Game Theory Flashcards
What is a dominant strategy?
Dominant strategy equilibrium is a set of choices where each player’s choices are optimal, given the choices of other players.
Nash Equilibrium
Doing the best you can, given what everyone else is doing. No incentive for anyone to change their behaviour
E.g if there are two individuals, and B makes an optimal choice, then A will make an optimal choice based on B’s optimal choice.
Payoff will be a function of your own choice and other player’s choices
Simultaneous Game Assumptions
- Symmetric
2. Complete information: I know the strategies and payoffs of other firms.
Nash Equilibrium equations
Let G= (A1, A2)(P1, P2)
A are strategy sets
P are payoff functions.
Rational Response:
If a1* ε A1 and a2* ε A2 is the outcome or solution of the game, then the strategy (a1, a2) must constitute a NE.
When does a Nash equilibrium hold?
- P1(a1, a2) ≥ P1(a1, a2) for any a1 ε A1.
The payoff of a1, a2* exceeds any other strategy for player 1, a1. Therefore, I don’t want to change my behaviour. Any other strategy would mean a lower payoff.
2.P2(a1, a2) ≥ P2(a1*, a2) for any a2 ε A2.
The payoff of a1, a2 exceeds any other strategy for player 2, a2. Therefore, they don’t want to change their behaviour. Any other strategy would mean a lower payoff.
Everyone cannot be made better off and is thus best responding.
Why can we have multiple Nash equilibria?
This can take place is there isn’t a dominant strategy. Firms best respond if the other firm changes their behaviour. If there is a dominant strategy, players will not be incentivised to change their decision as there is one outcome which is the best response for all.
What is the prisoner’s dilemma?
A game where the Pareto efficient outcome is strategically dominated by an inefficient outcome.
Game of entry deterrence
Incumbent monopolist with a threat of entry. The entrant’s payoff depends on Incumbent’s willingness to fight.
If the incumbent can make a credible threat, i.e. by purchasing extra capacity that will allow him to produce more output, then this would discourage entry from player 2.
