Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

Optimal Climate Change Policies When Governments Cannot Commit

This paper examines the optimal design of climate change policies in the context where governments want to encourage the private sector to undertake significant immediate investment in developing cleaner technologies, but the carbon taxes and other environmental policies that could in principle stimulate such investment will be imposed over a very long future. The conventional claim by environmental economists is that environmental policies alone are sufficient to induce firms to undertake optimal investment. However this argument requires governments to be able to commit to these future taxes, and it is far from clear that governments have this degree of commitment. We assume instead that governments cannot commit, and so both they and the private sector have to contemplate the possibility of there being governments in power in the future that give different (relative) weights to the environment. We show that this lack of commitment has a significant asymmetric effect. Compared to the situation where governments can commit it increases the incentive of the current government to have the investment undertaken, but reduces the incentive of the private sector to invest. Consequently governments may need to use additional policy instruments – such as R&D subsidies – to stimulate the required investment.