Topic 8 Game Theory Page 1
Game Theory: The Basics
The following is based on Games of Strategy, Dixit and Skeath, 1999.
Theory of Games and Economics Behavior –
John Von Neumann and Oskar Morgenstern (1943)
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Game Theory: The Basics and Theory of games and Economics Behavior, Slides of Game Theory
Game theory provides some general principles for thinking about strategic interaction, terminology and rules of games.
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Game Theory: The Basics The following is based on Games of Strategy , Dixit and Skeath, 1999.
Theory of Games and Economics Behavior –
John Von Neumann and Oskar Morgenstern (1943)
“To be literate in the modern age, you need to have a general understanding of game theory.” (Paul Samuelson)
When a person decides to interact with other people, there must be some cross effect of their actions.
What one does must affect the outcome for the other. For an interaction to become a strategic game, we need the participants’ mutual awareness of this cross effect.
It is the mutual awareness of the cross effects of actions and actions taken as a result of this awareness that makes strategy interesting.
Strategic Games vs. Decisions
Interactions between
mutually aware players.
Action situations where each person can choose without concern for reaction from others.
b) Players’ Interests: Total conflict Some commonality
Zero Sum Games:
- one player’s winnings are the others’ losses.
- Player interests in complete conflict.
- Players are dividing up any fixed amount of possible gain.
Most economic and social games are not zero-sum.
Example: Trade offers scope for deals that benefit everyone.
d) Do the Players have Full or Equal Information?
Players can release information selectively
- Signals – actions by the more informed player.
- Signaling – information given out.
- Screening – the player can create a situation where their opponent will have to take some action that credibly reveals his information.
- Methods are known as screening devices.
e) Are the Rules of the Game Fixed?
f) Are Agreements to Cooperate Enforceable?
- Cooperative Games: joint-action agreements are enforceable.
- Non-cooperative Games: joint-action agreements that are not enforceable or possible to enforce, and individuals must be allowed to act in their own interests.
(C) Rationality: The assumption that players are perfect calculators and flawless followers of their best strategies. It does not mean that players are selfish. It means pursuing one’s own value system consistently is rational.
(D) Common Knowledge of Rules:
- We assume players have a common understanding of the rules of the game “ at some level .”
Rules of the Game:
- List of players
- The strategies available to each player
- The payoffs of each player for all possible combinations of strategies pursued by all players
- Assumption players are rational maximizers.
Evolutionary approach: imported the biological ideas into game theory.
- Evolve; allow growth.
- Social / cultural
- Observation and imitation
- Teaching and learning
Uses of Game Theory
- 1- Explanation -- helps answer the “why did that happen?” questions.
- 2- Prediction
- 3- Advice or prescription
Games with Sequential Moves
Games with strict order of play. Players take turns making their moves. They know what players who have gone before them have done. Interactive thinking.
Players decide their current moves based on calculations of future consequences.
(2) Terminal node :
- End points of the game
- Has associated set of outcomes for players
- Outcomes represent the payoffs received by each player.
- Every decision node can have only one branch leading to it.
Initial node node terminal node