Week 8 - Game Theory Flashcards
What is game theory
A method of using mathematical models to study strategic situations.
Strategic situation
Situations where the outcome of a decision depends on the result of another player.
Non-strategic situation
Situations where the outcome of a decision does not affect or is not affected by another players decision.
Simultaneous games (normal/strategic form games)
Games where players make decisions without knowing what other players are doing.
What are normal form games made up of
Players, strategies and payoffs/utilities
Players
Number of players in a game
Strategies
The options each player has for each move
Difference between payoffs and outcomes
Outcome is a strategy profile that contains a strategy from each player.
A payoff is utility gained/lost from the result of an outcome.
What qualities must a solved game have
The outcome is stable - nobody has an incentive to change their move.
Outcome is reached from rational thinking: players are assumed to maximise their expected payoff.
Nash equilibrium
A way of finding a solution to a game by finding best responses and using this to identify a Nash equilibrium.
Nash equilibrium is a state where no player can improve their payoff by changing their strategy, assuming no other players have changed their strategies.
Strict dominance
A method of solving a game where one option will always give a better outcome than the other, no matter the other players choice.
This results in this option strictly dominating the other.
Iterated dominance
A method of solving a game where actions are sequentially deleted because they are illogical to play if we are thinking rationally until a dominant option is found.
What is prisoners dilema
A situation where 2 robbers are linked to a crime but cannot be charged unless one of the confesses.
Each robber can either defect (confess to the crime) or cooperate (keep silent). Defecting will give a lighter sentence to the confessor but both cooperating will give both players the lightest sentence.
However, because of the payoffs, defect strictly dominates cooperate so both prisoners having a less optimal outcome.
Prisoner’s dilemma is a scenario when rational decision-making results in an outcome that is not the optimal outcome.
Best response analysis
Used to find all stable outcomes in a game where there is multiple Nash equilibriums. Game theory won’t tell you which outcome to choose but will tell you if it is stable or not.
Take a players perspective and highlight their best option for each of the possible options the other player could choose. Do the same for the other player.
If both responses are highlighted then this is a Nash equilibrium because it is a stable outcome.
Can a game have no Nash equilibrium
Yes, if when doing best response analysis, there is no outcome where all players payoffs are highlighted, the game has no stable outcome and therefore does not have a pure strategy Nash equilibrium.
What are the 2 types of games
One shot games: interaction happens once.
Repeated games: interaction happens many times or happens periodically. Each repetition of the game is called a stage game. All the stage games make up the repeated game.
What are the 2 types of repeated games
Finitely repeated games.
Infinitely repeated games.
What are 2 famous strategies for infinitely repeated games
Grim trigger: I will first cooperate. But as soon as you defect, I will defect for the remainder of the iterated game.
Tit for tat: In the first round, I will cooperate. After the first round I will copy your previous action. E.g., if you cooperated in the previous round, I will cooperate this round or vice versa with defect.
Tit for tat has been very successful for the repeated prisoners dilemma.
Sequential games (extensive form games)
Games where moves are made one after another so players can clearly see past moves before making a new move.
What are the 2 types of sequential games (extensive form games)
Perfect information games: every player has complete knowledge of all previous actions and decisions made by other players up to the current point.
Imperfect information games: some players lack full knowledge of certain actions taken by others or other aspects of the game state.
How can extensive form game be represented
A game tree. Each branch on the tree represents a new choice and each end node has the outcome of the game with the choices.
Backward induction
Backward induction is a way to solve a perfect information, finite, sequential game.
It involves working backwards up the tree and comparing players options and ruling out options the player wouldn’t take if they can get a better outcome from the other option.
This process is repeated until 1 path is left which will lead to the optimal outcome to a game.
Behavioural games
A behavioural game is a different model to game theory and removes the assumption that players will only act in their own self interest.
Instead, it assumes that some people will not only want to maximise their own payoff but will want to maximise the whole groups payoff instead, even if this means sacrificing some of their own payoff.
What are attitudes people can have in game theory
Fairness: A preference for fair outcomes.
Altruism: Being willing to sacrifice your own payoff to benefit others.
Reciprocity: Rewarding kindness and punishing unkindness others.
