Chapter 10: Game Theory Inside Oligopoly Flashcards
Game Theory
Payoff depends on the actions taken by other players.
In a game, the players are firm managers who make decisions
The planned decisions of the players are called strategies.
The payoffs to the players are the profits or losses that result from the strategies.
Due to interdependence, the payoff to a player depends not only on that player’s strategy but also on the strategies employed by other players.
The order in which players make decisions is important
Oligopolistic Market
In an oligopolistic market consisting of two firms, each player must make a pricing decision.
Simultaneous-Move Game
Game in which each player makes decisions without knowledge of the other players’ decisions.
Example: Rock-Paper-Scissors
Sequential-Move Game
Game in which one player makes a move after observing the other player’s move.
Example: chess (players alternate moves).
Oligopoly Games: Setting Prices
If two firms must set prices without knowledge of each other’s decisions, it is a simultaneous-move game; if one firm sets its price after observing its rival’s price, it is a sequential-move game.
One-Shot Game
Game in which the underlying game is played only once.
Repeated Game
Game in which the underlying game is played more than once.
Normal-Form Game
A representation of a game indicating the players, their possible strategies, and the payoffs resulting from alternative strategies.
Strategy
In game theory, a decision rule that describes the actions a player will take at each decision point.
Simultaneous-Move, One-Shot Games
There are two players, whom we will call A and B to emphasize that the theory is completely general; that is, the players can be any two entities that are engaged in a situation of strategic interaction.
Hint: Think of the players as the managers of two firms competing in a duopoly.
Player A has two possible strategies: He can choose up or down. Similarly, the feasible strategies for player B are left or right. This illustrates that the players may have different strategic options.
Since the game is a simultaneous-move, one-shot game, the players get to make one, and only one, decision and must make their decisions at the same time.
The players cannot make conditional decisions; for example, A can’t choose up if B chooses right or down if B chooses left. The fact that the players make decisions at the same time precludes each player from basing his or her decisions on what the other player does.
Payoffs in a Normal Form Game: Example
The payoff to player A crucially depends on the strategy player B chooses.
The payoffs to the two players are given by the entries in each cell of the matrix. The first entry refers to the payoff to player A, and the second entry denotes the payoff to player B.
If A chooses up and B chooses left, the resulting payoffs are 10 for A and 20 for B.
Similarly, if player A’s strategy is up while B’s strategy is right, A’s payoff is 15 while B’s payoff is 8.
Optimal Strategy for a Player in a Simultaneous-Move, One-Shot Game
In simultaneous-move, one-shot games where a player has a dominant strategy, the optimal decision is to choose the dominant strategy. Doing so will maximize your payoff regardless of what your opponent does.
Note: A player may not have a dominant strategy in some games.
Dominant Strategy
A strategy that results in the highest payoff to a player regardless of the opponent’s action.
Secure Strategy (In the Absence of a Dominant Strategy)
A strategy that guarantees the highest payoff given the worst possible scenario.
This approach is not generally the optimal way to play a game, but it is useful to explain the reasoning that underlies this strategy.
By using a secure strategy, a player maximizes the payoff that would result in the “worst-case scenario.” In other words, to find a secure strategy, a player examines the worst payoff that could arise for each of his or her actions and chooses the action that has the highest of these worst payoffs.
It is a very conservative strategy and should be considered only if you have a good reason to be extremely averse to risk. Second, it does not consider your rival’s optimal decisions and thus may prevent you from earning a significantly higher payoff.
Secure Strategy: Example
Example:
Player B in Table 10–1 should recognize that a dominant strategy for player A is to play up. Thus, player B should reason as follows: “Player A will surely choose up since up is a dominant strategy. Therefore, I should not choose my secure strategy (right) but instead choose left.” Assuming player A indeed chooses the dominant strategy (up), player B will earn 20 by choosing left, but only 8 by choosing the secure strategy (right).
Put Yourself in Your Rival’s Shoes
If you do not have a dominant strategy, look at the game from your rival’s perspective. If your rival has a dominant strategy, anticipate that he or she will play it.