T2: 2.1: Game Theory Flashcards
What is a symmetric game?
When the players’ strategies are equivalent and payoffs are the same
What are pure strategies?
When a player picks one option and sticks with it regardless
What is a solution by elimination of dominated strategies?
If player 1 has a dominant strategy tf player 2 knows they will choose it and tf plays accordingly
What makes a strategy a best response?
If the player can’t gain more utility by switching to a different strategy, given what all other players are doing
What makes a set of strategies a Nash Equilibrium?
If and only if all players are playing best responses to what the other players are doing -> (can lead to more than one NE)
What is the idea behind mixed strategy Nash Equilibria(MSNE)?
Agents play the strategies with different probabilities, aim is to randomise choice so that the other player will be indifferent between playing their strategy (See my notes, learn and understand example!!!)
What are sequential games?
When one player goes first and then their opponent decides based on what they did (eg. oligopoly sometimes)
See notes
Working through backwards induction example
Note regarding sequential games and NE?
Sometimes there may be more than one PSNE in the normal form of the game, but it may be an unrealistic outcome in a sequential form of the game tf for sequential games must check using the extended (tree) form if a PSNE is feasible
When might cooperation be more likely to arise and lead to a better outcome for both players?
In repeated and simultaneous games
Explain collusion to keep prices high for oligopoly?
Profits are supernormal, if one firm undercuts the other they capture their market share, if both defect ->price war tf no SNP (See payoff table)
Explain cartel output setting for oligopoly?
Cartel chooses output level that a single monopoly would set, each get half of the profit (if duopoly)
If either firm defects and increases output, they reduce total profit but get a larger share for themself
If both defect -> lower price and higher quantity -> cournot equilibrium (see payoff matrix)
Why do cartels exist if there is an incentive to undercut/overproduce and gain more profit?
The Credible Threat of Punishment:
In period 0, if no one cheats both firms get high π(m), if you cheat you get π(D) and opponent gets π(B), but π(D)+π(B) your opponent will also cheat tf π(c)/r which is likely less (See and draw payoff matrix for this!)
When will cheating occur then?
Cheating will occur only if:
• 𝜋𝐷 is high enough (i.e. direct reward from cheating is big)
• 𝜋𝐶 is not too low (i.e. future cost of cheating is small)
• 𝜋𝐵 is low enough (i.e. being betrayed is really bad)
• 𝑟 is high enough (i.e. future is discounted a lot)
How are strategies given and how are payoffs given?
Strategies given in curly brackets and payoffs in square brackets
