2.1 — Oligopoly & Cartels

# 2.1 — Oligopoly & Cartels
## ECON 316 • Game Theory • Fall 2021
### Ryan Safner<br> Assistant Professor of Economics <br> <a href="mailto:safner@hood.edu"><i class="fa fa-paper-plane fa-fw"></i>safner@hood.edu</a> <br> <a href="https://github.com/ryansafner/gameF21"><i class="fa fa-github fa-fw"></i>ryansafner/gameF21</a><br> <a href="https://gameF21.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i>gameF21.classes.ryansafner.com</a><br>

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# Outline

### [Coordination Games](#3)
### [Multiple Equilibria](#41)
### [Rationalizability and the Role of Beliefs](#50)

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# Discrete vs. Continuous Strategies

.pull-left[
.smaller[
- We considered simultaneous games where strategies are .hi-purple[discrete]: a finite (usually small) number of strategies to choose from

- We now consider .hi-purple[continuous] strategies:
  - Practically infinite number of "strategies" to choose from
  - Example: firms don't just choose 1 out of 2 or 3 possible prices, but one from a large possible **range**
    - Must switch from game trees and payoff matrices to algebraic equations
    - Still keep concepts of "best response" and Nash equilibria
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# Quick Microeconomics Refresher

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# Demand Function

- .hi[Demand function] relates quantity to price

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$q=10-0.5p$$`
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- Not graphable (wrong axes)!

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# Inverse Demand Function

- .hi[*Inverse* demand function] relates price to quantity
    - Take demand function and solve for `$p$`

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=20-2q$$`
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- Graphable (price on vertical axis)!

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# Inverse Demand Function

- .hi[*Inverse* demand function] relates price to quantity
    - Take demand function and solve for `$p$`

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=20-q$$`
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- Graphable (price on vertical axis)!

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<img src="2.1-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
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# Demand and Marginal Revenue

<img src="2.1-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
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`$$\begin{align*}
\color{#0047AB}{p(q)}&\color{#0047AB}{=a-bq}\\
\color{#6A5ACD}{MR(q)}&\color{#6A5ACD}{=a-2bq}\\
\end{align*}$$`

- **Marginal revenue starts at same intercept as Demand `$(a)$` with twice the slope `$(2b)$`**
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# Perfectly Competitive Firms

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
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.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
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- .blue[Demand for a firm's product] is **perfectly elastic** at the market price
  - .blue[Marginal revenue = Firm's Demand = market price]
]

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# Perfectly Competitive Firms

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
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.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
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.smallest[
- Firms choose `$q^\star$` to maximize profits where .purple[MR(q)]=.red[MC(q)]
- In the long run, firms earn profit `$\pi=0$` due to .hi[free entry and exit]
]

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# Firm with Market Power

- Firm with market power is a .hi-purple[price searcher]

- Chooses `$q^\star$` to maximize profits where .purple[MR(q)]=.red[MC(q)]

- Marks up price (above .red[MC]) to consumers' max WTP (.blue[Demand])

- .green[Profit] = (.blue[p] — .orange[AC(q)])q

- Earns positive profits from .hi[barriers to entry]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />
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# Imperfect Competition

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# Application: The Econoomics of Oligopoly

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# Oligopoly

- .hi[Oligopoly]: industry with a few large sellers with market power

- Other features can vary
  - May sell similar or different goods
  - May have barriers to entry

- Key: Firms make .hi-purple[strategic choices], interdependent on one another

- For modeling simplicity: 
  - .hi-purple[Duopoly]: a market with 2 sellers 
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# Oligopoly: Modeling

- Depends heavily on assumptions made about interactions and choice variables:
  - .hi[“Bertrand competition”]: firms compete on **price**
  - .hi[“Cournot competition”]" firms **simultaneously** compete on **quantity**
  - .hi[“Stackelberg competition”]: firms **sequentially** compete on **quantity**

- One certainty: oligopoly is a .hi-purple[strategic interaction] between few firms

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# Equilibrium in Oligopoly

- What does .hi-purple[“equilibrium”] mean in an *oligopoly*?

- In competition or monopoly, a unique `$(q^*,p^*)$` for industry such that **nobody has incentives to change price**

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# Equilibrium in Oligopoly

- Oligopoly: use game-theoretic .hi-purple[Nash Equilibrium]: 
  - no player wants to change their strategy **given all other players’ strategies**
  - each player is playing a **best response** against other players’ strategies

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# As a Prisoner's Dilemma I

![:scale 100%](../images/applevsgoogle.jpg)
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- We will start with a .hi-purple[discrete] example to get the basics

- .hi-green[Example]: suppose we have a simple **duopoly** between .hi-red[Apple] and .hi-blue[Google]

- Each is planning to launch a new tablet, and choose to sell it at a **High Price** or a **Low Price**

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# As a Prisoner's Dilemma

- .hi-purple[Nash equilibrium]: (.hi-red[Low Price], .hi-blue[Low Price])
  - neither player has an incentive to change price, *given the other's price*

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![](../images/pdapplegooglenash.png)

Nash equilibrium
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# As a Prisoner's Dilemma

- .hi-purple[Nash equilibrium]: (.hi-red[Low Price], .hi-blue[Low Price])
  - neither player has an incentive to change price, *given the other's price*
  
- A possible **Pareto improvement**: (.hi-red[High Price], .hi-blue[High Price])
  - Both players are better off, nobody worse off!
  - Is it a Nash Equilibrium?

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![](../images/pdapplegooglecartel.png)

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# Cartels

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# As a Prisoner's Dilemma III

- Google and Apple could .hi-purple[collude] with one another and agree to both raise prices

- .hi[Cartel]: group of sellers coordinate to raise prices to act like a collective monopoly and split the profits

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# Instability of Cartels

- Cartels often **unstable**:

- Incentive for each member to cheat is too strong

- Entrants (non-cartel members) can threaten lower prices

- Difficult to monitor whether firms are upholding agreement

- Cartels are illegal, must be discrete

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# Attempts to Sustain Collusion I

Archer Daniels Midland (USA), Ajinomoto (Japan), Koywa Hakko Kogyo (Japan), Sewon American Inc (South Korea) held secret meetings to fix the price of lysine, a food additive to animal feed in the 1990s.

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# Attempts to Sustain Collusion I

An internal FBI informant brought the cartel down.

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