Why do we study game theory? As a mathematician, my answer is that game theory is mathematically interesting; I am content as long as I can study interesting models, develop interesting techniques to solve problems, and prove difficult results.
But some of us are closer to the real world than I am, and they claim that game theory is related to real problems. However, as we all know hardly any interactive situation that we encounter in real life fits any model of game theory. The prisoner’s dilemma, which anyone who talks about game theory mentions, was already discussed in this blog, and people noted that the matrix description of the game does not match the actual interaction: Are there no consequences to the prisoners’ decisions? Does the matrix correctly identify the prisoners’ utilities? Are the utilities common knowledge? I am sure that anyone who reads this post will be able to raise more issues with the game representation of the prisoner’s dilemma.
Auctions are another widely cited application of game theory, where a solid theory has been developed. But take the simplest auction: a sealed-bid first-price auction with two bidders; the bidders fight over a contract to supply specific goods to some firm. You may actually encounter such auctions in practice. Now, suppose that you are bidder 1 (or that you are a consultant who was hired to assist bidder 1). Your private value is $1M: this is the minimum amount that you would ask for the contract. You believe that your private value is below the other bidder’s private value by 10%. Well, about 10%. Because the marketing people of the other bidder may have convinced the board of directors that their actual private value is lower than $1.1M. Maybe $1.05M, or even $1M. What is the probability that the private value of the opponent is $1.1M, or $1.05M, or $1M? Give me a break, nobody can say. And what does the other bidder think about your private value? And is the distribution of the private value common knowledge? As you see, the great theory that the books tell us about is not much of a help.
Having said this, I do think that game theory is useful. In fact, very useful. And personally, I use it daily. As I see it, in any given interaction, game theory identifies aspects that each participant should consider before choosing an action. The basic model of game theory tells us that we should identify the game: who are the players, what are their actions, what are their goals. The area of Bayesian games tells us that we should think about the beliefs of the other players, their beliefs about other players’ beliefs, and so on. The area of repeated games tells us that coordination can be achieved by means of threats. Sequential games draw our attention to commitments, subgame perfectness, reputation. Games played by automata help us understand the role of computational power. In short, as I see it, people who do “real-life” game theory develop models that provide insights concerning how to better understand various types of interactive situations. Personally, I like the insights that we as a group provide.