Lecture 14 - Static Games - 12.1-12.2
docx
keyboard_arrow_up
School
University of British Columbia *
*We aren’t endorsed by this school
Course
295
Subject
Communications
Date
Apr 3, 2024
Type
docx
Pages
7
Uploaded by DukeSummerSalamander9
COMM 295 - Lesson 12.1 - 12.2 Static Games
Chapter 12.0: Introduction to Game Theory and Business Strategy
Chapter 12.0 - Introduction Game Theory
= a set of tools used by economics and others to analyze strategic decision-making -
This is when firms will recognize the plans and decisions of any other firm can significantly affect the profits of the other firm
** used in oligopolies (since it can evaluate how these firms set prices, quantities, and advertising levels)
Game = an interaction between players (individuals or firms), which players use strategies Strategy
= a battle plan that specifies the actions or moves that a player will make
Payoffs
= the pay offs of game are the benefits received by players from the outcomes of the game (like profits for the forms, or incomes/utilities for individuals)
A payoff function specified each players payoff as a function of the strategies chosen by all players. We assume that players goal is to MAXIMIZE payoffs Rules of the Game
= timing of players moves (whether one player moves first), and the actions possible at a
particular point in the game
Static Game
= single period game, in which each player acts only once and the players act simultaneously (without knowing the rivals action)
Common Knowledge
= a peice of informaiton known by all players (and all players know that all other players know this information)
Complete Information
= a situation in which the strategies and payoffs of the game are common knowledge
Chapter 12.1 - Oligopoly Games
Two firms that can only take one of only 2 actions
Dominant Strategies
Dominant Strategy
= a strategy that produces a higher payoff than any other strategy the player can use no matter what its rivals do. (so if company B has a dominant strategy, then no action that company A could take would make company B prefer a different strategy)
** this is not the strategy that maximizes the JOINED or combined profit. Instead, each firm chooses what is best INDIVIDUALLY for them.
Prisoners Dilemma
= when all players have dominant strategies that lead to a payoff that is inferior to what they could achieve if they cooperated. This strategy causes them to NOT maximize their joint profits
Best Responses
Since many games do not have a dominant strategy solution, for these games there is a
more general approach, which is when players want to use its best response!
This response maximizes a players payoff given its beliefs about its rivals strategies
RECALL:
Dominant Strategy
= a strategy that is a best response to ALL possible strategies that a rival might use. So a dominant strategy is a best response
BUT, if a dominant strategy does not exist, firms can then determine their BEST RESPONSE to any possible strategy chosen by its rival
This idea that players use best responses is the basis for the Nash equilibrium
Nash Equilibrium
= if when all other players use these strategy, no player can obtain a higher playoff by choosing a different strategy
For game theory: Nash Equilibrium is a pair of strategies where BOTH firms are using the BEST RESPONSE strategy so that neither firm would want to change its strategy
Failure to Maximize Joint Profits
This is for some profit matrixes, all firms would benefit if they could agree not to make a decision.
Since advertising is a dominant strategy for both firms (will result in the highest payout)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
But in this case, advertising will bring new customers to the market and then expand the market.
-
If they both advertise, they are collectively better off than if only one adversities or neither adversities (which is shown in the green bottom right corner)
-
This makes advertising a dominant strategy for a firm because it earns more, regardless of the strategy of the other firm -
This is also a nash equilibrium, since the firms combined profits are maximized.
Pricing Games in Two-Sided Markets
Two Sided Market
= an economic platform that has two or more user groups that provide each other with network externalities
(credit card companies connect merchants and consumers, and the more consumer who use a card, the more attractive accepting that card is to merchants)
-
And the strategic rivalry between mastercard and visa determines the equilibrium prices they charge the two user groups
-
They can choose to use balances or unbalanced pricing:
Balanced Pricing
= both merchants and consumer pay fees Unbalanced Pricing
= only merchants pay
Types of Nash Equilibira
1.
Multiple Equilibria
= having more than one Nash equilibrium
-
This is when we can use additional criteria to predict the likely outcome
Neither network has a dominant strategy since the best choice for each network depends on the
choice of its rival. Determining the Nash equilibria for this game:
Determine each firms best response
a.
If network 2 chooses wednesday, then network 1 looses 10 if it chooses wednesday and earns 10 if it chooses thursday. So Network 1s best response is thursday.
b.
Similarity, if network 1’s best response if wednesday if network 2 picks thursday, so thursday would be network 2 best response
c.
Since there are 2 areas where both choices are green, there are 2 nash equlibirums
Mixed Strategy Equilibria
RECALL:
Pure Strategy
= this is what we have been assuming, which specifies the action that a player will take in every possible situation in a game
NOW, we will consider games in which a firm uses a MIXED STRATEGY
Mixed Strategy
= in which a player chooses among possible pure strategies according to probabilities that the players set.
-
A pure strategy can be considered a specific case of a mixed strategy in which a player assigns a probability of one to a single pure strategy, and a probability of zero to all other
possible pure strategies
BUT, a MIXED STRATEGY: Assigns positive probabilities to two or more pure strategies
Only Mixed Strategy Equilibria
= no cell is a nash equilibrium since no area has both green cells, and if both firms use pure strategies, the game also does not have a nash equilibrium
But, this game has a mixed strategy Nash equilibrium in which each firm chooses the traditional design with probability 0.5. So the probability that both firms independently choose a given pair of cells is (0.5) x (0.5) = 0.25
So each of the gour cells in the table is equally likely to be chosen and has a one fourth chance of being chosen. Determining the firms profit: (20 x 0.5) + (-2 x 0.5) = 9
So, each firm must be indifferent between choosing either of the two
Both Pure and Mixed Strategy Equilibria
In this case, the entry game has two pure strategy Nash equilibrium and a mixed strategy Nash equilibrium.
Pure Strategy Equilibriums:
1.
Firm 1 enters and firm 2 does not enter 2.
OR firm 2 enters and firm 1 does not enter The equilibrium in which only firm 1 enters is a Nash Equilibrium because neither firm would regret its choice. And given that firm 2 did not enter, firm 1 would not regret its design to enter. Mixed Strategy Equilibriums:
1.
Each firm enters with ⅓ probability. (since no firm could raise its expected profit by changing its strategy)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help