Game theory is a crucial concept in economics, mathematics, and social sciences, used for understanding strategic interactions between individuals, firms, or nations. Game theory shows how rational actors make decisions when their outcomes depend on the actions of others. Let's take a deeper look.
Game Theory is the study of how individuals (referred to as players) make decisions in situations where the outcome depends not only on their own actions but also on the actions of others. These situations, known as games, involve multiple players, each with their own set of strategies and possible outcomes.
Key Elements of Game Theory
Players: The decision-makers in the game. Players could be individuals, firms, countries, or any entities capable of making strategic decisions.
Strategies: The possible actions each player can take. A strategy is a plan of action that a player follows throughout the game.
Payoffs: The outcomes of the game for each player, usually represented in terms of utility, profit, or another measure of value.
Information: The knowledge each player has about the game, which can be complete (all players know the strategies and payoffs) or incomplete (some information is unknown).
Equilibrium: A situation where no player has an incentive to unilaterally change their strategy, as doing so would not improve their payoff. The most famous equilibrium concept is the Nash Equilibrium, named after mathematician John Nash.
Types of Games in Game Theory
Cooperative vs. Non-Cooperative Games: In cooperative games, players can form alliances and negotiate strategies together. In non-cooperative games, players act independently, and any cooperation must be self-enforcing.
Zero-Sum vs. Non-Zero-Sum Games: In zero-sum games, one player's gain is another player's loss. In non-zero-sum games, it's possible for all players to benefit or lose, leading to win-win or lose-lose situations.
Simultaneous vs. Sequential Games: In simultaneous games, all players make decisions at the same time, without knowing the other players' choices. In sequential games, players make decisions one after another, with later players having some knowledge of previous actions.
Repeated vs. One-Shot Games: One-shot games occur only once, while repeated games happen multiple times, allowing strategies to evolve over time.
Although we know what game theory is, how can we apply it in the realm of economics?
Let's say we have two companies, Company X and Company Y. Every single day, both firms have the choice of either cooperating or defecting. If both firms cooperate, they benefit equally. If both firms defect, they both suffer greatly. However, if one firm cooperates and the other firm tricks them and instead defects, then the firm that cooperated will suffer more than the firm that defected. This shows the idea of oligopolies and how we can see the cooperation/defection between two big firms and its benefits/consequences in any oligopolistic market.
Let's talk more about Nash Equilibriums.
A Nash Equilibrium occurs when all players in a game are making the best possible decisions given the decisions of others. At this point, no player has anything to gain by changing only their strategy unilaterally.
Example: In the classic "Prisoner's Dilemma" game, if both prisoners choose to betray each other (leading to a worse collective outcome), they reach a Nash Equilibrium because neither prisoner can improve their situation by changing their strategy alone.
What's a Dominant Strategy?
A strategy is dominant if it is the best choice for a player, no matter what the other players choose.
Example: In a business competition, if one firm always profits more by lowering prices regardless of its competitor's actions, then price-cutting is a dominant strategy.
Famous Examples in Game Theory
Prisoner’s Dilemma
Scenario: Two criminals are arrested and interrogated separately. Each can either betray the other or remain silent. The dilemma shows how rational individuals might not cooperate, even if it's in their best interest.
Outcome: The typical outcome is that both betray each other, resulting in a worse collective result than if they had cooperated.
The Battle of the Sexes
Scenario: A couple is deciding how to spend their evening, with one preferring a sports event and the other a movie. They want to spend time together but have different preferences.
Outcome: Multiple equilibria exist (one where they go to the sports event, another where they go to the movie), highlighting coordination challenges in decision-making.
The Stag Hunt
Scenario: Two hunters can either hunt a stag together (which requires cooperation) or hunt a rabbit alone. The stag yields a higher reward but requires mutual cooperation, while the rabbit is a safer, lower-reward option.
Outcome: The game highlights the tension between safety and social cooperation, illustrating how trust and risk play roles in strategic decisions.
The Ultimatum Game
Scenario: One player (the proposer) is given a sum of money and must offer a portion to another player (the responder). The responder can accept or reject the offer; if rejected, neither player gets anything.
Outcome: This game explores concepts of fairness and rationality, as responders often reject offers they perceive as unfair, even at a cost to themselves.
In conclusion, Game Theory is a powerful analytical tool that illustrates strategic decision-making in competitive and cooperative environments. By understanding the principles of game theory, we can better anticipate the actions of others and make more informed decisions in complex environments. In economics, this can help us understand and predict behavior in oligopolistic markets.
