ECON-2006EG Study Guide - Quiz Guide: Strategic Dominance, Sequential Game, Jolla

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ceruleanraccoon367

7 Mar 2021

School

Laurentian

Department

Economics / Science Èconomique

Course

ECON-2006EG

Professor

Byron Eastman

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Document Summary

Chapter outline: simultaneous move games, nash equilibrium, applications of nash equilibria, how do people actually play such games, extensive-form games. Game theory is the study of situations in which the payoffs of one agent depend not only on his or her actions, but also on the actions of others. There are 3 key elements in any game: players, strategies, payoffs. This case is known as prisoners" dilemma and it is called a simultaneous-move game; in simultaneous-move games players pick their actions at the same time. A strategy of a player is a best response to the strategies of the others in the game if, taking the other player"s strategy as given, it gives greater payoffs than any other strategy available. In the prisoners" dilemma you should always chose to confess, because it is the best response in both cases, if josie chose to confess and to hold out.

Related Questions

4. Game theory terminology

Select the term that best describes each definition listed in the following table.

Definition	Nash Equilibrium	Dominant Strategy	Collusion	Tit-for-tat Strategy	Payoff Matrix	Prisoners' Dilemma
A player's best choice, if it exists, regardless of his or her opponent's strategy
A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents
A case in which individually rational behavior leads to a jointly inefficient outcome
A visual representation of a game showing all possible strategies for each player and all potential outcomes and payoffs

periwinklebuffalo937

The correct statements are [mark all that apply]:

A. The concept of best response strategy played in equilibrium by all players and no unilateral deviation are applicable for Bayesian games.

B. A game, where there are one firm 1 and two types of firms 2 (strong or weak) but firm 1 knows that firm 2 is strong with probability 0.7, can be described as a game of incomplete information.

C. A Bayesian Nash equilibrium is totally different from a Nash equilibrium in Bayesian games.

D. To be uncertain about others players' payoff functions is equivalent to saying that player 1 may be uncertain about the types of the other players.

Problem 1

In each of the three games shown below, let p be the probability that player 1 plays cooperates (and 1- p the probability that player 1 defects), and let q be the probability that Player 2 plays cooperates (and 1- q the probability that player 2 defects).

PrisonerÃ¢â¬â¢s Dilemma

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	10,80
	defect	80,10	40,40

Stag Hunt

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	5,40
	defect	40,5	40,40

Chicken

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	50,80
	defect	80,50	40,40

1. For each game, draw a graph with player 1Ã¢â¬â¢s best response function (choice of p as a function of q), and player 2Ã¢â¬â¢s best response function (choice of q as a function of p), with p on the horizontal axis and q on the vertical axis.

2. Using this graphs, find all the Nash equilibriums for the game, both pure and mixed strategy Nash equilibriums (if any). Label these equilibriums on the corresponding graph.

3. In those games that have multiple pure strategy Nash equilibriums, how do the expected payoffs from playing the mixed strategy Nash equilibrium compare with the payoffs from playing the pure strategy Nash equilibriums? Which type of strategy (mixed or pure) would players prefer to play in these games?

Problem 2

Two people are involved in a dispute. Player 1 does not know whether player 2 is strong or weak; she assigns probability ÃÂ± to player 2 being strong. Player 2 is fully informed. Each player can either fight or yield. Each player obtains a payoff of 0 is she yields (regardless of the other personÃ¢â¬â¢s action) and a payoff of 1 if she fights and her opponent yields. If both players fight, then their payoffs are (-1; 1) if player 2 is strong and (1;-1) if player 2 is weak. The Bayesian game is the following, depending on the type of player 2:

	Y	F		Y	F
Y	0, 0	0, 1	Y	0, 0	0, 1
F	1, 0	-1, 1	F	1, 0	1, -1
Player 2 is strong (ÃÂ±)			Player 2 is weak (1-ÃÂ±)			Player 2 is strong (ÃÂ±)

After writing all the strategies and payoffs in the same matrix, find the Bayesian Nash equilibriums, depending on the value of ÃÂ± (ÃÂ± Ã¢â°Â¤ 1/2 or ÃÂ± Ã¢â°Â¥1/2).

jadebuffalo465

ECON-2006EG Study Guide - Quiz Guide: Strategic Dominance, Sequential Game, Jolla

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