Unit 4 Strategic interactions and social dilemmas

4.14 Modelling the global climate change problem

Why has it proved so difficult for international negotiations to make progress in limiting climate change? The success of the Montreal Protocol in protecting the ozone layer contrasts with the relative failure to reduce emissions responsible for global warming. The reasons are partly scientific. The alternative technologies to CFCs were well developed and the benefits relative to costs for large industrial countries, such as the US, were much clearer than in the case of greenhouse gas emissions.

This article describes the disastrous floods in Pakistan in 2022.

Reducing carbon emissions requires much greater changes, across many industries and affecting all members of society. One of the obstacles at the United Nations’ annual climate change negotiations has been disagreement over how to share the costs and benefits of limiting emissions between countries—and in recent years, the heavy costs some countries now face from the effects of past emissions elsewhere.

To explore the possible situations facing climate negotiators, we will model them as a game between two large countries, hypothetically labelled China and the US, each considered as if it were a single individual. First, we identify possible equilibria when each country behaves strategically; then we can think about how an agreed outcome might be achieved.

Figure 4.23a shows the outcomes of two alternative strategies: Restrict (taking measures to reduce emissions, for example by regulating or taxing the use of fossil fuels) and BAU (continuing with ‘business as usual’).

This diagram shows China and the US’ available actions, which are Restrict and BAU. If both countries choose Restrict, the reduction in emissions is sufficient to moderate climate change. If China chooses Restrict and the US chooses BAU, the US free rides on Chinese emissions cutbacks. If China chooses BAU and the US chooses Restrict, China free rides on US emissions cutbacks. If both countries choose BAU, there is no reduction in emissions.
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Figure 4.23a Outcomes of climate change policies.

What we can expect to happen depends on the pay-offs in each outcome. The essential features of the problem can be captured using an ordinal scale from Best to Worst: it is the order of the pay-offs, not the size, that matters. Figure 4.23b shows two games, corresponding to different sets of hypothetical pay-offs.

There are two diagrams. Diagram 1 shows China and the US’ available actions in this prisoner’s dilemma game, which are Restrict and BAU. If both countries choose Restrict, both receive good payoffs. If China chooses Restrict and the US chooses BAU, China gets the worst payoff and the US gets the best payoff. If China chooses BAU and the US chooses Restrict, China gets the best payoff and the US gets the worst payoff. If both countries choose BAU, both countries receive bad payoffs. Diagram 2 shows China and the US’ available actions in a game with inequality aversion and reciprocity, which are Restrict and BAU. If both countries choose Restrict, both receive the best payoffs. If China chooses Restrict and the US chooses BAU, China gets the worst payoff and the US gets a good payoff. If China chooses BAU and the US chooses Restrict, China gets a good payoff and the US gets the worst payoff. If both countries choose BAU, both countries receive bad payoffs.
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Figure 4.23b Two different climate policy games.

If you work out the best responses and find the Nash equilibria in each case, you will realise that these two games are similar to cases we have already analysed. The left-hand one is a prisoners’ dilemma, in which BAU is a dominant strategy for each country, leading to a Bad outcome for both. The game on the right is a coordination game, similar to the rice–cassava game in Figure 4.21, except that the players would like to coordinate on the same strategy, rather than the opposite one. There are two Nash equilibria: one is the Best outcome, in which both countries restrict emissions. But the Bad outcome in which neither do so is also an equilibrium, and if each country expects the other to choose BAU following their past behaviour, we can predict that they may be stuck in the (BAU, BAU) equilibrium.

In each case, negotiation may be able to improve the outcome. Exercise 4.17 will help you work out which of these two games better represents the problem facing China and the US, and the implications for negotiations between them.

Exercise 4.17 Nash equilibria and climate change

Consider the two games presented in Figure 4.23b.

  1. Consider the pay-offs when one country plays Restrict while the other plays BAU. Why might a country view restricting when the other country plays BAU as the worst possible outcome?
  2. In the prisoners’ dilemma version (left panel), each country thinks the best possible outcome is that they play BAU while the other country plays Restrict. But in the coordination version (right panel), each country thinks the best possible outcome is that both play Restrict. Explain why they may hold these views and what that could indicate about their preferences, in either case.
  3. In both games, the outcome would be better for both countries if they could negotiate a binding treaty to restrict emissions. Use the concepts you have learned in this unit to explain why it might be difficult to achieve such a treaty.
  4. Choose one of the games shown (prisoners’ dilemma or coordination game) and describe the changes in preferences or in some other aspect of the problem that would convert that game to one in which (like the invisible hand game) both countries choosing Restrict is a dominant strategy equilibrium.

Figure 4.23c presents a third model. It also shows the players’ best responses, and hypothetical numerical pay-offs indicating the value of each possible outcome to the citizens of each country. The worst outcome for both countries is that both persist with BAU, thereby running a significant risk of human (and many other species’) extinction. The best for each is to continue with BAU and let the other one Restrict. The only way to moderate climate change significantly is for both to Restrict.

This is another coordination game with two equilibria, but now (as in Astrid and Bettina’s coding game) there is a conflict of interest between the players.

There are two diagrams. Diagram 1 shows China and the US’ available actions in this prisoner’s dilemma game, which are Restrict and BAU. If both countries choose Restrict, both receive good payoffs. If China chooses Restrict and the US chooses BAU, China gets the worst payoff and the US gets the best payoff. If China chooses BAU and the US chooses Restrict, China gets the best payoff and the US gets the worst payoff. If both countries choose BAU, both countries receive bad payoffs. Diagram 2 shows China and the US’ available actions in a game with inequality aversion and reciprocity, which are Restrict and BAU. If both countries choose Restrict, both receive the best payoffs. If China chooses Restrict and the US chooses BAU, China gets the worst payoff and the US gets a good payoff. If China chooses BAU and the US chooses Restrict, China gets a good payoff and the US gets the worst payoff. If both countries choose BAU, both countries receive bad payoffs.
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Figure 4.23c Best responses in a climate change game with a conflict of interest.

The hawk–dove game is sometimes called the chicken game: in the 1984 film, Footloose, two high-school students challenge each other by driving tractors towards each other, to see which one will ‘chicken out’ first.

hawk–dove game
A coordination game in which the players want to coordinate on the opposite action from their opponent, and in each of the Nash equilibria, (Hawk, Dove) and (Dove, Hawk), the Hawk obtains the higher pay-off; but both players choosing Hawk is the worst outcome for both.

This game is what is termed a hawk–dove game: players can act like an aggressive and selfish Hawk, or a peaceful and sharing Dove. In the climate change version, Doves Restrict and Hawks continue with BAU. The conflict of interest is that each country does better if it plays Hawk while the other plays Dove.

It captures a situation that is different from the previous two. Both countries have incentives to avoid catastrophic climate change. But they strongly prefer that the other should bear the costs of reducing emissions: each would like to wait to determine if the other will move first.

The Pareto-efficient allocation in which both countries restrict emissions also has the highest joint pay-offs. We can think of this as the best outcome for the world as a whole. But it is not an equilibrium.

Applying the hawk–dove game to climate policy

How do you think the hawk–dove game would be played in reality? Can the conflict of interest be resolved?

If one country could commit itself to BAU so that the other was certain that it would not consider any other strategy, then the other would play Restrict to avoid catastrophe. But this is true for both countries.

Negotiations are bound to be difficult, since each country would prefer the other to take the lead on restricting carbon emissions. The real climate negotiations are of course more complex—virtually all countries in the world are involved. Pay-offs may be different for these varied players. For example, in 2021 China produced 31% of the world’s total carbon emissions, the US was second with 44% of China’s level, followed by India. On a per-capita basis, China produced 55% of the emissions that the US did, and India produced 13% of US emissions.

Using public policy to change the game

How could the global social dilemma of climate change policy, as represented in this game, be solved?

Could the governments of the world simply prohibit or severely limit emissions that contribute to the problem of climate change? This would amount to changing the game by altering available strategies by making BAU illegal. But who would enforce this law? There is no world government that could take a government that violated the law to court (and lock up its head of state!).

If the climate change social dilemma is to be addressed, Restrict must be in the interests of each of the parties. Consider the bottom-left corner (China plays BAU, US plays Restrict) equilibrium. If the pay-offs to China for playing Restrict were higher, when that is what the US is doing, then (Restrict, Restrict) might become an equilibrium.

Indeed, in the eyes of many climate change scientists and concerned citizens, the aim of global environmental policy is to change the game so that (Restrict, Restrict) becomes a Nash equilibrium. A number of mechanisms, aided by policy, could accomplish this:

  • Sustainable consumer lifestyles: As a result of their concern for the wellbeing of future generations, people could come to prefer lifestyles that use fewer goods and services of the kind that result in environmental degradation. This would make the Restrict policy less costly and the BAU strategy less desirable.
  • Governments could stimulate innovation and the diffusion of cleaner technologies: They might do this by, for example, raising the price of goods and services that result in carbon and other emissions, which would discourage their use. In the process, the use of cleaner technologies would become cheaper, lowering the cost of Restrict. For example, renewable energy has become much cheaper. In some regions, it is now the cheapest energy option, which means Restrict is no longer more expensive than BAU. Self-interested behaviour will result in lower carbon emissions.
  • A change in norms: Citizens, non-governmental organizations (NGOs), and governments can promote a norm of climate protection and sanction or shame countries that do nothing to limit climate change. This would also reduce the attractiveness of BAU.
  • Countries can share the costs of Restrict more evenly: This is possible if, for example, a country for whom Restrict is prohibitively expensive instead helps another country where it is less expensive to Restrict. An example would be paying countries in the Amazon basin to conserve the rainforest.

After initial setbacks, China and the US issued a joint declaration at the 2021 climate summit in Glasgow, committing to work together towards the goals of the Paris Agreement.

Following the 2015 Paris Agreement, almost all countries submitted individual plans for cutting emissions. Although there is no way that the agreement could be enforced, and these plans are not yet consistent with the goal of limiting the global temperature rise to 1.5°C, it is widely considered as a basis for further international cooperation. The Paris Agreement should:

  • allow countries to better understand the costs of restricting emissions
  • encourage economic players to innovate in order to further lower the costs
  • strengthen norms that reduce the attractiveness of BAU
  • establish a base of trust to share some of the costs of Restrict and negotiate more ambitiously in the future.

Exercise 4.18 Summary of games in this unit

Use the categories in the table shown to classify each game presented in this unit. In the final column, write down one or two key features that help you identify a game that belongs to that category.

Type of game Categories Examples Key features
Simultaneous two-player games Invisible hand games
Prisoners’ dilemmas
Coordination games—without conflict of interest
Coordination games—with conflict of interest
Games with more than two players Public good games
Sequential two-player games Ultimatum game