Microeconomics (ECON0013) - Formulas, Definitions and FAQs

What is a strictly dominant strategy? A strategy which always provides a greater payoff when compared to other strategies (cannot provide an equal payoff; that would be weakly dominant). What is a weakly dominant strategy? A strategy which provides a greater than or equal payoff to other strategies. (Think of it as greater than or equal to) What is a pure strategy nash equilibrium? A nash equilibrium which arises from playing a specified strategy (I will play this action specifically) which results in an outcome where no player in the game wants to switch their strategy (holding the strategy of the other player(s) constant). What is a mixed strategy nash equilibrium? A nash equilibrium which arises from playing all action available to a player with a certain probability (I will player action A with probability 3/5 and action B with probability 2/5) which resolves to a game settup where each player would not change the probabilities they picked. What is the underlining method? Where we pick the best row for each column and the best column for each row (in terms of payoff). If payoffs are equal, underline both: How do you find a mixed strategy nash equilibrium? (2x2 game) - Assign each row a probability (p and 1-p) and each column a probability (q and 1-q). - Multiply the payoffs for that row/column by the probability of the column/row. - Make sure that both expressions for each row and each column equal each other. - Find the values of p and q respectively and you're all done :) How do you find the intersection of best responses? (Chapter 1, Generalised Method) - Start by finding both functions you'll be using. - Partially differentiate both with respect to the variable the individual can control. This should give you an equation in terms of both variables. - Find the intersection of the two equations you have derived. This is the nash equilibrium. What is a pareto dominant nash equilibrium? A nash equilibrium which provides the best possible outcome of the game. In this case, the nash equilibrium is (Stag, Stag) because it provides the highest payoff overall: What is a risk dominant nash equilibrium? A nash equilibrium which provides the least risky outcome of the game (a stable outcome). In this case, the nash equilibrium is (Rabbit, Rabbit) because it is the least risky option for players to play (as if the other player changes their strategy, they're still fine): What is a focal point?