Auctions, Prisoners and 3G Licenses: How Game Theory Sculpts Modern-Day Society
Although we may not be aware, the concept of game theory largely influences the decisions we make and can be used as a potent fuel for social, economic and environmental optimisation.
“One ten anyone? One ten. One twenty? One twenty, sir on the back row. One thirty anyone?… For the first time at one twenty, for the second time, for the third and final time at one hundred and twenty pounds… gone!”
I can still remember the times as a young kid returning home from a tough football match to hear the auctioneer from Bargain Hunt blaring through the television, as my mum sat there engrossed by what I thought was such an awful programme. Years later, I could never have predicted I would be writing an article about one of the things that bored me most as a child.
An auction is a type of game. A good or service is sold to an individual, through different types of bidding processes, which there are many. The English auction is called an ascending bid, where the auctioneer starts from a low bid and keeps raising the price until no one wants to bid more. The Dutch auction, also called a descending bid auction, begins at a very high price and the price is dropped until somebody accepts the latest price. Finally, sealed bid auctions involve the buyers all submitting a bid without others seeing it, and the winner will either pay their own highest bid (first-price auction) or the second-highest bid (second-price auctions.)
Auctions are prime examples of a concept known as game theory.
According to the Stanford Encyclopaedia of Philosophy:
“Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents”
In simpler terms, it is the science of strategy. It is the theoretical framework for conceiving social situations among competing players, involving a game whereby players deploy strategies in order to receive a payoff (this can be anything in quantifiable form.) The concept was formulated first by John von Neuman and Oskar Morgenstern, a mathematician and economist respectively.
Although, the concept has been dated back to ancient times. In two of Plato’s texts, Socrates recalls an episode from a battle whereby a soldier has the opportunity to stay at his post and fight or run away and not risk his life. His decisions are based on the outcomes of the battle, and whether his own personal contribution is essential. Based on game theory reasoning, it appears that the soldier is better off running away regardless of the anticipated outcome of the battle. This is a very simplified example.
Today game theory is used widely across many subject and affairs. It appears in psychology, evolutionary biology, war, politics, economics and business to name a few.
However, it has its limitations. It assumes that all humans are self-interested, utility-maximising rational actors. Of course, this is not always the case. Oftentimes we put others before ourselves and act on incentives beyond personal satisfaction and benefits. Game theory fails to take into account the benevolence and care that humans have for the welfare of others. Despite being formulated almost 80 years ago, it is still a young and developing science.
Further, it was developed by a duo of super-intelligence; two humans vastly unrepresentative of the average person. Therefore, it presumes the players are hyperrational supercomputers able to solve mathematical equations to arrive at an optimal strategy. This is far from the truth, which limits its ability to predict how people actually act.
A simplified, but classic, example of a game in practise is one called the ‘prisoner’s dilemma’.
Consider this:
- Two criminals have been arrested who the police know to have committed a crime together
- However, the jury lacks enough admissible evidence for conviction, but enough evidence to lock up each prisoner for two years
The inspector makes the following offer to each of the thieves:
- If you both confess to the crime, you will each get five years
- If you confess to the crime but your partner does not, you will be set free, and your partner will get ten years, and vice versa
- If neither of you confess to the crime, then you will both get two years
This leaves the two criminals in an uncomfortable situation. Assuming they are rational beings, they must act in their own self-interest of serving as little time in prison as possible. However, they realise that their partner will act accordingly. Therefore, they must consider the strategy that will give each of them the least time locked up.
Assume prisoner II confesses. Prisoner I has two choices; to confess or not to confess. If he confesses, he and his partner will get five years. If he does not, he will face ten years in prison. The optimal strategy here is to confess.
Now assume prisoner II does not confess. If prisoner I confesses, he will be set free, but his partner would be sentenced to ten years. If he does not confess, they will both get two years. Again, the optimal strategy here is to confess.
Therefore, prisoner I is better off confessing regardless of what prisoner II chooses. This first action ‘strictly dominates’ the second one, as it is the superior action regardless of what the other prisoner chooses.
The Prisoner’s Dilemma can be represented using a Matrix like this one:
This evidences that whatever the decision of the prisoner’s partner, the ideal choice is to confess.
Beyond a hypothetical situation involving crooks, game theory applies very much to auctions. Auctioned goods have either a private value, when each bidder places a personal value on it, or a common value, when it has the same fundamental value to everybody.
As a bidder, a strategy must be devised in order to win the auction without paying more than what they value it to be worth. The bidder knows how much they value to good or service but doesn’t necessarily know how much others value it. In comes game theory.
As mentioned before, second-price auctions conclude by the sale of the good or service to the highest bidder, at the second highest bid price.
Assuming this is used to sell a phone in which I value the at £50. I then chose to place a bid at £60. There are three consequent outcomes:
- I am outbid by a rival who bids £65, and I do not get the phone. Or…
- A rival bids £40, and I win! I end up paying £40 for a phone I valued at £50 — result. Or…
- A rival bids £55. In this case I win again. However, I end up paying £55 for a phone I valued at 10% less.
Therefore, bidding above my valuation in no case will make be better off. Bidding at my valuation is a ‘weakly dominant’ strategy, unlike the prisoner’s dilemma where there was a ‘strictly dominant’ strategy. I am at least as well off by bidding at my valuation than I am bidding at any other price.
If I was to bid below my valuation, all I am doing is lowering my chances of winning the phone. By bidding differently to my valuation, all I am doing is lowering the chance of winning or increasing the price of which I am paying for the phone.
Across all four auctions, the expected selling price is the same, and this is known as the revenue equivalence theorem.
The final study involves a UK auction for five 3G mobile phone licenses in 2000. Paul Klemperer and Ken Binmore, two experts in game theory, were in charge of designing an auction to achieve three things: to assign the spectrum efficiently; to promote competition; and to “realise the full economic value.”
Through years of testing and computer simulations, they came up with a model that they believed to be the most effective. This involved multiple rounds of simultaneous bids from the entrants. In order to stay in the auction, the bidder had to either hold the top bid for a license or raise the bid by at least the minimum bid increase.
The best strategy for the telecom executives to win a license is to look at all the licenses and submit a bid on whichever looked the most appealing. This meant that bidders were learning from each other of what the 3G licenses were likely to be worth. As the bids went higher, the bidders felt more and more confident that the value was reasonable, so continued to bid.
The government had predicted around £2–3 billion would be raised from these taxes. After almost a month of bidding, on 3rd April, with £10 billion already raised, the first company, Crescent, withdrew. Over the next few days bidders began to drop out. This shows that many of the valuations that the companies had put on the licenses were similar, and as soon as one dropped out, confidence fell, and others realised that maybe the contracts weren’t as valuable as they may have seemed.
By the 27th of April, the auction finally came to an end. The total amount raised stood at £22.5 billion, around nine times the total amount that was expected. Clearly, it was a huge success, and, in the process, it had become the biggest auction sale in history.
Its success was put down to its early planning allowing them time to think through and test their ideas. Furthermore, attracting 13 entrants enabled a competitive bidding prices and even those who did not win any licenses played a role in pushing the prices up higher. The computer simulations as an educational tool were also of great importance in ensuring a smooth bidding process.
However, it must be noted that auctions are not a ‘one-size-fits-all’. Subsequent auctions across Europe had varying success. Deep economic analysis and intellectual endeavour is required in order to come up with appropriate auctions for different economic situations. It’s safe to say that the UK economists got it spot on.
Thus, game theory plays an influential role in society, but also in our everyday actions that we take to increase our outcomes. It still has far to come though, and advancements in its understanding and formulation can bring great benefits to humans; be it world peace or economic optimisation. The younger generation will continue to work upon its foundations and use it as a tool for innovation, equality and power in the future.
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Ted Jeffery
