Feb 1, 2021 —

In the prior post, I concluded that the UN climate game, since the signing of the Kyoto accord, has been a voluntary public-goods game and that such games are known to cause a downward spiral of ambition (altruism). An alternative (the Preface Game) described in the preface of Global Carbon Pricing (free PDF), showed that changing the game could dramatically improve player cooperation. However, this game unrealistically contained a small amount of enforcement. So another game is needed.

There are many possibilities, but the most obvious is to look for a game that mimics the Preface Game without any enforcement. As a reminder, the Preface Game is this:

1. On each turn, players make a binding pledge of between $0 and $10.
2. A referee accepts from each player only a contribution equal to the minimum pledge, and this is added to the common pot.
3. The money in the pot is doubled and divided equally among the players.

Hence, if the minimum pledge is $2,  each player will contribute $2, which is doubled and each receives $4 for a net gain of $2. Doubling reflects the fact that climate benefits are greater than abatement costs.

A Reciprocal-Voluntary-Agreement Game

The first step in designing the new game is to drop the referee who enforces the least-pledge rule. Because forcing countries to do less than they are willing to do, is a rather weak sort of enforcement, we are not giving up too much.

The next step toward realism is to admit that players cannot voluntarily cut their contributions to equal the lowest contribution in a single turn. If a country pledges $10 and contributes $1, other players will not find that out until it’s too late. So if players are to reciprocate, it must be with a one-turn delay.

The next problem is that the referee provides coordination by imposing the same partial strategy on all players. Doing without this coordination is a major problem. A related problem is that most players probably will not invent an effective strategy. Few would guess that having a referee restrict all contributions to the lowest pledge would cause perfect cooperation.

The solution to both the coordination and good-strategy problems should be sought in a cooperative agreement. As I’ve noted, this needs to be voluntary (at least in the early years). And as in the Preface Game, the agreement should be reciprocal, which means something like Tit for Tat. If someone contributes little, everyone else does the same on the next turn. If all contribute a lot, then everyone does that again on the next turn.

So what we are looking for is an RVA, a reciprocal voluntary agreement, that mimics the Preface Game.

A sketch of the RVA climate Game

Tit for Tat (TFT) gets a little confusing when there are many players. To make sense of it, I will classify players as either Good or Bad. All are initially classified as Good.

To keep the agreement simple it will specify a contribution Norm at the start of each turn and the agreement will be that all will contribute the Norm amount.

Of course, there is no force behind this agreement so no one is explicitly penalized if they contribute less than the norm or even $0. However, anyone who contributes less than the Norm is re-classified as “Bad.”

The complicated part of the agreement is the rule for calculating the Norm. Roughly it works like this:

1. If all players are Good, the Norm = the cooperative Goal
2. Otherwise the Norm = Min( Bad player contributions )
3. A Bad player is reclassified as good when her contribution ≥ the Norm

The next post will explain the “Goal” and give an example to show how similar the RVA game is to the Preface Game, and why it might fail if players are too altruistic.