Burden Sharing and Self-enforcing Climate Agreements〇⼤堀秀⼀1，太⽥勝憲2
Shuichi Ohori, Katsunori Ohta
1. Introduction
A world's scientific consensus maintains that climate change is due primarily to the human useof fossil fuels and carbon dioxide released is the main greenhouse gas (GHG). Recent IPCC
report (2018) requires the unprecedented change of society and the drastic reduction of GHG
emissions asked to stop climate change over 1.5 degrees and to avoid the worst-case scenarioof climate change. However, since climate change is a global public bad and there is nosupranational enforcement authority, individual countries are tempted to free-ride and letothers abate. For the settlement of this issue, the global community has struggled to makeinternational environmental agreements over the past three decades, and it has considered theallocation of emissions among countries.
This paper aims to find a new scheme of burden sharing to make the agreements stable byderiving the optimal allocation of GHG emissions among countries. Equity that is the principleof `fairness' is the basis of burden sharing in climate agreements. All countries have widelyaccepted the principle in the agreements such as the Kyoto Protocol and the Paris Agreement.
However, how equity considerations make the treaties self-enforcing in the long term is lessclear. Hence, we address this question by using the dynamic framework. Further, to focus on
the burden sharing rules, it is necessary to consider heterogeneity in the payoff structure
between countries.

2. Basic setup
This paper presents the repeated-game framework in which heterogeneous countries emit
GHG in every period. For simplicity, we assume that the two countries are members of theclimate agreement, and all emission decisions are observable. We can interpret a country as agroup. The agreement chooses the target level of total emissions that is less than the oneshot Nash equilibrium level, and then allocates the emission quotas for the countries. We
describe the agreement as to the trigger strategy in which a deviation from the agreement
results in the withdrawal of all countries from the agreement. Making the agreement selfenforcing, we construct the trigger strategy that describes the agreement as a subgameperfect equilibrium.

1

関⻄⼤学総合情報学部 Faculty of Informatics, Kansai University,

2-1-1, ohori@kansai-u.ac.jp
2

和歌⼭⼤学経済学部 Faculty of Economics, Wakayama University〒569-1095 ⼤阪府⾼槻市霊⼭寺町

3. Results
One of the main results in this paper is about a scheme of allocating emission quotas
to make the agreement the most stable. We find the optimal emission quotas that equalize
the incentive to comply with the agreement between countries. Compliance incentive
equalization means that the temptations to deviate from the agreement should be equalized
between countries through finding the optimal emission quota. Suppose one country has
a stronger temptation to deviate from the agreement. That is, the opponent country
has a greater slack of incentive to comply with the agreement. In this situation, transferring
the slack of the incentive across countries through reallocating emission quotas makes
the agreement more stable. This is because permitting more emissions mitigates thetemptation to deviate. The improvement of the stability continues until the two countries'
compliance incentives become equal. We show that the more emitting country in the status quo(the one-shot Nash equilibrium) can emit more in the optimal emission quota. This type ofemission allocation could be associated with the grandfathering rule, which means that future
emission quotas should depend proportionally on existing and/or past emissions level of thecountry. We can justify the grandfathering rule from the viewpoint of compliance incentives. On
the other hand, we also show that there are cases in which a country who emits less in thestatus quo should have a larger reduction rate of emission at the optimal emission quota.
Some comparative statics and an extension lead to several policy implications. First, weconsider the effect of mitigating total target emission level. We show that avoiding an ambitious
target total emission level is in the interest of countries with a larger burden. It might lead tothe deviation of the countries permitting small emission reduction rate. Second, we consider
the effects of technology investments on the stability of agreements. In particular, clean
technology investment that decreases the marginal benefit of the own emission results in thedecrease of the emission level in the status quo. This improves the compliance incentive forthe investing country, while it worsens the other’s incentive. The former effect comes fromdecreasing cost of emission reduction for the investing country. The latter arises from thesmaller status quo emission level, which means weaker punishment. The result implies that thetransfer of clean technology improves the compliance incentive of the recipient country.
Finally, we apply the idea of allocating emission quota to improve the stability of climateagreements to the situation where countries have heterogeneous discount factors. The
transfer of clean technology investment also works to improve the stability in such a situation.
This is because the transfer of clean technology improves the compliance incentive of therecipient country at the sacrifice of the donor country.

References
IPCC, 2018. Global warming of 1.5, https://www.ipcc.ch/sr15/.