In a cost-benefit analysis one should assess the damage due to the increase in the average surface temperature of the atmosphere and seek a balance between the cost of emission reductions and the benefit resulting from the reduction in damage. In a cost-effectiveness analysis, on the other hand, one would set a constraint, e.g. limiting the concentration of GHGs in the atmosphere, or limiting the temperature increase to 1.5oC, and try to satisfy this constraint at least cost. In general, economists prefer the cost-benefit approach, but in the case of climate economics the difficulty of translating the ecological damage caused by an increase in atmospheric and oceanic temperature into monetary units is immense. That is why, at COP 21, when the Paris agreements were signed, a simple target was formulated to limit the temperature increase by the end of the 21st century to 1.5oC or 2oC in the worst case. In addition, the climate dynamics community has proposed a concept that is very easy to take into account in a cost-effective approach, that of a "cumulative safety emissions budget". To keep the temperature increase below 2oC by the end of the 21st century with a sufficiently high probability, the cumulative sum of all GHG emissions since the beginning of the industrial revolution (around the year 1870) would have to be less than about 1000 Gigatonnes of carbon (3600 Gt of CO2). ORDECSYS therefore sought to integrate this constraint on the cumulative emissions budget into a cost-effective approach to assessing the macro-economic effects of the Paris agreements.

Olivier Bahn and Alain Haurie. A cost-effectiveness differential game model for climate agreements. Dynamic Games and Applications, Vol. 6, issue 1, pp. 1-19, 2016.

In this paper, we propose a model of a dynamic (i.e. competitive) game between industrialised, emerging and developing countries that must together meet a global climate constraint. For each group of countries, a model of economic growth is formulated in which two different types of economies can coexist, called respectively 'low-carbon' and 'high-carbon', each with different productivities of capital and emissions due to energy use. This allows us to schematise the necessary energy transition and its costs.

We assume that each group of countries participating in the negotiations has identified a damage function, which determines a loss of GDP due to global warming, and also has the possibility of investing in a type of capital (equipment, know-how, etc.) allowing adaptation to climate change. The climate agreements we consider have two main components: (1) they define an overall emissions budget for a commitment period and impose it as a limit on cumulative emissions during that period; (2) they distribute this overall budget among the different coalitions of countries participating in the agreement. This implies that the game now has a coupled constraint for all participants in the negotiations. The outcome of the agreement is thus obtained in the form of a generalized equilibrium or "Nash-Rosen equilibrium" which can be chosen from a variety of such solutions. We show that the family of Nash equilibria in games obtained by distributing the total budget among the different parties corresponds to the variety of normalised equilibria. We then propose a fair distribution of this total emission budget.

IPCC, Climate Change 2022

Mitigation of Climate Change 

Historical cumulative net CO2 emissions from 1850 to 2019 were 2400 ± 240 GtCO2 (high confidence). Of these, more than half (58%) occurred between 1850 and 1989 [1400 ± 195 GtCO2 ], and about 42% between 1990 and 2019 [1000 ± 90 GtCO2 ]. About 17% of historical cumulative net CO2 emissions since 1850 occurred between 2010 and 2019 [410 ± 30 GtCO2 ].10 By comparison, the current central estimate of the remaining carbon budget from 2020 onwards for limiting warming to 1.5°C with a probability of 50% has been assessed as 500 GtCO2 , and as 1150 GtCO2 for a probability of 67% for limiting warming to 2°C. Remaining carbon budgets depend on the amount of non-CO2 mitigation (±220 GtCO2 ) and are further subject to geophysical uncertainties. Based on central estimates only, cumulative net CO2 emissions between 2010 and 2019 compare to about four-fifths of the size of the remaining carbon budget from 2020 onwards for a 50% probability of limiting global warming to 1.5°C, and about one-third of the remaining carbon budget for a 67% probability to limit global warming to 2°C. Even when taking uncertainties into account, historical emissions between 1850 and 2019 constitute a large share of total carbon budgets for these global warming levels.11,12 Based on central estimates only, historical cumulative net CO2 emissions between 1850 and 2019 amount to about four-fifths of the total carbon budget for a 50% probability of limiting global warming to 1.5°C (central estimate about 2900 GtCO2 ), and to about two thirds of the total carbon budget for a 67% probability to limit global warming to 2°C (central estimate about 3550 GtCO2.