ECON10004 Study Guide - Final Guide: Fundamental Solution, Nash Equilibrium, Strategic Dominance

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orangemole587

25 May 2018

School

University of Melbourne

Department

Economics

Course

ECON10004

Professor

John Freebairn, Eik Swee

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Players choose their actions in isolation, with no information about what other players have done or

will do

A player can reason through the game from the perspective of her opponent to determine her

opponent's best play

Games with simultaneous moves

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Normal form/strategic form

Dimension = no. of players

Size of table = no. of strategies available to players

Represented diagrammatically using a game table (game matrix/payoff table)

Zero

sum vs non

zero

sum games:

In a two

player zero

sum game, list in each cell payoff to first player

In a non

zero

sum game, separately show a payoff for each player in each cell

Zero

sum = constant

sum

Non

zero

sum = variable

sum

Constructing a game table:

First player's strategies are used to label rows

Second player's strategies are used to label columns

Payoffs are shown in each cell

Illustrating simultaneous

move games

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Nash equilibrium:

Equilibrium of a general non

cooperative game is a configuration of strategies such that each

player's strategy is best for him

At a Nash equilibrium, each player must be satisfied with the strategy choice he has made/no player

should want to change his strategy

Fundamental solution concept for noncooperative games

Pure strategies specify nonrandom courses of action for players

Mixed strategies specify that an actual move will be chosen randomly from the set of

underlying pure strategies with specific probabilities

Nash equilibrium strategies in simultaneous

move games are either pure or mixed

Beginning with least general method that works for only a small class of games, but easiest to

apply

Increasingly more general but less easy methods

Methods of identifying pure

strategy Nash equilibrium can be ranked in order of generality and

difficulty

Nash equilibrium

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Document Summary

Pla(cid:455)e(cid:396)s (cid:272)hoose thei(cid:396) a(cid:272)tio(cid:374)s i(cid:374) isolatio(cid:374), (cid:449)ith (cid:374)o i(cid:374)fo(cid:396)(cid:373)atio(cid:374) a(cid:271)out (cid:449)hat othe(cid:396) pla(cid:455)e(cid:396)s ha(cid:448)e do(cid:374)e o(cid:396) (cid:449)ill do. A pla(cid:455)e(cid:396) (cid:272)a(cid:374) (cid:396)easo(cid:374) th(cid:396)ough the ga(cid:373)e f(cid:396)o(cid:373) the pe(cid:396)spe(cid:272)ti(cid:448)e of he(cid:396) oppo(cid:374)e(cid:374)t to dete(cid:396)(cid:373)i(cid:374)e he(cid:396) oppo(cid:374)e(cid:374)t"s (cid:271)est pla(cid:455) Rep(cid:396)ese(cid:374)ted diag(cid:396)a(cid:373)(cid:373)ati(cid:272)all(cid:455) usi(cid:374)g a ga(cid:373)e ta(cid:271)le (cid:894)ga(cid:373)e (cid:373)at(cid:396)i(cid:454)/pa(cid:455)off ta(cid:271)le(cid:895) Size of ta(cid:271)le = (cid:374)o. of st(cid:396)ategies a(cid:448)aila(cid:271)le to pla(cid:455)e(cid:396)s. I(cid:374) a t(cid:449)o-pla(cid:455)e(cid:396) ze(cid:396)o-su(cid:373) ga(cid:373)e, list i(cid:374) ea(cid:272)h (cid:272)ell pa(cid:455)off to fi(cid:396)st pla(cid:455)e(cid:396) I(cid:374) a (cid:374)o(cid:374)-ze(cid:396)o-su(cid:373) ga(cid:373)e, sepa(cid:396)atel(cid:455) sho(cid:449) a pa(cid:455)off fo(cid:396) ea(cid:272)h pla(cid:455)e(cid:396) i(cid:374) ea(cid:272)h (cid:272)ell. Fi(cid:396)st pla(cid:455)e(cid:396)"s st(cid:396)ategies a(cid:396)e used to la(cid:271)el (cid:396)o(cid:449)s. Se(cid:272)o(cid:374)d pla(cid:455)e(cid:396)"s st(cid:396)ategies a(cid:396)e used to la(cid:271)el (cid:272)olu(cid:373)(cid:374)s. E(cid:395)uili(cid:271)(cid:396)iu(cid:373) of a ge(cid:374)e(cid:396)al (cid:374)o(cid:374)-(cid:272)oope(cid:396)ati(cid:448)e ga(cid:373)e is a (cid:272)o(cid:374)figu(cid:396)atio(cid:374) of st(cid:396)ategies su(cid:272)h that ea(cid:272)h pla(cid:455)e(cid:396)"s st(cid:396)ateg(cid:455) is (cid:271)est fo(cid:396) hi(cid:373) At a nash e(cid:395)uili(cid:271)(cid:396)iu(cid:373), ea(cid:272)h pla(cid:455)e(cid:396) (cid:373)ust (cid:271)e satisfied (cid:449)ith the st(cid:396)ateg(cid:455) (cid:272)hoi(cid:272)e he has (cid:373)ade/(cid:374)o pla(cid:455)e(cid:396) should (cid:449)a(cid:374)t to (cid:272)ha(cid:374)ge his st(cid:396)ateg(cid:455) Nash e(cid:395)uili(cid:271)(cid:396)iu(cid:373) st(cid:396)ategies i(cid:374) si(cid:373)ulta(cid:374)eous-(cid:373)o(cid:448)e ga(cid:373)es a(cid:396)e eithe(cid:396) pu(cid:396)e o(cid:396) (cid:373)i(cid:454)ed.

Related Questions

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

QUESTION 1

Stackelberg duopoly game is also known as the ________ model. If we change the Stackelberg ______ competition game to a simultaneous-move game, we get the ______ game results.

	A.	leader-follower, quantity; Cournot
	B.	Competitive fringe; price; backward induction
	C.	leader-follower, quantity; Bertrand
	D.	entry, price; Cournot

QUESTION 2

Comparing Stackelberg and Cournot competition results, we can say that the _____ is better off while the ______ is worse off under Stackelberg than under Cournot results. This result show that there is _______________ advantage.

	A.	entrant, incumbent, investment
	B.	leader, follower, first-mover
	C.	follower, leader, a size
	D.	incumbent, entrant, first-mover

QUESTION 3

Mark all the FALSE statements

	A.	An equilibrium is a collection of strategies (and a strategy is a complete plan of action), whereas an outcome describes what will happen only in the contingencies that are expected to arise, not in every contingency that might arise.
	B.	In games of complete but imperfect information, backward induction is still the strongest process to solve the model to get unique equilibrium.
	C.	All subgame perfect Nash equilibria (SPNE) are Nash equilibria (NE), but not all Nash equilibria is SPNE
	D.	We cannot apply the notion of Nash equilibrium to dynamic games of complete information if we allowed a player s strategy to leave unspecified actions in some contingencies.
	E.	A game can be of perfect information whenever Nature or Luck does not play, each information set does not necessarily need to have a single node.

QUESTION 4

True or false. Mark the correct sequence:
I. Simultaneity of moves means that these games have imperfect information.
II. Dynamic games of complete and perfect information do not necessarily need that a player observes all the previous moves, just part of them are fine.
III. Backward induction and subgame perfect equilibrium concept lead to the same result in games of incomplete information.
IV. Any game in extensive form is a subgame itself.

	A.	TFFT
	B.	TTTF
	C.	FTFF
	D.	TTFT

QUESTION 5

The subgame perfect Nash equilibrium is the equilibrium associated with ____________ outcome. Subgame perfect equilibrium ________ non-credible threats.

	A.	Maxmin; involves
	B.	the backward induction; does not involve
	C.	Iterative deletion of weakly dominated strategies; rules out
	D.	the backward induction; includes

Objectives:

ÃÂ· Learn how individuals contribute to teamwork

ÃÂ· Experience some of the features of group work and teamwork

ÃÂ· Understand what managers and organizational developers do to transform

ÃÂ· groups into teams

ÃÂ· Articulate the tangible benefits (both quantitative and qualitative) of

ÃÂ· high-performing teams

ÃÂ· Finish with an interest in learning more about these concepts and

ÃÂ· techniques to apply what you learn

Background: For this assignment, you will plan and play a game with your family or friends, or at work based on the idea of the classic prisoner's dilemma. If you have had a class on game theory, you will be well aware of this concept. It forms the basis of many TV game shows. The prisoner's dilemma was illustrated in Truman Capote's book, "In Cold Blood" concerning the 1959 robbery of a Kansas farmhouse by Perry Smith and Dick Hickock, who murdered their victims in order to eliminate the witnesses. After the men were captured, the police interrogated them separately. To get a confession, the police offered the men a reduced sentence for cooperating. Failure to cooperate would result in a death penalty charge for both.

In the prisoner's dilemma, if both parties cooperate they are mildly punished; if one betrays another, one is severely punished while the other goes free; and if both betray one-another, both are moderately punished. Can you think of settings where you work in which the organizational structure has created a prisoner's dilemma? Competition can (but does not necessarily) bring out conflict.

In game theory, there are non-cooperative and cooperative games. A non-cooperative zero-sum game has a definite winner and loser. For one to win, one must lose. We often think of politicking as an element of that. A cooperative game is where everyone who plays is better off for having played than not having played the game. That is not to say that everyone is equally well off, but simply better off than they were before playing. Hence, even in a cooperative game, some people will likely benefit more than others.

Instructions

Review in your textbook, the Big Five personality dimensions, pp. 82Ã¢ï¿½ï¿½84, and then consider the 3.1 Personality Insights inventory, pp. 89Ã¢ï¿½ï¿½91
Select four or five friends, coworkers, or family members and have them take the personality inventory
Plan and play a game with the participants
Write a 5-10 page paper that addresses the assignment questions below

As you plan and play your game, you will negotiate the type of game you want to play and your role in it. Strive to determine some personal characteristics of the game participants a head of time, or by observing them. Consider how the personal characteristics of the individuals in the game manifest themselves in the informal roles they assume during the planning and execution of the game.

For the purpose of this assignment, you will want both a cooperative and a competitive element. To do that, you can form several groups to compete and cooperate with each other, or you can have individuals in one group compete and cooperate. You can use rewards and/or punishments to create the competitive/cooperative motivations.

Evaluation: When groups are formed, we want to consider how organizational structures, processes, and situations impact on group motivation, politics, and goals achievement. Alignment of all of these structural, personal, and interpersonal components will help to ensure that the group will meld into a team. A defining feature of teamwork (versus group work) is cooperation!

One of the factors that affect cooperation is conflict. Conflict is defined as when someone perceives that his/her interests are opposed or negatively impacted by another. Conflict can at times produce positive results depending on the basis for the conflict and how the conflict is handled (functional conflict). The worst kind of dysfunctional conflict produces betrayal.

Note that team performance can be observed in how well the team coordinates their interdependencies, works efficiently, communicates, and accomplishes their mission. Consequently, as you implement your game, assess your players based on these factors and the informal roles they play.

After you have played the game, reflect on the personality assessments your participants took, and then consider how they planned and played the game.

Write a (5- 10) page analysis to address the following questions:

1. How well did the personality assessments reflect in the behaviors participants displayed during the game?

2. What do these assessments tell us about how we perceive ourselves versus how others perceive us?

3. What informal roles did participants assume during the game, and were they different from the planning portion from the playing portion of the exercise?

4. What did I learn about myself? For example, did the exercise show that you have characteristic ways of relating to others that are distinctive, or similar, to those the others? Did the exercise show that in a particular type of situation you acted in a particular way, or that when others acted in a particular way, you felt happy or anxious or angry, etc.?

5. What did I learn about someone else in the exercise? Did you see something new about them, such as "they seemed more capable than I imagined," or "inattentive when things were stressful?"

6. In playing your game, what could you have done to increase cooperative behaviors?

7. Based on your game experience, what are some of the key factors involved in gaining cooperation from people in a business setting?

8. How would you go about getting cooperation from a "difficult" co-worker? Give an example or scenario.

Please provide a unique type of game theory preferably instead of Mafia Game.

Text:

Organizational Behavior and Management 10th Edition

John Ivancevich, Robert Konopaske, Michael Matteson

cyanfox187

ECON10004 Study Guide - Final Guide: Fundamental Solution, Nash Equilibrium, Strategic Dominance

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