When the question is asked regarding whether great powers are finding it more difficult to cooperate, my immediate response is that perhaps the wrong question is being asked. Difficulty in cooperation implies a desire for cooperation, an effort being made that is somehow failing due to inability despite action or an outside force that is intervening. This, arguably, isn’t the case. While the clear divide of the bipolar system that existed during the Cold War is gone, that is no reason to claim that all countries, even all great powers, now have the same interests. Given these differing interests, cooperation may not always be in the best interest of the great powers.
Mearsheimer describes the idea of “cheating” as being one of the primary concerns that liberal institutionalism focuses on; essentially, states may be reluctant to join in agreements with each other out of fear of the other breaking the agreement and doing possible devastating damage. As he points out, this reason for hesitation in forming agreements is only relevant when the states have some common interests to begin with, and is unhelpful when discussing states that have no goals which overlap in relation to the proposed treaty or agreement. If State A wants X and State B wants Y, the idea of them forming an agreement is nonsensical. As such, for the question of Ukraine, as pointed out by Schroeder and Banks, the question may not be whether or not there is some external force stopping them, but that their goals are just too different for an agreement to be made about actions that need to be taken.
To step away from a semantics debate, perhaps the more interesting question is whether these troubles—whether in finding common ground or in actually working together once that common ground has been found—are because of new power relations in the world.
The obvious answer to this question is yes. The Cold War is over, having left what was once the Soviet Union in shambles. The world isn’t a bipolar system anymore, and even if it were, it seems unlikely that the argument would be made for Russia being the other half of the power block anymore.
There are also more states in the world now than there have ever been. The number of UN member states has close to doubled since 1960, and even since the end of the Cold War the number of UN member states increased from 179 to 193. The massive change in the number of states inherently includes some corresponding changes in the power system of the world.
On the other hand, the world is still in the same basic system as it has been since decolonization following the World Wars. Gone are the days of empires, and instead the world is in the stage of independent sovereign states. The United Nations is decades old, and theoretically any settling of the system to be done has already happened, and it will not change dramatically going forward.
Overall, it’s not simple to say either way regarding the newness of the power relations in the world. Perhaps that is why there is a lack of agreement, but perhaps the reason is a difference in interests.