game theory
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Game Theory and Strategic Behavior
Developed in 1950s by mathematicians John von Neumann and economist Oskar Morgenstern
Designed to evaluate situations where individuals and organizations can have conflicting objectives
Any situation with two or more people requiring decision making can be called a game.
A game is a description of strategic interaction that includes the constraints on the actions that the players can take and the players’ interests, but does not specify the actions that players do take.
A strategy is a course of action taken by one of the participants in a game
Payoff is the result or outcome of the strategy Game theory is about choices (finite). While game
theory cannot often determine the best possible strategy, it can determine whether there exists one.
Game theorists may assume players always act in a way to directly maximize their wins (the Homo economicus model)
Objective – Increase profits by price change Strategies1.Maintain prices at the present level2.Increase prices
Above matrix shows the outcomes or payoffs that result from each combination of strategies adopted by the two participants in the game
10, 10 100, -30
-20, 30 140, 35
No Price Change
Price IncreaseNo Price
Change
Price Increase
Firm 2
Firm 1
Defined as a set of strategies such that none of the participants in the game can improve their payoff, given the strategies of the other participants.
Identify equilibrium conditions where the rates of output allowed the firms to maximize profits and hence no need to change.
No price change is an equilibrium because neither firm can benefit by increasing its prices if the other firm does not
For some games, there may be no Nash equilibrium; continuously switch from one strategy to another
There can be more than one equilibrium
10, 10 100, -30
-20, 30 140, 25
Firm 2
Firm 1
No Price ChangeNo Price
Change
Price Increase
Price Increase
Both firms increasing their price is also a Nash equilibrium
One firm’s best strategy may not depend on the choice made by the other participants in the game
Leads to Nash equilibrium because the player will use the dominant strategy and the other will respond with its best alternative
Firm 2’s dominant strategy is not to change price regardless of what Firm 1 does
An alternative that yields a lower payoff than some other strategies
a strategy is dominated if it is always better to play some other strategy, regardless of what opponents may do
It simplifies the game because they are options available to players which may be safely discarded as a result of being strictly inferior to other options.
A strategy s¡ in set S is strictly dominated for
player i if there exists another strategy, s¡’ in S such that,
Πi(s¡’) > Πi(s¡) In this case, we say that s¡’ strictly
dominates s¡ In the previous example for Firm 2 no
price change is a dominant strategy and price change is a dominated strategy
Highly competitive situations (oligopoly)
Risk-averse strategy – worst possible outcome is as beneficial as possible, regardless of other players
Select option that maximizes the minimum possible profit
Each firm first determines the minimum profit that could result from each strategy
Second, selects the maximum of the minimums Hence, neither firm should introduce a new
product because guaranteed a profit of at least $3 million
Maximin outcome not Nash equilibrium- loss avoidance rather than profit maximization
4, 4 3, 6
6, 3 2, 2Firm 1
Firm 2
Firm 2 Minimum
Firm 1 Minimum
New Product
No New Product
No New ProductNew Product
3
2
23
Pure strategy – Each participant selects one course of action
Mixed strategy requires randomly mixing different alternatives
Every finite game will have at least one equilibrium
Non cooperative gamesCooperative gamesRepeated gamesSequential games
Not possible to negotiate with other participants
Because the two participants are interrogated separately, they have no idea whether the other person will confess or not
Possibility of negotiations between participants for a particular strategy
If prisoners jointly decide on not confessing, they would avoid spending any time in jail
Such games are a way to avoid prisoner’s dilemma
• Yet another way to escape prisoner’s dilemma
• If exercise is repeated multiple times, reactions become predictable
• Acc. to eg in PD, both firms select high advertising & capture max. profit
• But, if this exercise is repeated, outcomes may change
• Advantage becomes temporary• Winning strategy- ‘tit for tat’
Infinitely Repeated Game Co-operative behaviour is a rational
response to a tit for tat strategy
Finite Number of Repetitions Strategise to take action in the last period
of time in order to have a long term effect
One player acts first & then the other responds
2 firms contemplating the introduction of an identical product in the market
1st firm- develop brand loyalties, associate product with the firm in minds of consumers
Thus, first mover advantage
Firm 2
No new productIntroduce new product
Firm 1
No new product $2, $2 $-5, $10Introduce new product $10, $-5 $-7, $-7
• Assume firms use maximum criterion, so neither should introduce a new product and earn $2 mn each
• Firm 1 introduces a new product, firm 2 will still decide to stay out because right now it is losing $5 mn, opposed to $7 mn otherwise.
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