Game Theory Final EXAM QUESTION & ANSWERS 100% VERIFIED

Game Theory Final EXAM QUESTION & ANSWERS 100% VERIFIED Game - ANSWER-A situation where an individual's payoff depends upon her own actions and upon the actions of other agents. A game consists of: - a a set of player N={1,...,N} - For each player i a set of strategies Si from which a player chooses a strategy si∈Si -A strategy profile (s1,...,sn) Strategy profile - ANSWER-s=s1,...sn Preferences - ANSWER-We assume that players want to choose the strategy that maximizes the expected value of their utility E[Ui(si,s-i) Prisoner's Dilemma - ANSWER-Two players. Each player has two strategies, either C(ooperate) or D(efect). Player 1 prefers U1(D,C)>U(C,C)>(D,D)>U(C,D) Player 2 prefers U2(C,D)>(C,C)>(D,D),U(D,C) Prisoner's dilemma models a situation in which there are gains from cooperation, but each player has an incentive o free ride no matter what the other player does. The nash equilibrium of a prisoner's dilemma (D,D) is NOT socially efficient because it is pareto dominated by (C,C). BoS game - ANSWER-Battle of the sexes. Two players agree to cooperate but disagree on the best outcome. Look at card 1 front for example. Strict Dominance - ANSWER-A pures trategy si strictly dominates another pure strategy si' if for all s-i∈S-i, Ui(si,s-i)>Ui(si',s-i). If a strategy is strictly dominated then it should never be played by a rational player and so will never be a Nash equilibrium. A strictly dominated strategy is NEVER a best reply. Common knowledge of rationality - ANSWER-We assume each player is rational (seeks to maximize his expected payoff) and knows that other players are rational. So rationality is common knowledge. Iterated strict dominance (and the 3 steps to using it) - ANSWER-The exclusion of strictly dominated strategies. It makes the game simpler. 1. Eliminate all strictly dominated strategies for all players (this reduces the game) 2. In reduced game, eliminate any strictly dominated strategies for all players 3. Repeat this until there are no further eliminations possible Best reply - ANSWER-Given a strategy profile s, a best reply is a strategy that maximizes player i's payoff conditional on others playing s:BRi(s)=argmax{ui(x,s-i)}.