PERVERSE PAYOFF

Dick Pountain/15 July 2007/14:35/Idealog 156

At some time or other you may have used a piece of utility software from the cover disk given away with this magazine: I certainly have, examples including Fineprint, pdfFactory Pro and FTP Explorer. However I'd like to believe that you buy PC Pro for the rivetting reading it contains, particularly its internationally-reknowned columnists, rather than because of the contents of that wretched disk. Why wretched? Because it costs us good money to assemble and mount that disk that might have been spent on other editorial, and we are after all in the words business, not the software business. But we have to keep doing it so long as all our competitors do because we can't take the risk that you might switch brands if we stopped. The logic is that of the Cold War nuclear arms race, where neither side could quit and there's a constant tendency toward escalation. I notice with a certain amount of malicious glee that we're not alone, because the national newspapers have just got themselves into the same fix over giveaway movie DVDs.

 Since it costs all of us publishers so much to give away cover disks, it would pay us to collude by all agreeing to drop the disks simultaneously, but that would be an illegal restraint of trade, a cartel, and mustn't happen. So here you have an example of a perverse market incentive that persuades all of us to behave in a way that reduces our profits. I've written in this column before about my interest in Games Theory, in particular its application to economics, and this cover disk saga is an example for which I've recently encountered a lovely games theoretic model.

 The game was invented in 1994 by Professor Kaushik Basu of Cornell University, who called it The Traveler's Dilemma to emphasise its similarity to the far better-known Prisoner's Dilemma (which models the advantages and disadvantages of cooperation versus competition). The scenario runs like this: Dave and DeeDee are returning from a holiday in Cambodia carrying identical temple lamps as souvenirs, but these both get broken by their budget airline's crazed baggage handlers. The airline manager at Stansted agrees liability and offers compensation, but he has no idea how much the lamps were worth, and being a cynical type reasons that simply asking Dave and DeeDee what they paid will tempt them to lie and inflate the value. Being also adept in Games Theory he instead devises a cunning plan which goes like this: he asks Dave and DeeDee separately to write down their price as an integral number of pounds between £2 and £100, without conferring. If they both write the same price he'll pay them each that sum, but if they write different prices he assumes the higher one is fibbing and will only pay the lower price. What's more, to reward honesty he'll take £2 away from the high-price fibber and give it to the low-price truth teller. So for example if Dave wrote £100 and DeeDee wrote £40, then he'd pay DeeDee £42 and Dave only £38.

 Now if I were in this situation with someone I knew well, after no more than a sly sideways glance we'd both write £100 and trouser that amount as a result. But if we did that we'd be acting irrationally, and not at all as the sort of value-maximising machines that modern economists believe us to be. The problem is that were either of us very greedy, we could get paid more than £100: if I guess that my friend is going to write £100 I could write £99 which means that I'll get paid £101 and she only £97. A further problem is that, she being as smart as me sees this coming and in fact decides to write £98, which means she'll get £100 and I only £96. By repeatedly following such reasoning we would each keep undercutting one another all the way down to £2 which, believe it or not, is the "rational" solution that economists would predict using John F. Nash's equilibrium theory (that same Nash portrayed by Russell Crowe in "A Beautiful Mind").

 If you shrink the permitted price range from £2-100 to £2-3, then Traveler's Dilemma (TD) becomes identical to Prisoner's Dilemma (PD) in which the rational solution is also for both parties to act treacherously and greedily and hence receive less than they would have done by being nice. Both TD and PD undermine the libertarian assumption that people acting selfishly will automatically produce the best outcome for society as a whole (an assumption often attributed to Adam Smith who in fact believed nothing of the sort). In TD the most efficient outcome is not the rational outcome but the one produced by irrationally cooperating, namely £100 each. TD also illustrates the logic of arms races (or cover disk races) in which gradually, by taking small and wholly rational steps, the parties move toward worse and worse outcomes. Most players of TD actually choose numbers in the high '90s rather than the Nash equilibrium £2, and the best guess as to why is that most of us are torn between greed and niceness, leaning toward the latter, and are not much good at games theory...