An Information Technology Example Revisited

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When we looked at "Choosing an Information Technology," one of the two introductory examples, we came to the conclusion that it is more complex than the Prisoners' Dilemma in several ways. Unlike the Prisoners' Dilemma, it is a cooperative game, not a noncooperative game. Now let's look at it from that point of view.

When the information system user and supplier get together and work out a deal for an information system, they are forming a coalition in game theory terms. (Here we have been influenced more by political science than economics, it seems!) The first decision will be whether to join the coalition or not. In this example, that's a pretty easy decision. Going it alone, neither the user nor the supplier can be sure of a payoff more than 0. By forming a coalition, both choosing the advanced system, they can get a total payoff of 40 between them. The next question is: how will they divide that 40 between them? How much will the user pay for the system? We need a little more detail about this game before we can go on. The payoff table above was net of the payment. It was derived from the following gross payoffs:

Table A-2

How much will be paid? Here are a couple of key points to move us toward an answer:

 
• The net benefits to the two participants cannot add up to more than 40, since that is the largest net benefit they can produce by working together.
• Since each participant can break even by going it alone, neither will accept a net less than zero.

Using that information, we get Figure A-1:

Figure A-1

The diagram shows the net payoff to the supplier on the horizontal axis and the net payoff to the user on the horizontal axis. Since the supplier will not agree to a payment that leaves her with a loss, only the solid green diagonal line -- corresponding to total payoffs of 40 to the two participants -- will be possible payoffs. But any point on that solid line will satisfy the two points above. In that sense, all the points on the line are possible "solutions" to the cooperative game, and von Neumann and Morgenstern called it the "solution set."

But this "solution set" covers a multitude of sins. How are we to narrow down the range of possible answers? There are several possibilities. The range of possible payments might be influenced, and narrowed, by:

• Competitive pressures from other potential suppliers and users,
• Perceived fairness,
• Bargaining.

There are game-theoretic approaches based on all these approaches, and on combinations of them. Unfortunately, this leads to several different concepts of "solutions" of cooperative games, and they may conflict. One of them -- the core, based on competitive pressures -- will be explored in these pages. We will have to leave the others for another time.

There is one more complication to consider, when we look at the longer run. What if the supplier does not continue to support the information system chosen? What if the supplier invests to support the system in the long run, and the user doesn't continue to use it? In other words, what if the commitments the participants make are limited by opportunism?

Roger A. McCain