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 of what others will do,
to decide our best choice
One
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 since pure strategies are special cases of mixed strate
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) see Solutions for Q2 in Quiz 1
5.2 The following are all
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 extensive form of the BoS game should look
the same (with the r
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 to each other player. Formally, a Nash equilibrium is
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 unique subgame perfect Nash equilibrium, and it can be found
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 begins by playing b;
each player plays b in every subseq
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 in.
1.
Economists have used game theory to try to unde
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: playing c, which
give the payoff of 0 or 7, dominates playi
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 begins
from the red node.
Coke
O
E
P epsi
T
A
T
Coke
(0, 1
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 picking n, the
separating equilibrium is not possible.
24.4 L
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, cH with probability
1 p (P(ti )
Nature picks is cost i
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 equilibrium
Dynamic games of complete information : sub
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 to strategies of other players si
It just isnt always
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
(1 p)
Incumbent (either type) can either Build campaign
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 usual strategic player with standard PD
payoffs
Player
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 battles - Sun Tzu
So far we assume each player knows ac
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 observing , Decision maker called P chooses a
policy p: a
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 than playing
Making Each Other Indifferent in Matching
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 information because every information set has a single decisi
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.
Question 1: Consider the simple poker game we discusse