Managerial Econ. CH 10
which two strategies often correspond with each other?
Dominant and "cheating" strategy
Firms A must decide whether or not to introduce a new product. If Firm A introduces a new product, Firm B must decide whether or not to clone the product. The payoff structure of the game is depicted in the above tree diagram. The sub-game perfect Nash equilibrium to this game is
Firm A plays "Do Not Introduce"; Firm B plays "Clone" if Firm A plays "Introduce"
simultaneous- move game
Game in which each player makes decisions without knowledge of the other players' decisions
Which of the following is a correct statement about a Nash equilibrium in a two-player game?
Given another player's strategy, no player can improve her welfare by unilaterally changing her strategy.
low price high price low (9,10) (8,15) high (7,-10) (11,11) Is there a dominant strategy for firm A?
No
Management and a labor union are bargaining over how much of a $50 surplus to give to the union. The $50 is divisible up to one cent. The players have one shot to reach an agreement. Management has the ability to announce what it wants first, and then the labor union can accept or reject the offer. Both players get zero if the total amounts asked for exceed $50. If you were the labor union, which type of "rules of play" would you prefer to divide the $50 surplus?
One-shot, sequential-move game with labor union as the first mover
t1 t2 t3 S1 (4,10) (3,0) (1,3) S2 (0,0) (2,10) (10,3) Which of the following strategies constitutes a Nash equilibrium?
S1, t1
Advertise Do not advertise Advertise ($0,$0) ($175,$10) Don't advertise ($10,$175) ($125,$125) Suppose there is a 20 percent chance that the advertising game depicted in Figure 10-17 will end next period. The collusive agreement {(not advertise, not advertise)} is:
Sustainable since $175<$625
what is a characteristic of infinitely repeated games?
Theory and factors affecting collusion in pricing games
Every perfect equilibrium is what?
a Nash equilibrium
Finitely repeated game
a game which is repeated a finite number of times
normal-form game
a representation of a game indicating the players, their possible strategies, and the payoffs resulting from alternative strategies
Trigger strategy
a strategy that is contingent on the past play of a game and in which some particular past action "triggers" a different action by a player
dominant strategy
a strategy that results in the highest payoff to a player regardless of the opponent's actions
If there is a deterred entry you should..?
act to prevent entry
Why are multistage games different from other games?
because of the timing of decisions in games.
How can infinitely repeated games players collude?
by using trigger strategies given a sufficiently low interest rate
decision nodes
circle indicating points where a decision is made. At that point is where a particular play must choose a move
if there is an accommodated entry you should..?
does not pay to prevent, reduce output from monopoly to duopoly to maximize profit
strategy
in game theory, a decision rule that describes the actions a player will take at each decision point
A coordination problem usually occurs in situations where there is...
more than one Nash equilibrium
for infinitely repeated games there is a disconnect between current decisions and future payoffs, what does this suggest?
payoffs must be appropriately discounted
What should you do if you don't have a dominant strategy?
put yourself in your rivals shoes, and look at the game form their perspective. If your rival has a dominant strategy, anticipate that he or she will play it.
What happens when you choose the dominant strategy?
you will maximize your payoff regardless of what your opponent does
firms 1 and 2 must independently decide whether to charge high or low prices. high price low price high (10,10) (5,-5) low (5,-5) (0,0) Suppose the game is infinitely repeated. Then the "best" the firms could do in a Nash equilibrium is to earn _________ per period.
(10,10)
firms 1 and 2 must independently decide whether to charge high or low prices. high price low price high (10,10) (5,-5) low (5,-5) (0,0) Which of the following are the Nash equilibrium payoffs (each period) if the game is repeated 10 times?
(10,10)
if you advertise and your rival advertises, you each will earn $5 million in profits. If neither of you advertises, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million. Which of the following is true?
- A dominant strategy for firm A is to advertise - A dominant strategy for firm B is to advertise - A Nash equilibrium is for both firms to advertise
characteristics of repeated game:
- game that reoccurs - May cooperate and not compete strongly - rival reciprocates - Examples: Pepsi and Coke, Walmart and Target, Boeing and Airbus
Characteristics of a finitely repeated games
-Games with an uncertain final period -Games with a known final period: the end-of-period problem
factors affecting Collusion in pricing games:
-Number of firms in the market -Firm size -History of the market -Punishment mechanisms
What are some important determinants of collusion in pricing games?
-The number of firms - firm size - history
Factors affecting collusion in an infinitely repeated pricing game:
-number of firms -firms size -history
what are ways to coordinate on one equilibrium ?
1. permit player communication 2. government set standard
Sustaining collusion via trigger strategies is easier when firms know what factors?
1. who their rivals are, so they know whom to punish if need be. 2. who their rival's customers are, so they can "steal" those customers with lower prices 3. when their rivals deviate, so they know when to begin punishment 4. be able to successfully punish rival
secure strategy
A strategy that guarantees the highest payoff given the worst possible scenario.
when can collusion not work?
When this game is repeated some known, finite number of times and there is only one Nash equilibrium
In sequential, or multi-stage, games collusion can only be supported when...?
threats are credible
what happens during a Nash bargaining game?
two players "bargain" over some object of value
End-of-period problem
when players know precisely when a repeated game will end.
When can collusion not be supported?
when players know when the game ends due to unraveling
What are the advantages to "first- mover" firms?
•May be better prepared •May preempt entry of rival •Rival must respond
firms 1 and 2 must independently decide whether to charge high or low prices. high price low price high (10,10) (5,-5) low (5,-5) (0,0) Which of the following are Nash equilibrium payoffs in the one-shot:
(10,10)
low price high price low (10,9) (15,8) high (-10,7) (11,11) What are the Nash equilibrium strategies for firm A and firm B, respectively, in a one-shot game?
(low price, low price)
characteristics of multistage games
-Players make sequential, rather than simultaneous, decisions. -Represented by an extensive-form game
games consist of the following components:
1. players or agents who make decisions 2. planned actions of players, called strategies 3. payoff of players under different strategy scenarios 4. a description of the order of play 5. a description of the frequency of play or interaction
mixed (randomized) strategy
A strategy whereby a player randomizes over two or more available actions in order to keep rivals from being able to predict his or her action.
Nash Equilibrium
A condition describing a set of strategies in which no player can improve her payoff by unilaterally changing her own strategy, given the other players strategies
subgame perfect equilibrium
A condition describing a set of strategies that constitutes a Nash equilibrium and allows no player to improve his own payoff at any stage of the game by changing strategies.
extensive-form game
A representation of a game that summarizes the players, the information available to them at each stage, the strategies available to them, the sequence of moves, and the payoffs resulting from alternative strategies.
Trigger strategy example
Both firms charge the high price, provided neither of us has ever "cheated" in the past (charge low price). If one firm cheats by charging the low price, the other player will punish the deviator by charging the low price forever after.
Game theory is best applied to the analysis of...
Oligopoly
Consider the following information for a simultaneous move game: If you advertise and your rival advertises, you each will earn $5 million in profits. If neither of you advertises, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million. If you and your rival plan to be in business for 10 years, then the Nash equilibrium is:
for each firm to advertise every year
multistage games
framework permits players to make sequential decisions rather than simultaneous decisions
sequential-move game
game in which one player makes a move after observing the other player's move
repeated game
game in which the underlying game is played more than once
one- shot game
game in which the underlying game is played only once
infinitely repeated game
is a game that is played over and over again forever, and in which players receive payoffs during each play of the game
game theory
is a general framework to aid decision making when agents (firm) payoffs (profits) depends on the actions taken by other players (firms).
Trigger strategies are common with..?
repeatedly played games
