What are the economics and incentives to various parties in the system to cooperate and behave?

Every atom submitted to a public network is submitted with a transaction fee. This transaction fee is shared equally by the nodes that provide the temporal proof. Nodes which provide the temporal proof are selected randomly, with a bias towards those that are maintaining both shards of a transaction span (almost all transactions are inter-shard due to the huge shard space and the way that a shard address is generated). Only a valid temporal proof receives a fee.

For more information, see: https://papers.radixdlt.com/incentives/#incentives