Concepts

Game: A situation of strategic interaction with defined players, strategies, and payoffs.
Players: Participants making decisions (firms, countries, individuals).
Strategies: The available courses of action.
Payoffs: The outcomes (profit, utility) for each combination of strategies.
Payoff matrix: A table showing payoffs for all combinations.

Prisoner's Dilemma

A classical example: two suspects, each can either keep silent or confess.

	B keeps silent	B confesses
A keeps silent	(-1, -1)	(-10, 0)
A confesses	(0, -10)	(-5, -5)

Analysis:

For each player, the dominant strategy is to confess.
Result: both confess (-5, -5).
But if both stayed silent, it would be better (-1, -1).
Individual rationality leads to a collectively worse outcome.

Nash Equilibrium

Definition: A combination of strategies such that no player wants to change their strategy if the others do not change theirs.

In the prisoner's dilemma: (confess, confess) is a Nash equilibrium.

Properties:

Stability—no one deviates unilaterally.
Not necessarily efficient.
There can be multiple Nash equilibria.

Oligopoly as a Prisoner's Dilemma

Pricing:

	B: High Price	B: Low Price
A: High Price	(100, 100)	(20, 150)
A: Low Price	(150, 20)	(50, 50)

Analysis:

Mutually high prices are the best collective outcome (100, 100).
But for each player, the dominant strategy is to lower the price.
Nash equilibrium: (low, low) = (50, 50).
Price wars are the result of this logic.

Repeated Games

If the game is repeated:

Cooperation is possible based on the threat of punishment.
Tit-for-tat: start with cooperation, then copy the opponent’s actions.
Reputation and trust become important.

Conditions for cooperation:

Infinite horizon (or indefinite end).
A sufficiently low discount rate (future is valued).
Ability to observe and punish.

Cartels and Collusion

Cartel: explicit collusion to maintain high prices.
Stability problem: Each participant has an incentive to “cheat”—lower the price and take market share.
Prisoner's dilemma—a cartel is unstable.

What helps cartels:

Small number of participants (easier to coordinate).
Homogeneous product (easier monitoring).
Stable demand.
Punishment for deviation (OPEC).

Why cartels fall apart:

Temptation to cheat.
Changing conditions.
Entry of new players.
Antitrust prosecution.

For the Investor

Game theory helps to understand:

Probability of price wars.
Sustainability of price discipline.
Strategic decisions of companies.

Signs of a stable oligopoly:

History of price discipline.
Non-price competition.
Price setting transparency.
Market leader as a “price umbrella”.

Signs of instability:

Excess capacity.
New aggressive players.
Lowering of entry barriers.
Commodity-like nature of the product.