Game Theory
The game begins with a case that occurred on two prisoners. Both prisoners were suspected criminals and their work. Both prisoners were placed in a different room, then to be given the question of whether it is true they are committing a crime or not. Option given is: If the prisoner A prisoner confessed while B does not confess, then A will be free, while B will get a 6 month sentence. If they plead not guilty, then it will get a 1 month prison sentence. And if both confess, they will each get a 3 month prison sentence. Zerosum game
In game theory and economic theory, a zero–sum game is a mathematical representation of a situation in which a participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.
Prisoners dilemma game is an archeptypal example of of a nonzero sum game.The distinction between a zero sum game and a nonzero sum game is crucial.In zero sum game,with two players for simplicity,the utilities of players always sum to zero wathever the game’s outcome.On certain simplifying assumption,a zero sum game is equivalent to a zero money sum game.In this circumstances,zero sum game are such that,whatever the outcome,one player’s monetary is gane and the other is loss.This contrast with nonzero sum games,where outcome do not simply involve transfer of money or utility between players.In nonzero sum gamess the interest of the players are not directly opposed and hence it may be possible for the players to gain from cooperation.Hence the assumption that the game is non cooperatively played takes on added aignificance with nonzero sum games Nonzero–sum
Many economic situations are not zerosum, since valuable goods and services can be created, destroyed, or badly allocated in a number of ways, and any of these will create a net gain or loss of utility to...
...problem, what is the Nash equilibrium in prices?
p1 = p2 = MC = 6
5. (20 total points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:
Player 2
Player 1
Left
Right
Top
1 2
5 3
Bottom
2 2
3 1
where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.
a) (2 points) Does player 1 have a dominant strategy, and if so what is it? NO
b) (2 points) Does player 2 have a dominant strategy and if so what is it? NO
c) (2 points each) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:
i) Top/Left FALSE
ii) Top/Right TRUE
iii) Bottom/Left TRUE
iv) Bottom Right FALSE
d) (2 points) If each player plays their maximin strategy, what payoff will each of them receive?
BOTTOM/LEFT (2,2)
e) (2 points) Suppose the game is player where Player 1 chooses its strategy first and then Player 2 chooses its strategy. Using the backward induction method we discussed in class, what will be the outcome of the game?
TOP/RIGHT (5,3)
f) (4 points) This game has a unique Nash Equilibrium in mixed strategies where Player 1 plays Top with...
...the Stackelberg leader.
5. Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve
P = 30  Q,
where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero. True or false: as a result, the market price will rise to the monopoly level.
True.
If only one firm were in this market, it would charge a price of $15 a unit. Marginal revenue for this monopolist would be
MR = 30  2Q,
Profit maximization implies MR = MC, or
30  2Q = 0, Q = 15, (using the demand curve) P = 15.
The current situation is a Cournot game where firm 1's marginal costs are zero and firm 2's marginal costs are 15. We need to find the best response functions:
Firm 1’s revenue is
and its marginal revenue is given by:
Profit maximization implies MR1 = MC1 or
which is firm 1’s best response function.
Firm 2’s revenue function is symmetric to that of Firm 1 and hence
Profit maximization implies MR2 = MC2, or
which is firm 2’s best response function.
Cournot equilibrium occurs at the intersection of best response functions. Substituting for Q1 in the response function for firm 2 yields:
Thus Q2=0 and Q1=15. P = 30  Q1 + Q2 = 15, which is the monopoly price.
6. Suppose that two identical firms produce widgets and that they are the...
...marksRevision materials on the Economics blog: AS Micro  AS Macro  A2 Micro  AS Macro A2 Markets & Market Systems Oligopoly  GameTheory 

“When I am getting ready to reason with a man I spend onethird of my time thinking about myself and what I am going to say, and twothirds thinking about him and what he is going to say.”
Abraham LincolnA game occurs when there are two or more interacting decisiontakers (players) and each decision or combination of decisions involves a particular outcome (payoff.) The fate (or the payoff) of a player in a game depends not only on the actions of that player but also on the other players!The Monty Hall problem!
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number 3, which has a goat. He says to you, “Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors?
Possible answer to the Monty Hall problemGame theory is mainly concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions. The Prisoners’ DilemmaThe classic example of gametheory...
...2. With reference to an industry of your choice, identify a realworld example of firms formally or tacitly engaging in collusion, taking care to fully explain the nature of the collusive conduct. Using the economic theory presented in class, analyse the drivers of collusion in your chosen case. Also, critically evaluate the effects of an eradication of collusion – which would strengthen the competition between these industry rivals – on both the welfare of consumers and the financial performance of the firms themselves.
In 2002, according to publications by the Toy Industries of Europe (2003), the UK was the largest consumer of toys and games in the EU with a 24.2% share of the €12.7bn market. That equates to over €3bn spent on toys each year in the UK. However, despite these figures, the toy and gaming industry was facing difficulties in Western Europe with child population numbers on the decrease and the tendency for children to mature more quickly, meaning their propensity to use toys and games was diminishing at an earlier age (Keynote, 2002). These two factors combined to mean that the target market for toy and game makers was decreasing rapidly.
However, as disposable income rose, so did the average spent on toys per child to a staggering €173 per year. The market for higher end children’s toys with increasing electronic complexities was dramatically on the rise, partially as a result of increasing...
...Topic 5: GameTheory Applied to the Movie and Aviation Industries
I. Case study: GameTheory Applied to the Movie Business
In the movie business, one of the trickiest decisions producers face is what type of movie to make. Suppose there are 2 movie studios and that their producers are trying to decide whether to make an Action Adventure (AA) or Romantic Comedy (RC) movie. Suppose each of the studios does not know what type of movie the competing studio is planning to make that same year and that they do not trust each other in the least. They face the following payoff matrix.
Studio 1
RC AA
Studio 2 RC (50,50) (90,60)
AA (60,90) (75,75)
(Figures show total estimated box office revenues in $ millions for Studio 1, Studio 2.)
What strategy (make an AA or RC movie) should each of the studios chose?
What is the payoff to each of the 2 studios given the strategies they choose?
Answer:
From Studio 1’s perspective:
Studio 1’s payoff
RC 50
RC
AA 90
Firm 2
RC 60
AA
AA 75
Same result from Studio 2’s perspective.
From studio 1’ s perspective: if studio 2 makes a RC, studio 1’s payoff is $50 million if it also makes a RC and $90 million if it makes an AA. If studio 2 makes an AA movie, studio 1’s payoff is $60 million if it makes a RC and...
...Gametheory is defined as “the study of the ways in which strategic interactions among economic agents produce outcomeswith respect to thepreferences of those agents, where the outcomes in question might have been intended by none of the agents” by the Stanford Encyclopedia of Philosophy (Ross 1997). The disciplines most involved in gametheory “are mathematics, economics and the other social and behavioral sciences” (McCain 1997).Gametheory was created to confront the problem and provide a theory of economic and strategic behavior. In gametheory, "games" have always been a metaphor for more serious interactions in human society. But gametheory addresses the serious interactions using the metaphor of a game: in these serious interactions, as in games, the individual's choice is essentially a choice of a strategy, and the outcome of the interaction depends on the strategies chosen by each of the participants (McCain1997).
John von Neumann a great mathematician founded gametheory. The legend of John Von Neumann gives a good insight on who John Von Neumann was and his theory. John von Neumann was a child prodigy, born into a banking family in Budapest, Hungary, “when he was only six years old he could divide eightdigit numbers in his...
...consult the experts of the gametheory at this point. In the 1980’s Axelrod and Hamilton worked on a famous problem in the gametheory, the Prisoner’s Dilemma, exactly because it deals with this problem. The rational pursuit of individual selfinterest drives everybody into an outcome that is not favored by anybody. Imagine two partners in a crime being interrogated at the same time. Each one has two options, cooperate with the other and keep quiet or betray the other and confess. Case C, we can say, is if both cooperate then the police cannot get much out of them and they will both get a light sentence (2 years); if one defects and the other keeps quiet then the traitor will get an even lighter sentence (1 year) – this is case B. If the one who cooperates gets the longest sentence (10 years), this is the worst end of the deal and we can call this case S. In a case when both betray one another they will both get a sentence (6 years) longer than if they had cooperated but lighter than if one had kept quiet and the other spoke, and this is case D.
Out of the four outcomes, B is the best and S is the worst from an individualistic point of view, while the order of preference is B, C, S, D. We should realize that this is a nonzero sum game. In a zerosum game, my loss is your gain; for example, if we are trying to divide a certain amount of money in the bank into two, anything over fifty...
...Topic Ten: Oligopoly and GameTheory
1. Suppose Penguin and Joker are the only two firms in the death ray market. Each firm is considering two possible pricing strategies – either P = $700 or
P = $1500 – for their goods. The following payoff matrix gives the profit outcomes (in $m).
Joker
 P = $700  P = $1500 
Penguin
P = $700  30
35
 27
41

P = $1500  35
29
 38
39

(a) What price will each of the firms choose if they make their decisions independently, following a maximin strategy? Explain how you determined your answer.
(b) What is meant by the term collusion? In general, what is the incentive for firms in an oligopoly market to collude? Explain.
(c) Based on the payoffs for Penguin and Joker (shown above) and your solution in (a), could these firms benefit by colluding? Explain.
2. Suppose Alpha and Romeo are the only two firms in the automobile market. Each firm plans to put only one model onto the market. They are considering two possible choices – a standard model at P = $50,000 or a luxury model at
P = $80,000. The following payoff matrix gives the profit outcomes (in $m).
Romeo
 P = $50,000  P = $80,000 
Alpha
P = $50,000  40
35
 45
30

P = $80,000  35
40
 30
45

(a) What price will each of the firms choose if they make their decisions independently, following a maximin strategy?...