Introduction
Game theory is a fundamental concept in economics and social sciences that studies the strategic interactions among decision-makers, also known as players. These players make decisions based on the anticipated actions and responses of other players. A critical classification in game theory is between games of complete information and games of incomplete information. Understanding the difference between these two types of games is essential for analyzing economic and strategic behavior in various real-life situations like markets, negotiations, or conflicts.
What are Games of Complete Information?
A game is said to have complete information when all players know the structure of the game. This includes:
- The set of players involved
- The strategies available to each player
- The payoffs or outcomes associated with each combination of strategies
In simple terms, everyone knows everything about the rules of the game and the potential results of all possible actions. However, complete information does not mean players know what choices the other players will make; it only means they know what choices are available and the consequences of each.
Example of Complete Information
The classic Prisoner’s Dilemma is an example of a game with complete information. Both prisoners know the consequences (jail terms) of confessing or staying silent. They don’t know what the other will choose, but they understand the full structure of the game.
Key Features of Complete Information Games
- All players are aware of the rules and payoffs.
- Strategies and preferences of other players are known.
- Used in normal-form or extensive-form games.
- Rational behavior is expected based on this knowledge.
What are Games of Incomplete Information?
A game has incomplete information when players lack full knowledge about some elements of the game. This could include:
- The payoffs of other players
- The strategies available to them
- The types or characteristics of other players (e.g., risk preferences, private information)
These types of games are also known as Bayesian games because players form beliefs about unknown elements and update their strategies accordingly.
Example of Incomplete Information
Suppose two firms are competing in a market. Firm A doesn’t know whether Firm B has low or high production costs. This uncertainty makes it a game of incomplete information. Firm A has to form a belief (a probability) about Firm B’s type and then decide how to act.
Key Features of Incomplete Information Games
- Players do not have full knowledge of all parameters.
- Beliefs and probability distributions are used to make decisions.
- Players must think strategically about what they don’t know.
- Bayesian Nash Equilibrium is often used to find solutions.
Comparison Table
| Feature | Complete Information | Incomplete Information |
|---|---|---|
| Knowledge of Payoffs | Known to all players | Uncertain or private |
| Strategies of Others | Known | May be unknown |
| Player Types | Known | Unknown (types assumed) |
| Example | Prisoner’s Dilemma | Market competition with unknown costs |
| Solution Method | Nash Equilibrium | Bayesian Nash Equilibrium |
Why the Distinction Matters
The distinction between complete and incomplete information games helps economists and policymakers understand how people or firms behave under uncertainty. In the real world, most interactions are based on incomplete information. For instance:
- Buyers may not know the quality of a used car (asymmetric information)
- Investors may not know the financial risks of a startup
- Countries may not know each other’s true military power or intentions
Studying how decisions are made under such uncertainty helps design better markets, contracts, and institutions.
Conclusion
Games of complete and incomplete information are two major categories in game theory that differ based on the level of knowledge players have about the game’s structure. Complete information games assume full transparency among players, while incomplete information games involve uncertainty and hidden information. Understanding these differences is crucial for analyzing real-life economic and strategic situations, where incomplete information is more common and significantly influences decision-making.