Game Theory

Game Theory

Study of interdependent decisions of agents.

Elements of a Game

Skill, Strategy, Luck

Skill

A male peacock has beautiful feathers. A chess player has a high IQ (CANNOT BE CHANGED)

Strategy

Depends on skill (I like horses so i’ll only move the knights)

Luck

Not required but may be useful with incomplete info

Timings of Games (Classification of Games)

Simultaneous & Sequential

Simultaneous

Players pick strategy at the same time, without observing the other (Rock-paper-scissors) (Nash & Dominant Strategy Eq’m)

Sequential

Players take turns, and observe the others previous move (Tic-tac-toe) (Subgame Perfect Eq’m)

Repetition (Classification of games)

One-shot games & Repeated games

One-shot games

You play the game & Collect the payoff (Chess)

Repeated Games

You play the game & collect the payoff, and repeat however often you need to. (Best 2 out of 3) (They require the same players each game)

Payoff Structure (Classification of Games)

Zero-sum game & Win-win games

Zero-sum Game

Winner, loser, or tie (A constant sum game, which means the winnings can be split or go one way but always equal the same thing, in this case nothing)

Win-win games

Everyone can win (Trade Agreements) (Not a constant sum game because the value of the winnings can change depending on the circumstances)

Perfect Info (Classification of Games)

When at least some players can observe other players actions (Sequential move game (not always the case))

Imperfect Info (Classification of Games)

When no players observe any other players (Simultaneous Games)

Complete Info (Classification of Games)

A game where each player knows the rules, available strategies, and exact payoff functions of all other players as common knowledge (Perfect Bayesian Eq’m)

Incomplete info

A game where the payoffs are unknown, the players skill-level is unknown, and the component of luck is unknown (Bayesian Nash Eq’m)

Non-cooperative Games

When contracts aren’t enforceable (contracts have an exit clause)

Fixed Rules (Classification of Games)

The rules are common knowledge and unchangeable.