Game Theory

What would I do if he does that?

Look forward and reason back.

Players are RATIONAL. They will try to maximise their own gains.

In a Nash Equilibrium: It is a set of strategies such that both players and playing their best response, there is no incentive to deviate and is the only possible combination of strategies.

Dominant strategies are played regardless of whatever the other player is playing.

Weakly dominant strategies are strategies that are no worse off from being played by the player. It is as at least as good as any other strategies.

Dominated strategies have no reason to be chosen because there exists a strategy that is strictly better than it.

In pure strategy there is no probabilities of strategies being played or not. They are either chosen or not.

In a mixed strategy game the strategies have probabilities of being played. When solving questions: Players need to feel indifferent between the strategies being played p*payoff1 + (1-p)*payoff2 = p*payoff3 + (1-p)*payoff4. Find the intersection by drawing a graph for the NE.

Sequential games. Players play strategies one after the other. Look forward to the future for the ideal result/payoff for yourself and reason back to your original position anticipating what the other player will do.

a sequential game where there is an incentive to deviate: payoff*[discount rate/(1-discount rate)]

a strategic option is credible, observable and irreversible

Pure Strategy: A complete contingent plan of action that specifies an action that a player would choose under any contingency the player may face in a game

Dominant Strategy: A strategy has to outperform every other strategy, strictly higher payoff, no matter the strategy played by the other player.

Nash strategy are predictions of what the players will play if they are rational.

Pure strategy subgame perfect nash equilibria: A profile of strategy that constitutes a nash equilibrium for every subgame of a game