Game Theory by Selcuk Ozyurt

目录

Strategic interation (i.e., Game) Describing Components:

  1. Players
  2. Actions
  3. Information (what players know when they act)
  4. Outcomes
  5. Preferences (rank of outcomes)

Game tree (decision tree)

  • Decision nodes (belong to only 1 person)
  • Terminal nodes
  • Branch (each node can be reached by only 1 path)
  • Outcomes
  • Information set (a collection of decision nodes)

Strategy is a complete contingent plan for a player in the game. A strategy must specify each action player will take at each decision node or information set. One information set has only one action.

Normal (Strategic) Form Representation of Games

Belief of a player is his/her assessment about the strategies of others in the game.

Mixed strategies is probability distribution over the set of pure strategies available to a player. Pure strategy is the strategy probability equal to 1.

Rationality: players behave consistently according to their preference (e.g., maximizing their own payoffs, minimizing opponent’s payoff, etc.).

Common Knowledge: game structure is the common knowledge among players.

A strategy profile is efficient if there is no other profile existing is more efficient (all players get equal or higher payoffs).

Contract: an agreement about behavior that is intended to be enforced. Contract is self-enforced if players have incentive to abide by the terms of the contract. Contract is externally-enforced if players motivated externally by a judge or arbitrator.

Reputation of the player can impact the strategy.

  • Defendent: the person breaches the contract
  • Plantiff: the person abide the contract