Benefiting from Prisoners Dilemma


Benefiting from Prisoners’ Dilemma

If you’re being charged too much, you should consider exploiting prisoners’ dilemma. Prisoners’ dilemma creates varying degrees of pressure for firms to betray each other and lower prices. Imagine that two firms supply your company with widgets and the following facts hold:

  • You buy 1,000 widgets a week from each of two suppliers.

  • Both suppliers sell widgets for $10 each.

  • Both suppliers can make widgets for free.

  • Your firm is a major purchaser of widgets.

The widget companies are making significant profits from you, since it costs them nothing to make each widget. I imagine that you would first try to negotiate a discount with each supplier. The suppliers, however, prefer charging high prices and should lower their prices only if you can make it in their interests to do so by, say, plunging them into a prisoners’ dilemma. A prisoners’ dilemma must involve both a reward and a punishment. To create a prisoners’ dilemma for the widget firms, you should reward a firm if it is the only company to lower prices, and punish a firm only if it does not offer a discount.

Currently, both firms sell you 1,000 widgets a week for $10 each, making a profit of $10,000 a week. To create a prisoners’ dilemma you need to offer a firm a profit of more than $10,000 a week if only it lowers prices. If only one firm cuts prices, you should (a) buy all your widgets from this firm and (b) offer this firm a price so that it will make more than $10,000 a week in profits.

Let’s say you give this firm a profit of $6 a widget. So you tell both firms that if only one of them lowers its price to $6, you will buy all 2,000 widgets from that firm, giving it a profit of $12,000 a week. Clearly, since it costs nothing to produce this good, both firms would prefer to sell 2,000 widgets at $6 each than 1,000 widgets at $10 apiece. If one firm lowers its price and the other does not, the firm that doesn’t cut prices will get zero profit. If both firms lower their price to $6 each, assume that you will still buy 1,000 widgets from each firm. Figure 43 shows the new prisoners’ dilemma game you have created in which both players have a dominant strategy to charge $6 per widget.

click to expand
Figure 43

Unfortunately, your task may not be finished, for you have just created a repeated prisoners’ dilemma game. If a repeated prisoners’ dilemma game has no definite ending date, then it’s still possible that the two firms will continue to charge $10 a widget. Each firm may reason that yes, it could make more this week by charging $6 a widget, but it’s better off in the long run if both firms keep charging $10 a widget and split the market. If the game had a definite ending date, then the logic of prisoners’ dilemma would compel the firms to immediately lower their price to $6.

Even if it would be a lie, you might want to tell both suppliers that after a certain date you would no longer want any widgets. A last period would make it much more difficult for the firms to maintain high prices. Remember, in the last period in a prisoners’ dilemma game rational players will always betray each other and knowledge of this future betrayal will cause the players to betray each other in every previous period. Unfortunately, if these two suppliers also sell widgets to other companies, then the game won’t end when you leave the market. The fewer widgets the firms expect to sell in the future, however, the greater incentive each firm has to betray its competitor today. Thus, your falsely announcing that you will soon leave the market will increase the incentives for both firms to cheat by lowering prices. You could also induce the firms to cheat by exploiting hidden action problems.

Imagine that in this example both firms refused to lower their price to $6. What would happen if you started buying all your widgets from just firm one? You would still have to pay this firm $10/widget, but what would the other firm think? Firm two might suspect its luckier rival was really giving you a discount. Even if firm one promised its rival that it wasn’t cutting prices, the rival might still suspect treachery. After all, if firm one really were charging you $6 a widget, it would obviously have an incentive to lie about it to firm two. To add to the mistrust you might even want to lie to firm two by asking it to match firm one’s price of $6. If firm two thought that it was being taken advantage of, it would almost certainly lower its price. Of course, even if firm two did not believe that firm one had lowered its price, firm two would still be upset if you gave firm one all of your business and might lower its price anyway.

Chaos is your friend when seeking lower prices. If you are an important customer to your suppliers, then they strongly benefit from charging you high prices. Whenever suppliers are charging you high prices they are in a repeated prisoners’ dilemma game. All suppliers know that they could significantly increase their sales to you by lowering their prices a bit. Fear of retaliation may prevent a supplier from cutting its price. Each supplier, however, also knows that if it could secretly charge you a lower price, then perhaps it could increase its sales without having other firms lower their prices too. Since all suppliers realize the game they’re in, they should never fully trust each other. Random fluctuations in prices could cause a supplier to believe it is being betrayed. If market prices just happen to fall, a supplier might suspect its rival is giving secret discounts and respond by lowering its price. To multiply suppliers’ mistrust you should do something strange like giving all your business to just one supplier so the other suppliers might suspect treachery. Perhaps you should even give all of your business to the supplier who appears to be charging the most. The other suppliers might then become convinced that they are being taken advantage of; otherwise why would the high-price supplier be getting all of your business? By creating chaos you can multiply the mistrust the suppliers have toward each other and perhaps cause them to betray their competitors by decreasing prices.




Game Theory at Work(c) How to Use Game Theory to Outthink and Outmaneuver Your Competition
Game Theory at Work(c) How to Use Game Theory to Outthink and Outmaneuver Your Competition
ISBN: N/A
EAN: N/A
Year: 2005
Pages: 260

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