Dominance and Nash Equilibrium
Dominance: The idea, and an example
Deciding what to do in games
Best strategy to choose in a game depends on choices of
others
So we need a belief or expectation
PS135: Game Theory in the Social Sciences
Answers to Quiz 2
Due 11:59 PM, July 3, 2016
1. False, because if all players have strictly dominant strategies, we know theres an NE
in pure strategies. And
PS135: Game Theory in the Social Sciences
Answers to Practice Quizzes - Not for distribution!
Week 2
Due 11:59 PM, June 30, 2016
Practice Quiz 3
5.1 a) Prisoners Dilemma, b) Battle of Sexes, and c) se
PS135: Game Theory in the Social Sciences
Answers to Practice Quizzes - Not for distribution!
Week 5
Due 11:59 PM, July 21, 2016
Practice Quiz 10
14.2 (a) See Figure 13.5 in the textbook. The extensiv
PS135: Game Theory in the Social Sciences
Answers to Quiz 1
Please do not circulate.
Due 11:59 PM, June 26, 2016
1. (a) A Nash equilibrium is a strategy profile in which each player is best responding
PS135: Game Theory in the Social Sciences
Answers to Quiz 3
Due 11:59 PM, July 17, 2016
1. (a) The game tree can be drawn as follows:
1
S
H
2
S
(3, 3)
2
H
(0, 1)
S
(1, 0)
H
(1, 1)
(b) There is a uniqu
PS135: Game Theory in the Social Sciences
Answers to Quiz 4
Due 11:59 PM, July 24, 2016
1. (a) A straightforward example of such a strategy would be a Nash trigger strategy as
follows:
each player be
Fall 2015
GAME THEORY IN THE SOCIAL SCIENCES
Problem Set 4
(Due in lecture on Thursday, November 19)
Please put your name and your GSIs name in the top right-hand corner before
turning your assignment
PS135: Game Theory in the Social Sciences
Answers to Practice Quizzes - Not for distribution!
Week 6
Practice Quiz 13
20.3 Regardless of the types of player 2, the payoff of player 1 is the same: play
PS135: Game Theory in the Social Sciences
Answers to Practice Quizzes - Not for distribution!
Week 4
Practice Quiz 8
13.1 There are three subgames; one is the whole game, and each of the other two beg
PS135: Game Theory in the Social Sciences
Answers to Practice Quizzes - Not for distribution!
Week 7
Practice Quiz 15
24.3 Since both types of player 2 have incentive to send the same signal by pickin
Bayes Nash Equilibrium: Examples
Incomplete information Contributions game
Example: Contributions game
Suppose is cost is either cL =
1
4
or cH =
3
4
(Ti )
Nature picks cL for i with probability p,
Dynamic games of incomplete information
Incomplete information in extensive form games
Typology of games and equilibrium concepts
So far weve considered.
Static games of complete information : Nash e
Nash Equilibrium in Strategic Form Games
Analyzing games with no dominant strategy solution
Best response and beliefs about others
In all games in this class, players always have a best
response
PBE in signaling games
Signaling games and the war chest game
War Chests and campaign entry: extensive form
2 politicians, Incumbent and Challenger
Incumbent can be Tough (prob. 0 < p < 1) or Weak
(
Cooperation in the finite prisoners
dilemma
Repeated PD with incomplete information
Repeated PD with simultaneous moves
Repeated PD with simultaneous moves and
incomplete information
Player 1 is the
Games of Incomplete Information:
Structure and Equilibrium
Introducing incomplete information
Knowing your opponent
If you know the enemy and know yourself, you need not fear
the result of a hundred b
Models of Delegation to an Expert
Choosing under uncertainty
Choosing under uncertainty: a baseline
Nature chooses a state of the world cfw_1, 2, 3, 4, 5
equal probability for all values
Without ob
Mixed Strategy Nash Equilibrium
Nash equilibrium in mixed strategies
Making Each Other Indifferent in Matching Pennies
= = .5
If = = .5, 2 is willing to mix
.and in particular, cannot get higher EU
PS135: Game Theory in the Social Sciences
Answers to Practice Quizzes - Not for distribution!
Week 3
Due 11:59 PM, July 8, 2016
Practice Quiz 6
11.2
Practice Quiz 7
11.4 It is a game of perfect inform
Fall 2015
GAME THEORY IN THE SOCIAL SCIENCES
Problem Set 3
(Due in lecture on Tuesday, October 13)
Please put your name and your GSIs name in the top right and corner when you
turn your assignment in.