December 5, 2000

**Relevant Review:**-
**Oligopoly** - Game Theory Intro
- Dominant Strategy
- Dilemmas
- Sequential Games

Major U.S. television networks predict or "call" the outcomes of elections while voting is still going on in many locales. As we were reminded in the most recent U.S. election, network predictions are not always correct. Most TV news operations called Florida first for Gore, then for Bush, then called the election for Bush, then changed their Florida and thus election prediction to "too close to call."

Network critics argue that the practice of calling results quickly affects voter turnout and thus election outcomes in areas where polls are still open. Our goal here is not to argue whether or not networks should change this practice, or whether or not results are affected by it. Our goal is to attempt to explain why any networks call election results early, despite criticism this practice entails, and to also ask why **all** major network news organizations engage in this practice.

It turns out that game theory can provide a plausible explanation for this result. Once we realize that television revenues come from selling commercial time and the larger the audience (all else being equal) the more stations can charge for commercial time, it becomes simple to set up a game structure that is consistent with the observed behavior.

We begin with a simple payoff matrix as if there are only two networks. We assume that each network has only two strategies available on election night, **Call** and **Don't Call**. A network pursuing the **Call** strategy will predict the outcome of the election in each state as quickly as possible. A network pursuing the **Don't Call** strategy would, if they are covering the election, only air official vote results as they are released by the states. **Network A's** strategies are shown along the left hand side of the matrix and on top we show **Network C**. The empty cells will show the payoffs to each network. Naturally, our assumption is that firms (networks in this case) will always prefer higher profits to lower.

To the right is a payoff matrix with possible payoffs filled in. The payoff numbers in the cells can represent relative profits or relative numbers of viewers. Since more viewers mean more profit, it doesn't matter. These are "made up" numbers, meant to illustrate payoffs that would lead to the observed outcome. The first number in each cell, in **dark green**, is the payoff to **Network A**. The second number in each cell, in **blue**, is the payoff to **Network C**. So, if both networks choose to Call the election (the upper left cell) they both earn payoffs of **100**. If **Network A** chooses **Call** (top row) and **Network C** chooses **Don't Call** (right column), **Network A** earns a payoff of **500** while **Network C** earns a payoff of only **10**.

To solve a simple game like this, the first thing to look for is the existence of a **dominant strategy** (a dominant strategy is a strategy that is always best, in terms of payoff, no matter what the other player chooses to do). To the right we show the payoffs only for **Network A**. A very quick inspection of these numbers makes it clear that **Network A** has a dominant strategy, to always **Call** the election results (choose the top row). No matter what **Network C** does, **Network A** will earn higher payoffs by choosing **Call**.

**Network C** faces the same game. Whatever strategy **Network A** follows, **Network C** is better off calling the election (choosing the left column). Simply put, it is more interesting to most viewers to hear early predictions, even if they turn out to be wrong, than to wait for official results. We show payoffs far higher for each network if the other network chooses "Don't Call" because it will find almost all viewers choose the network that offers quick predictions. Both networks will choose "Call" no matter what the other network(s) choose. This is an example of a **dominant strategy** and we know that solving games in which all players have a dominant strategy is easy.

The solution is obvious but let's examine how this game is solved anyway. As we saw above, **Call** is a dominant strategy for each network. This means that no matter what the other network does, either network is better off calling the election results as soon as possible. Neither network will consider the Don't Call strategy, so we may remove those strategies from consideration. We do this by crossing out the bottom row for **Network A** and crossing out the right column for **Network C**. The only remaining possibility is that both networks will **Call** and each will earn a payoff of **100**.

Suppose we imagine that one of the networks takes a "wait and see" attitude. **Network C** might choose to do this if **Network A** is the recognized "standard setter" for the television news industry. To the right we show the basic game tree for the case where **Network C** makes its decision only after it learns what **Network A** is going to do. Each decision is a branch on the tree. Since **Network A** moves first it is shown as the left most node and we read the tree from left to right. **Network A** can either choose **Call** or **Don't Call**. If **Network A** chooses **Call**, **Network C** finds itself on the top branch of the tree where it can choose either **Call** or **Don't Call**. If **Network A** chooses **Don't Call** then **Network C** finds itself on the bottom branch, again able to choose either **Call** or **Don't Call**.

We'll use the same payoffs we used before. As shown to the right, the payoffs are listed at the end of each final branch. The first payoff in each pair is **Network A's** while the second is **Network C's**. For example, if **Network A** chooses **Call** and **Network C** chooses **Don't Call** the game ends at the next-to-top branch with **Network A** earning a payoff of **500** and **Network C** earning a payoff of **10**.

Remember that sequential games are solved backwards (backward induction). We start by considering the choices facing the last player to choose, **Network C**. If **Network C** finds itself choosing among the top two branches (if **Network A** chose **Call**) it can earn a payoff of **100** if it chooses **Call**, but only **10** if it chooses **Don't Call**, so we can eliminate **Don't Call** in that case. **Network C** will also earn a higher payoff if it chooses **Call** if it's choosing between the lower two branches, so we know that **Network C** will choose **Call** whatever **Network A** does.

This is a game of full information. This means that each network knows the payoffs faced by the other so **Network A** can figure out what **Network C** will do. Thus, **Network A** faces a simplified game tree where it can either earn payoffs of **100** or **10**. It is clear that **Network A** will also choose **Call** so the game is solved with the same solution as before, both networks Call the election as early as possible, despite criticism.

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