Econ 661 - CH 10
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.
Advertising in Oligopolies
Advertising increases demand. Use framework for simultaneous-move, one-shot games for analyzing advertising decisions too.
Finite Games with Known Final Period
In final period, use strategy of one-shot version because no possibility of playing again. Each player will charge low price on final period. Collusion cannot work if know when game will end.
What is true of collusion in a repeated game with a known final period?
It is not possible.
If the profits earned by the firm are the same in each period and the horizon is infinite, the present value of a firm is given by:
PVfirm=(1+i/i)π
A representation of a game that summarizes the players, the information and strategies available to them at each stage, the sequence of moves, and the payoffs associated with each strategy is called
an extensive-form game.
When strategies for a multistage game are a Nash equilibrium, but involve a threat that is not credible, then we say that these strategies
are not a subgame perfect equilibrium.
In a repeated game with a known final period, why are promises to cooperate generally broken?
- "Backwards unraveling" continues until players know that no punishment can be used in any period. - Players understand that there is no effective punishment in the last period.
In order to be considered a subgame perfect equilibrium, a set of strategies must
- be a Nash equilibrium - be a Nash equilibrium for each subgame
In an infinitely repeated game,
- collusion is possible - players receive payoffs during each play of the game
A Bertrand duopoly game has which characteristics?
- it is a simultaneous-move game - it involves two firms
In order to sustain punishment strategies, it is important for firms to
- know when their rivals deviate from a collusive agreement - be able to punish rivals for deviating
The normal-form of a game includes all of the following:
- players in the game - the possible strategies of the players - the payoffs that result from the alternative strategies
In order to sustain a cooperative outcome in an infinitely repeated game, players should
- punish a player that cheats by selecting the one-shot, Nash equilibrium strategy. - cooperate provided no player has ever cheated.
Indicate which of the following are applications of multistage games.
- sequential bargaining - entry game - innovation game
End-of-period problems
- shirking results from resignation and quits - snake oil salesman leaves before local consumers can punish reputation
Can sustain collusive arrangements via punishment strategies when...
1. know who rivals are (know who to punish) 2. know who rival customers are (steal em with lower prices) 3. know when rivals deviate from collusive arrangement (start punishment) 4. can successfully punish rivals
Firm A and Firm B are playing a finitely repeated pricing game with an unknown number of periods. If Firm A cooperated with Firm B, they receive $12 each period the game is played. If Firm A cheats, they receive a one-time payment of $80 and $0 every other period of play. If θ = 0.2, Firm A has an incentive to ________.
12/.02 = 60 < 80 Cheat
Players find it in their interest to maintain a collusive agreement when πCheat - πCoop _____ 1/i(πCoop - πN)
<=
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. Every player is doing the best he/she can, given what other players are doing. Other strategy combos aren't Nash equilibrium because at least one player would like to change his or her strategy given the strategy of the other player.
infinitely repeated game
A game that is played over and over again forever and in which players receive payoffs during each play of the game. Payoffs during first repetition of the game is worth more than dollar earned in later repetitions. When interest rate low, firms best interest to collude and charge high prices.
normal-form game
A representation of a game indicating the players, their possible strategies, and the payoffs resulting from alternative 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
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.
Which of the following describes a dominant strategy?
A strategy that results in the best possible outcome regardless of choices by other players.
dominant strategy
A strategy that results in the highest payoff to a player regardless of the opponent's action. In simultaneous-move, one-shot games where a player has a dominant strategy, the optimal decision is to choose the dominant strategy. By doing so, you will maximize your payoff regardless of what your opponent does. In some games, a player may not have a dominant strategy.
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.
A simultaneous-move pricing game played by two firms is often called a duopoly game.
Bertrand
Bertrand duopoly
Bertrand competition is a model of competition in which two or more firms produce a homogenous good and compete in prices. EX: Two gas stations
Consider the following payoffs available to two firms, "A" and "B", in a one-shot game.When "A" and "B" both advertise: $3, $3, respectivelyWhen neither "A" nor "B" advertise: $12, $12, respectivelyWhen "A" advertises and "B" does not: $20, $2, respectivelyWhen "A" doesn't advertise and "B" does: $2, $20, respectivelyWhat is the Nash equilibrium?
Both advertise
Consider the payoffs for the following simultaneous, one-shot game:Firm A charges low, Firm B charges low: 0,0, (respectively)Firm A charges low, Firm B charges high: 50, -10 (respectively)Firm A charges high, Firm B charges low: -10, 50 (respectively)Firm A charges high, Firm B charges high: 10,10 (respectively)What is the outcome of the game?
Both charge low
How history of market affect collusion
Can explicitly meet, collude, and threat Can tacit collusion where don't explicitly conspire to collude but do it indirectly
In a simultaneous-move, one-shot game, a Nash outcome is often inferior to the outcome that would result if the firms colluded. Which of the following is a reason why firms do not collude to reach a "better" outcome?
Collusion is illegal in the U.S.
Entry Game lesson
Does not pay to heed threats made by rivals when threats are not credible.
How number of firms affect collusion
Easier when fewer than many. Total amount of monitoring in the market because have to monitor each other: n x (n - 1) Cost of monitoring rivals reduces gains to colluding
True or false: A secure strategy is a strategy that results in the highest payoff to a player regardless of the opponent's action.
False
simultaneous-move game
Game in which each player makes decisions without knowledge of the other players' decisions. Two firms set prices without knowledge of each other's decisions.
sequential-move game
Game in which one player makes a move after observing the other player's move. One firm sets price after observing rival's price.
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.
coordination game
Game where firms have similar objectives and both firms will do better by coordinating decisions. Has two Nash equilibria. Firms can talk to each other because no incentive to cheat. Game of coordination vs conflicting interests. EX: type of electrical plugin for appliances
finitely repeated game
Games in which players do not know when the game will end; and games in which players know when it will end
collusion
Illegal. Firms not allowed to meet and "conspire" to set high prices to max profits. Firms benefits at expense of consumers and leads to deadweight loss.
secure strategy
In absence of a dominant strategy, play the strategy that guarantees the highest payoff given the worst possible scenario. Play in absence of dominant strategy. Two shortcomings: A conservative strategy. Should only do it if you have good reason to be extremely averse to risk. Doesn't take into account optimal decisions of rival and may prevent higher payoff.
strategy
In game theory, a decision rule that describes the actions a player will take at each decision point.
Games with uncertain final period
It mirrors the analysis of infinitely repeated games. Calculation of chance that game will end: (1 - 0/)^t Profit(coop) = Earn/probability game will terminate after one play
How firm size affect collusion
Monitoring and policing costs constitute greater share of total cost for small vs large firms
Entry and exit into and out of a market can often be analyzed using which of the following game representations?
Multistage games
A ___ equilibrium is a condition describing a set of strategies in which no player can make themselves better off by unilaterally changing their strategy, given the other players' strategy choices.
Nash
In a __________ game, two players "bargain" over some object of value.
Nash bargaining
When every player is doing the best that he or she can do, given the actions of other players, this outcome is referred to as a _______.
Nash equilibrium
Consider the following payoffs available to two firms, "A" and "B", in a one-shot game.When "A" and "B" both advertise: $3, $3, respectivelyWhen neither "A" nor "B" advertise: $12, $12, respectivelyWhen "A" advertises and "B" does not: $20, $2, respectivelyWhen "A" doesn't advertise and "B" does: $2, $20, respectivelyThe "best" outcome for BOTH firms occurs when:
Neither firm advertises
If firms seek to be infinitely lived, what can firms do if low-quality goods are produced out of honest error?
Offer product guarantees
A criticism of sequential bargaining applications of multistage games includes which of the following? Multiple choice question.
Players don't know the true payoffs to other players.
Multistage games
Players make sequential decisions. First player can't make decision conditional on second player like second player can.
Suppose πCheat−πCoop/πCoop−πN ≤1/i, where πCheat is the maximum one-shot payoff if the player cheats, πCoop is the cooperative, one-shot payoff, πN is the one-shot Nash equilibrium payoff, and "i" is the interest rate.
The cooperative outcome can be sustained.
What occurs if players know precisely when a repeated game will end?
The end-of-period problem
When an employee announces his intention to quit an existing job, he has an increased incentive to "shirk" work on his last (or next-to-last) day. What is this an example of?
The end-of-period problem
Suppose πCheat - πCoop ≤1/i(πCoop - πN), where πCheat is the maximum one-shot payoff if the player cheats, πCoop is the cooperative, one-shot payoff, πN is the one-shot Nash equilibrium payoff, and "i" is the interest rate. What does the left-hand side of the equation represent?
The one-time gain of breaking a collusive agreement.
Suppose πCheat - πCoop ≤1/i(πCoop - πN), where πCheat is the maximum one-shot payoff if the player cheats, πCoop is the cooperative, one-shot payoff, πN is the one-shot Nash equilibrium payoff, and "i" is the interest rate. What does the right-hand side of the equation represent?
The present value of what is given up in the future by cheating in the present.
It is possible for firms to collude without the fear of being cheated on when they adopt which of the following strategies?
Trigger strategy
The assumption that bargaining ends as soon as the second player rejects or accepts an offer is a criticism of sequential-move bargaining game.
True
True or false: A Nash bargaining game is an application of a simultaneous-move, one-shot game.
True
True or false: A strategy is a decision rule that describes the actions a player will take at each decision point.
True
Engaging in Punishment
When quote different prices to different customers, cost reduced in engaging in punishment b/c can continue to charge same price to current customers while charging lower prices to competition customers instead of having to charge low prices for ALL customers.
Consider the payoffs for the following simultaneous, one-shot game:Firm A charges low, Firm B charges low: 0,0, (respectively)Firm A charges low, Firm B charges high: 50, -10 (respectively)Firm A charges high, Firm B charges low: -10, 50 (respectively)Firm A charges high, Firm B charges high: 10,10 (respectively)What is the game's result if the firms collude?
both charge high
In a sequential-move game, the player who moves first
cannot make decisions based on what the other player does.
Games in which players know a game will end, but they do not know when the game will end are called ___ ____ games
finitely repeated
Games in which players know a game will end, but they do not know when the game will end are called ____ ____ games.
finitely repeated
Games in which a player knows the game will end AND knows when it will end are called
finitely repeated games.
A game that is played over and over and provides payoffs during each repetition is called a(n) ____ ______ game
infinitely repeated
If firms seek to be infinitely lived,
it does not pay to cheat customers if the one-time gain is offset by a loss in future sales.
In a finitely repeated game, a firm has no incentive to cheat if
it expects to earn less from cheating than from not cheating.
When firms know who their rivals are and who their rivals' customers are
it is easier to sustain a collusive agreement.
By pursuing a dominant strategy, a player ensures that he/she will
maximize payoff independent of other players' actions.
When oligopolistic firms compete a finite, but uncertain, number of times, the firms
may or may not collude.
Which game strategy prevents rivals from easily predicting a player's actions?
mixed strategy
The __________ -form of a game indicates the number of players, the potential strategies, and the payoffs to alternative strategies.
normal
The value of a firm is the
present value of all future profits.
Sustaining Cooperative Outcomes with Trigger Strategies
profit (cheat) <= [profit(coop)*(1+i)/i] Cooperative (collusive) outcome can be sustained in the infinitely repeated game with trigger strategy. Provided no player cheats. If cheats, punish player by choosing Nash equilibrium forever after. profit(cheat) - profit(Coop) <= (1/i)*[profit(coop) - profit(Nash)] Left reps one-time gain of breaking agreement. Right side reps PV of what's given up in the future by cheating today.
Suppose a manager flips a coin to decide whether or not she should monitor employees' production. This is an example of a(n) ___ strategy.
randomized
In the absence of a dominant strategy, a player might pursue a strategy that guarantees the highest payoff given the worst possible scenario. Such a strategy is call a(n) ___________.
secure strategy
A game in which a player moves after observing another player's move is called a ____ -move game.
sequential
A game in which each player makes decisions without knowledge of the other players' decisions is called a ____________-move game.
simultaneous
A decision rule that describes the actions that a player will take at each decision point is called a
strategy
A(n) ________ is a condition describing a set of strategies that constitutes a Nash equilibrium and allows no player to improve his or her own strategy at any stage of the game by changing strategies.
subgame perfect equilibrium
Non-credible threats prevent strategies for a multistage game from being
subgame perfect equilibrium
In the last period of a repeated game with a known end, players behave
the same as they would in a one-shot game.
Oligopolistic firms are more likely to collude and charge high prices in a finitely repeated game played an uncertain number of times if
there is a high probability that the game will be played in subsequent periods.
In order for punishments to work,
there must be a way to link the past, future, and present to the seller.
In a one-shot game, firms have incentive
to sell shoddy products.
Suppose Player "A" adheres to the same action each time the game is played until Player "B" takes an action that causes Player "A" to shift his approach. Player "A" has adopted a ____ strategy
trigger
Nash bargaining game
two players bargain over some object of value. Outcomes are difficult to predict because generally multiple Nash equilibria.