Every day, humans encounter scenarios involving conflict, competition and cooperation. We make moves, tender counteroffers and call bluffs. Politicians, economists and business people alike make strategic decisions that can make or break their days.

Game theory is the study of social interactions between rational decision makers and has direct applications in the day-to-day decisions of managers and employees. It is also used in large-scale decision making, from corporate strategy to M&As and competitive pricing. Apart from business, it’s also relevant to economics, politics, war, psychology and biology. This article introduces three scenarios from game theory: the Prisoner’s Dilemma, second price auctions and Hotelling’s game.

Prisoner’s Dilemma

Perhaps the most famous game in game theory is the Prisoner’s Dilemma. Picture two suspects accused of stealing a priceless jewel. The police have proof beyond reasonable doubt of trespassing and have temporarily jailed them in separate cells with no means of communicating with each other. However, for the more serious charge of theft, they need a confession. The police make each of them a bargain. They give both prisoners the opportunity to defect by testifying that the other committed the crime, or cooperate with the other by remaining silent. There are three possible outcomes:

  • if neither confesses, both will get a one-year sentence for trespassing;
  • if one confesses and the other doesn’t, the detectives will release the confessor as a reward for his testimony and sentence the other to twenty years in jail; and
  • if both confess, each will receive five years in jail.

You can represent this scenario as a matrix, with prisoner A’s move on the left and prisoner B’s move on the top. If you were prisoner A, what would you do?

prisoner's dilemma
First, consider what you would do for each of prisoner B’s choices. If prisoner B confesses, then looking at the first column, it would be better to confess and serve for five instead of twenty years. But if prisoner B remains silent, then looking at the second column, it would still be better to confess and serve no time rather than one year. In both cases, prisoner A’s best option would be to confess. Confessing is prisoner A’s dominant strategy because he is always better off to do so regardless of what prisoner B does.

Prisoner B will have the same reasoning and also chooses to confess. Thus, both prisoners will confess and receive five years in jail. The dilemma is in the irony that it would have been better for them to cooperate by both remaining silent than both defecting, yet such an option is not rational because of self-interest.

The Prisoner’s Dilemma might seem like an unusual situation for your business but in fact, models many different situations in psychology and economics, to name a few. For example, you can apply it to internal people management or collaboration between you and your team. If you are a manager, you can set team goals and promote how cooperative behaviour benefits everyone including sharing knowledge and acknowledging credit where it’s due. On the other hand, you can explain how defective actions, such as framing others, keeping information secret and taking credit from others lead to worse outcomes for all. As an employee, you can also foster a cooperative culture when working with your colleagues and clients.

We can see another example of the Prisoner’s Dilemma in competitive pricing. Two major competitors, such as the soft drink giants Coca-Cola and PepsiCo, can decide to either maintain their product prices or drop them – analogous to remaining silent (cooperating) and confessing (defecting) respectively. If one drops their prices, but the other doesn’t, they will attract a larger market share and generate more profit, assuming the gains from additional sales offset the drop in price. However, if they both drop their prices, the effect cancels out, and they will both lose on revenue. In this case, they would both be better off by maintaining higher prices.

Second Price Auction

Another game theory scenario is a blind second price auction. In this auction, the highest bidder wins the good but pays the price the second-highest bigger offered. All bids are secret until the end. That is how Google AdWords determines the ranking order of paid advertising for search results. Google AdWords technically charges one cent more than the second-highest price. So for example, if there are three bidders for the keyword ‘game theory’ and they bid $1, $2 and $8 respectively, the $8 bidder would get the top rank on the page and pay only $2.01.

The top bidder should be confident that they are okay with paying $8 for the keyword. If they think that it is worth $2 and someone else bids $7, they’d be in trouble.

Interestingly, in such auctions, bidders will only bid what they think the good is worth – no more and no less. Why? First imagine the case where a bidder’s preferred price won’t be the highest amongst all bids. If they bid higher, they might end up with buyer remorse (i.e. paying more than they think the good is worth) while bidding lower won’t change the outcome of the auction.

On the other hand, if the bidder’s preferred price would result in the highest bid, then bidding higher gives no advantage as they would still pay the second-highest price while bidding lower just introduces the risk of losing the auction.

Therefore all bidders, if bidding rationally, would bid at the exact price at which they value the good. This situation is a stable equilibrium and results in the best outcome. In fact, this balance is also quite slick as it rewards honest opinions, provides for receiving the good at a lower price than its perceived value, and doesn’t involve having to consider other people’s strategies.

Hotelling’s Game

Another popular scenario is Hotelling’s game. Economic theorist Harold Hotelling observed that in many markets, it is rational gameplay for products from different competitors to be as similar as possible (also known as the Principle of Minimum Differentiation).

Imagine two ice-cream vendors on a long, thin and sweltering beach. The vendors have mobile stands that can move along the beach, and beachgoers are attracted to the stand closest to them. If the vendors start at different points on the beach, they would quickly realise that they can gain a greater market share by moving toward the centre – increasing the amount of beach area where they are a closer stand than their rival. In fact, after much shuffling about, they would find that the only stable equilibrium is when the vendors are both in the middle of the beach, with each getting half the business.

In choosing the same location for their stands, the vendors reduce geographic differentiation of their products. You can think of the beach as a metaphor for another product characteristic, such as ice-cream scoop size, sweetness or colour, where there is a range of options in the spectrum but for which competitors would try to minimise differentiation to attract the greatest market share.

If you have a small business, consider products where customer preferences are likely to be evenly distributed across its different features. For example, in selling a new type of sports shoe, preferences are likely to vary with colour, purpose and design. Choosing characteristics that somewhat appeal to everybody will appeal to a bigger customer base, and therefore a larger market share, than choosing a mix of features to appeal to a niche segment.

While the Principle of Minimum Differentiation is the opposite of product differentiation, it is especially advantageous in commoditised markets – that is, for products where brand and uniqueness are not important, such as socks, refrigerators or fast food. However, firms often employ both strategies simultaneously. An example is with competing airlines differentiating on flight experience and price, but servicing the same routes from the same airports.

Key Takeaways

Game theory underlies our daily interactions, decisions and interests. It provides a rigorous model of interactions between different ‘players’ that one can solve to find the most beneficial outcome. Considerations include cooperation or self-interest, competitors’ strategies, best responses to opponents’ moves and stable market equilibria. So the next time you find yourself caught along with your partner in crime, make a pact to cooperate. It just might save you doing some time.

How have you observed game theory in your professional or personal life? Let us know your thoughts on LegalVision’s Twitter @legalvision_au.

Jonathan Ling

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