7. Strategic Interdependence and Game Theory Basics Flashcards
Introduction: 2 paradigms
Course starts from a precise paradigm we should know:
First premise of the course:
Structure-conduct-performance paradigm: How do firms & industries evolve?
It tells you structure underlies firm behaviour. Structuralistic perspective
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In economics, structure is basically decided by the markets.
Formal structural models of competition:
Perfect competition; Monopoly; Oligopoly
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Second premise of the course:
Neoclassical profit maximization logic: Are there alternative perspectives.
Many firms also have other objectives now. They often act not only ACC to rational logic but also irrational patterns of behaviour.
Firms are social institutional.
We will explore resource-based views and other logics that firms might use to behave.
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Structure-conduct-performance paradigm: gives static equilibrium however it’s not always static, firms evolve through growth strategies so we will also understand this. Many ways in which firms can grow, we will expand on the logic of the growth strategies, modalities and also the objectives of these growth strategies.
Oligopolies and Strategic Interdependence
The term Oligopoly means (from Greek): oligos=few; polein=sell
The number of companies in the market, N, is small
The behavior of each firm significantly affects the behavior of other firms, which leads to strategic interdependence
Basic analytical tools. What tools do we need?
What tools do we need?
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Neoclassical profit maximization logic –> profit maximization rule
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Strategic interdependence —> game theoretical insights
Game Theory
Game theory is the formal modeling of optimal decision-making in contexts of strategic interaction.
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In its simplest version (simultaneous game, two players, pure strategies):
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- There are 2 players
- Each player has a set of possible actions, which may be discrete or continuous. (discrete: absolute value 1,2, etc ; cont: any val 2.53..)
- Different combinations of actions unambiguously determine different outcomes.
- Each outcome is unambiguously associated with a pay-off (an outcome/ result) for each player.
- Players are perfectly rational and perfectly informed.
- Players decide their actions simultaneously, aiming for pay-off maximization. (no player gets to see the other’s decision before making their own)
Let’s define two key concepts: Reaction function and Nash Equilibrium
1) Reaction function: function associating each possible strategy of one player with the optimal response of the other player.
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2) Nash equilibrium: configuration of strategies where each player’s strategy is the best response to the strategy of the other player. A configuration of strategies is a Nash equilibrium if no player could improve the resulting pay-off by unilaterally deviating from the selected strategy.
A discrete example: The prisoner’s dilemma (discrete because we can count)
A stays silent –> B betrays
B stays silent–> A betrays
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A betrays –> B betrays
B betrays –> A betrays
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A betrays <–>B betrays is the only Nash equilibrium
A continuous example: (quantitative)
A graph
Quantity for Firm A
Quantity for firm B
Reaction function for both
(Need to understand what’s the point of finding the reaction function)
A variant: sequential games
In sequential games (simplest version):
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- There are 2 players
- Each player has a set of possible actions, which may be discrete or continuous.
- Different combinations of actions unambiguously determine different outcomes.
- Each outcome is unambiguously associated to a pay-off for each player.
- Players are perfectly rational and perfectly informed.
- Players decide their actions sequentially, aiming for pay-off maximization. The player acting first is known as the leader, while the other is known as the follower.
Solving sequential games
- Discrete sequential games are typically represented as decision trees.
- Sequential games can be easily solved by backward induction: you start by determining the pay-off maximizing strategy of the follower. Then, you base the strategy of the leader on this information.
- The sequence of optimal actions obtained through backward induction is known as subgame perfect Nash equilibrium.
Sequential games: a discrete example
Two-stage sequential game of entry deterrence:
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Entrant
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(enter) (stay out)
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(incumbent) (0,10)
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(Price war) (Acquiantence)
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(-5,-5) (5,5)
Types of oligopolistic models
Models can be:
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1. Collusive (e.g. cartel)
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2. Competitive: no collusion (Bertrand, Cournot, Stackelberg).
Simultaneous models (Bertrand, Cournot).
Sequential models (Stackelberg).
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Key variables:
Prices adopted by each company (Bertrand)
Quantities offered by each company (Cournot, Stackelberg)
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Extra
The relevant outcomes measures (prices, quantities, profits, consumers’ surplus, social welfare) are in the middle of those that emerge in perfect competition and monopoly, In both cases, firms don’t care about other firms’ reaction: there is no strategic interaction. In Oliogopoly, there are few firms and each decision taken by each single firm can influence other firms’ profits. There is a strategic interaction studied through the game theory. Thus, oligopoly is more realistic. The number of companies in the market is limited, higher than one but not tending to infinite, they are the price-makers.
Game theory models
Models can be:
Collusion
We can introduce the concept of collusion, which means companies jointly agree on prices and/or quantities in order to maximize the industry profit. They jointly behave as monopolist. The collusion is modeled in the game theory through cooperative games. It is possible to demonstrate that:
pi (monopoly) > summation of N to i=1 of pi (oligopoly)
dominant strategy
Analyzing the game theory, we can identify a dominant strategy, which is the best strategy regardless the strategy of the other player. This dominant strategy eliminates the dominated strategies.
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The solution can be:
