*DISCLAIMER: We going to get a bit geeky this week, so prepare to mull. *

*Establishing value-driven measurement is an integral step in cementing PR’s seat at the table. But what about other catalysts (beyond metrics) that can used in rational, strategic decision making?*

*Below is a write up done by our stellar summer intern, Harry Rackmil. Harry brought a numerous insightful contributions to AirPR, one of which was his application of Game Theory to PR.*

*Besides being a fascinating read, Harry also cooked up some nifty visuals to illustrate the model’s important conclusions. Your head might spin a little during your first read, but that’s just your brain thanking you for seeking yet another angle that proves the value of PR. Enjoy!*

Public Relations and Game Theory seem to have little in common, but that doesn’t mean they don’t pair nicely.

Game theory, to paraphrase Wikipedia, is the study of strategic decision making by rational, intelligent agents. It’s easy to see how this could apply to Public Relations – every decision in a PR campaign, from which messages to pitch to which journalists to target, is a carefully considered choice, influenced in part by the strategic choices of the competition’s rational.

But then again, “strategic decision making by rational, intelligent agents” is vague enough to cover just about everything. This is intentional – it means practically any strategic decision can be tweaked into a game modelled by a mathematical game theoretical framework with a few well-placed assumptions. But it also means some important details will have to be glossed over – John Nash never incorporated the influence of the blogosphere into his equilibrium calculations.

With a few simplifying assumptions we can apply game theory to a common situation in PR and explain why increasing PR investment might not increase sales, but *not *investing in PR at all will cause even more damage.

**How PR relates to “competitive advantage.”**

Let’s look at a very specific case when two competitors are vying for the same fixed pool of customers. This is certainly not the only PR hypothetical – it is often employed to bring in new customers, coax current customers into spending more, or simply prevent unforeseeable press disasters.

Think of a presidential election – television ads are airing constantly so almost everyone knows the candidates’ names (high brand awareness), but these ads weren’t convincing enough and a number of swing voters still haven’t decided. If nothing further is done, approximately half should vote for each candidate just by random chance. But if one candidate’s PR team gets an article published making a convincing appeal to these voters and the other candidate is silent, the first candidate could get all of their votes.

Now if the second candidate’s PR team gets a second, equally effective article published favoring their candidate, the decision isn’t so straightforward and the split is back to 50/50. So both candidates have spent a lot of money on PR and they’re no better off than if they’d never hired PR pros in the first place.

So if this is the outcome, why invest in PR at all?

**Here’s where game theory comes into play.**

Let’s model PR spending as a turn-based game. Each week a company and its competitor both decide whether to run a PR campaign with a known cost in dollars, and a known benefit in dollars. For now we’ll assume this benefit outweighs the cost.

If company A runs the campaign and company B does not, company A will gain the benefit and lose the cost, so its net payoff is **[b – c]**. But remember, this is a fixed pool of customers – if A increases its customer base by 100 people, B has lost 100 customers. Thus, company B’s net payoff is **[-b].**

**What if company B decides to run the campaign too? **

Now both A and B are incurring the cost of running this campaign, but the campaigns effectively cancel each other out, so the benefit is **zero**. This means both A and B have a net payoff of **[–c]**.

If neither company runs the campaign, no difference is made and no cost is incurred so the payoff is zero for both companies. There are two strategies each company can choose and 4 potential outcomes, so let’s make a payoff matrix.

Company A’s choices are on the top, and their payoffs are the top triangle of each square.

Now we’re going to look for a *Nash equilibrium* – a set of decisions by A and B where neither company has incentive to switch. Let’s start with the *zero PR strategy*. Neither player is losing money here, but is it equilibrium?

Unfortunately, it is not. Since **benefit is greater than cost**, both companies have incentive to buy PR to go from zero payoff to positive payoff.

Let’s say company A buys PR, but company B does not. This isn’t an equilibrium either. Of course company A would rather net **benefit-cost** than just **-cost**, but company B would prefer **-cost** to its current **-benefit** (since as we assumed earlier, cost < benefit), so company B has incentive to switch to buying.

Now both companies are buying PR, and both are losing money.

Where are the incentives pointing? Company A knows company B is buying, so if company A stops buying they will spare the low cost, but lose the high benefit. Similarly, B knows that A is buying so B is better off buying as well. There is no incentive to switch, so we’ve found a *Nash Equilibrium*.

It’s important here to note that game theory isn’t meant to tell your company how to behave; rather it’s telling your company how you *will *behave, given your competitor’s behavior. The assumption that you’re making the most profitable decision is already made, so you can’t game the system by choosing a non-equilibrium strategy. As we’ve already shown, not buying will result in a loss greater than the cost of a PR campaign. The value of this model is in explaining why the optimal decision you made may not seem so optimal in your budget.

**So we’ve found an equilibrium, but what does this mean? **

Does this mean that competing PR teams with equal costs and benefits will always increase spending on PR, and never gain a thing? For a while yes, but as time passes and more and more articles are published, the benefit of a single campaign starts to fall. If you and your competitor have published one million well-placed, well-written articles each, one extra article will tend to be lost in the sea of press. After a large number of turns benefit falls, so eventually benefit < cost.

When this happens, benefit – cost < 0, so the incentives switch. Drawing out the payoff matrix again with this new assumption, we find that **both not buying** is the new *Nash equilibrium*.

So both firms will continue to buy until there is no longer a large benefit to buying more PR, at which point both firms will stop buying. So the firms’ behaviors mirror each other exactly.

Does this mean they will always be evenly matched?

Yes – but only if they face the same costs and benefits. Since we’re looking at the purchase of a single campaign, the benefit should be roughly the same from company to company. This is a big assumption and may seem like sacrilege to some seasoned PR pros, but it’s not too far-fetched to say similar companies will gain roughly the same amount of business from similar PR campaigns, even if there’s a lot of random variation between campaigns.

The effort that goes into the roughly similar campaigns, though, may vary immensely. Some companies draw the public’s eye (Apple, Google, Amazon) and journalists will write about them with little prompting. This may take only a few paid hours of work by a small team. A smaller company will have to do more work, and getting a mention in the New York Times may take a large team of expensive PR professionals. Even companies with equal media interest can face different costs for the same task depending on the efficiency of their PR team.

So let’s look at the case when company A faces a low cost, (**cost _{L }**), and company B faces a high cost,

**(cost**. If the benefit is still higher than both costs, the result will be the same as the initial case and the equilibrium will be that both companies buy PR. Similarly, if benefits are less than both costs, both firms will not buy PR.

_{H})If **cost _{L }< benefit < cost_{H}**, the high cost company will be better off not buying and the low cost company will be better off buying, leading to an equilibrium where only the low cost company will buy PR.

So when the benefit of PR is more than its cost of your PR spending, even if it is producing great press and public opinion, it may not increase your sales at all. But not spending is even worse – **it spares the cost but opens your market to your competition**. The only way to get a truly positive benefit from PR in this situation is through more pitch-able products or more efficient PR.

Or at least hope you’re a more rational, intelligent agent than your competition.