class: center, middle, inverse, title-slide # 2.3: Stackelberg Competition ## ECON 326 · Industrial Organization · Spring 2020 ### 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/IOs20"><i class="fa fa-github fa-fw"></i> ryansafner/IOs20</a><br> <a href="https://IOs20.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i> IOs20.classes.ryansafner.com</a><br> --- # Stackelberg Competition .left-column[ .center[  .smaller[ Henrich von Stackelberg 1905-1946 ] ] ] .right-column[ - .hi["Stackelberg competition"]: Cournot-style competition, two (or more) firms compete on **quantity** to sell the **same good** - Again, firms' joint output determines the market price faced by all firms - But firms set their quantities **sequentially** - .hi-purple[Leader] produces first - .hi-purple[Follower] produces second ] --- # Stackelberg Competition: Example .content-box-green[ .hi-green[Example]: Return to .hi-red[Saudi Arabia `\\((sa)\\)`] and .hi-blue[Iran `\\((i)\\)`], again with the market (inverse) demand curve: `$$\begin{align*} P&=200-3Q\\ Q&=\color{red}{q_{sa}}+\color{blue}{q_i}\\ \end{align*}$$` ] -- - We solved for Saudi Arabia and Iran's .hi-purple[reaction functions] in **Cournot competition** last class: `$$\begin{align*} \color{red}{q_{sa}^*}&\color{red}{=30-0.5}\color{blue}{q_i}\\ \color{blue}{q_i^*}&\color{blue}{=30-0.5}\color{red}{q_{sa}}\\ \end{align*}$$` --- # Stackelberg Competition: Example `$$\begin{align*} \color{red}{q_{sa}^*}&\color{red}{=30-0.5}\color{blue}{q_i}\\ \color{blue}{q_i^*}&\color{blue}{=30-0.5}\color{red}{q_{sa}}\\ \end{align*}$$` - Suppose .hi-red[Saudi Arabia] is the .hi-purple[Stackelberg leader] and produces `\(q_{sa}\)` **first** -- - Saudi Arabia knows exactly how Iran will respond to its output `$$\color{blue}{q_i^*}\color{blue}{=30-0.5}\color{red}{q_{sa}}$$` -- - .hi-red[Saudi Arabia], as leader, essentially faces **entire market demand** - But **can't** act like a pure monopolist! - knows that .hi-blue[follower] will still produce afterwards, which pushes down market price for both firms! --- # Stackelberg Competition: Example - Substitute .hi-blue[follower]'s reaction function into (inverse) market demand function faced by .hi-red[leader] -- `$$\begin{align*} P&=200-3q_{sa}-3(30-0.5q_{sa})\\ P&=110-1.5q_{sa}\\ \end{align*}$$` -- - Now find `\(MR(q)\)` for .hi-red[Saudi Arabia] from this by doubling the slope: -- `$$MR_{Leader}=110-3q_{sa}$$` --- # Stackelberg Competition: Example - Now .hi-red[Saudi Arabia] can find its optimal quantity: `$$\begin{align*} MR_{Leader}&=MC\\ 110-3q_{sa}&=20\\ 30&=q_{sa}^*\\ \end{align*}$$` -- - .hi-blue[Iran] will optimally respond by producing: `$$\begin{align*} q_i^*&=30-0.5q_{sa}\\ q_i^*&=30-0.5(30)\\ q_i^*&=15\\ \end{align*}$$` --- # Stackelberg Equilibrium, Graphically .pull-left[ <img src="2.3-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" /> ] .pull-right[ - **Stackelberg Nash Equilibrium**: `$$\big( \color{red}{q^*_{sa}=30}, \color{blue}{q^*_{i}=15} \big)$$` ] --- # Stackelberg Competition: Example - With `\(\color{red}{q^*_{sa}=30}\)` and `\(\color{blue}{q^*_i=15}\)`, this sets a market-clearing price of: `$$\begin{align*} P&=200-3(45)\\ P&=65\\ \end{align*}$$` -- .pull-left[ - .hi-red[Saudi Arabia's] profit would be: `$$\begin{align*} \pi_{sa}&=30(65-20)\\ \pi_{sa}&=\$1,350\\ \end{align*}$$` ] -- .pull-right[ - .hi-blue[Iran's] profit would be: `$$\begin{align*} \pi_{i}&=15(65-20)\\ \pi_{i}&=\$675\\ \end{align*}$$` ] --- # Stackelberg Equilibrium, The Market <img src="2.3-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" /> --- # Cournot vs. Stackelberg Competition .center[  ] - **Leader** Saudi Arabia `\(\uparrow\)` its output and `\(\uparrow\)` profits - **Follower** Iran forced to `\(\downarrow\)` its output and accept `\(\downarrow\)` profits --- # Stackelberg and First-Mover Advantage .pull-left[ <img src="2.3-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" /> ] .pull-right[ - Stackelberg **leader** clearly has a .hi-purple[first-mover advantage] over the **follower** - **Leader**: $q^*=30 \text{ , } \pi=\$1,350$ - **Follower**: $q^*=15 \text{ , } \pi=\$675$ - If firms compete **simultaneously** (.hi[Cournot]): $q^*=20 \text{ , } \pi=\$1,200$ each - Leading `\(\succ\)` simultaneous `\(\succ\)` Following ] --- # Stackelberg and First-Mover Advantage .pull-left[ <img src="2.3-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" /> ] .pull-right[ - Stackelberg Nash equilibrium requires .hi-purple[perfect information] for **both** leader and follower - Follower must be able to **observe** leader's output to choose its own - Leader must **believe** follower will see leader's output and react optimally - .hi-purple[Imperfect information] reduces the game to (simultaneous) .hi[Cournot competition] ] --- # Stackelberg and First-Mover Advantage .pull-left[ <img src="2.3-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" /> ] .pull-right[ - Again, leader *cannot* act like a monopolist - A strategic game! Market output (that pushes down market price) is `\(Q=q_{sa}+q_{i}\)` - Leader's choice of 30 is optimal **only if** follower responds with 15 ] --- # Comparing All Oligopoly Models .center[  ] - Output: `\(Q_m < Q_c < Q_s < Q_b\)` - Market price: `\(P_b < P_s < P_c < P_m\)` - Profit: `\(\pi_b=0 < \pi_s < \pi_c < \pi_m\)` Where subscript `\(m\)` is monopoly (collusion), `\(c\)` is Cournot, `\(s\)` is Stackelberg, `\(b\)` is Bertrand --- # Stackelberg Competition: Moblab .center[  ] --- # Stackelberg Competition: Moblab .pull-left[ .center[  ] ] .pull-right[ - Each of you is one Airline competing against another in a duopoly - Each pays same per-flight cost - Market price determined by *total* number of flights in market - **LeadAir** first chooses its number of flights, publicly announced - **FollowAir** then chooses its number of flights ]