Game Theory Flashcards
What is game theory used to analyse?
The choice between cooperation and conflict
What is game theory?
The study of problems of cooperation and conflict among independent decision makers
What is a Nash Equilibrium?
A situation in a game where no player has an incentive to unilaterally change their strategy, assuming the other players stick to their strategies. It may not be unique but it always exists
What is a dominant strategy equilibrium?
Each player’s optimal play is a constant
Draw the strategic form of an example battle of the sexes game
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What characterises a battle of the sexes game?
Each player’s optimal strategy depends on what they think the other will do
What is a pure strategy?
A player uses a deterministic algorithm to decide what to do
What is a mixed strategy? When is it used?
Players use a randomised algorithm to decide what to do. Used when some games have no Nash equilibrium with deterministic algorithms
Draw the strategic form of an example prisoners’ dilemma game
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What characterises a prisoners’ dilemma game?
The dominant strategy equilibrium is not optimal for the players. Both players will cheat rather than cooperate, with a bad outcome
How can the not-optimal solution to a prisoners’ dilemma game be fixed?
Play the game repeatedly. ‘Tit-for-tat’ - cooperate at round 1, then at round n do what the other guy did at round n-1. This gets locked into (defect, defect). ie. forgive the other guy occasionally
How can price fixing arise implicitly?
Try charging double the price of your competitor and see what they do. If they ‘defect’ by competing, play tit-for-tat
Give an example of prisoners’ dilemma
Setting competing prices
Draw the strategic form of an example stag hunt game
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What characterises a stag hunt game?
People can hunt rabbits on their own, but have to work together to hunt a stag. If your buddy runs off after a rabbit, the stag will escape. Different from PD because (stag, stag) is now a Nash equilibrium
What is the difference between PD and SH?
Different from PD because (stag, stag) is now a Nash equilibrium. PD is payoff-dominant, SH is risk-dominant.
Draw the strategic form of an example chicken game
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What characterises a game of chicken?
Two players compete against each other to see who will “chicken” first. A player can force the Nash Equilibrium where they win
Draw the strategic form of an example matching pennies game
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What characterises a matching pennies game?
It is a zero-sum gain. A’s loss is B’s gain
Give an information application of matching pennies
Attacker vs defender in cybersecurity. Eg. network security system where attackers and defenders must continuously adapt and guess each other’s moves
Defender may not have resources to patch all possible vulnerabilities
Attacker may know which vulnerabilities are undefended
Give an information application of prisoners’ dilemma
Two organisations who both want a secure communication channel. Eg. security standard agreements between competing companies
Cooperation is costly encryption, defection is saving encryption costs, determined whether communication can be compromised or is safe.
If repeated interaction, cooperation more likely to emerge
Give an information application of battle of the sexes
Systems negotiating which communication protocol to use. Eg. distributed computing and network protocols where systems need to agree on standards like TCP/IP vs UDP
May have two systems with different preferences. Both systems prefer to coordinate, but hard to agree on which one
List the different Game Theories
- Matching pennies
- Battle of the sexes
- Prisoners’ dilemma
- Stag hunt
- Chicken
