Kyoto's underlying principle - that countries that emitted more in 1990 are allowed to emit more in the future - is unacceptable to developing countries, as is granting greater emission rights to countries with a higher GDP. The only principle that has some ethical basis is equal emission rights per capita (with some adjustments - for instance, the US has already used up its share of the global atmosphere, so it should have fewer emission allowances). But adopting this principle would entail such huge payments from developed countries to developing countries, that, regrettably, the former are unlikely to accept it.
Economic efficiency requires that those who generate emissions pay the cost, and the simplest way of forcing them to do so is through a carbon tax. There could be an international agreement that every country would impose a carbon tax at an agreed rate (reflecting the global social cost).
I disagree. There is a good reason that developed countries are given more emission credits than developing countries under Kyoto: it is far more costly to replace an existing carbon-intensive energy infrastructure than to build a new one from scratch. Kyoto recognizes this through its allocation of emission permits on the basis of 1990 emissions levels. Through the trading system, it encourages emission abatement to happen where it is most cost-effective. That usually means in developing countries, who get paid to abate.
If Stiglitz believes that allocating emissions rights to countries on the basis of population is a non-starter for developed countries, then a global tax is even more of a non-starter for developing countries. China would be required to pay more than the United States, even though it is far poorer and had little part in the atmospheric carbon build-up of the past century.
Kyoto may not be perfect, but it is the best idea we have had so far. Given the unknowably high cost of reducing emissions enough to reverse climate change, we owe it to ourselves to seek the most cost-effective ways to do so. That means, to put it bluntly, outsourcing most of the emission reductions to developing countries, which Kyoto lets us do.