[Ethereum] How does Casper solve the “Nothing at Stake” issue

The friendly Ghost

Casper is a security-deposit based economic consensus protocol. This means that nodes, so called bonded validators, have to place a security deposit, an action called bonding, in order to serve the consensus by producing blocks.

In Casper style proof of stake anyone can participate in block production by posting a bond. After posting a bond you have an opportunity to bet on which block will be included next. The incentives are such that you make money by betting with the eventual consensus and lose money by betting against the consensus. Any crypto-graphically provable misbehavior results in the forfeit of the bond.

An analogy can be made to proof of work where each miner is betting with their hash power on which block will be accepted. If they bet wrong then any block they produce will be orphaned causing them to lose money.

This protocol has several nice properties:

• Anyone can participate
• Consensus can be reached in a timely manner
• It quickly converges on an irreversible consensus
• It is free of politics

Casper in non-economic terms

Casper is an eventually-consistent blockchain-based consensus protocol. It favours availability over consistency, see the CAP theorem. It is always available, and consistent whenever possible. It is robust to unpredictable message delivery times because nodes come to consensus via re-organization of transactions, after delayed messages are eventually received. It has an eventual fault tolerance of 50%, in the sense that a fork created by >50% correct nodes scores higher than any fork created by the remaining potentially-faulty validators. Notably, though, clients cannot be certain that any given fork created with 51% participation won’t be reverted because they cannot know whether some of these nodes are Byzantine. Clients therefore only consider a block as finalized if it has the participation of a supermajority of validators or bonded stake.

You don't lose anything from behaving badly, you lose nothing by signing each and every fork, your incentive is to sign everywhere because it doesn't cost you anything.

So as it doesn't cost you anything, it's a good strategy to work on each and every chain should a fork occur and double spend a digital good.

Maybe the wiki explains it better :

However, this algorithm has one important flaw: there is "nothing at stake". In the event of a fork, whether the fork is accidental or a malicious attempt to rewrite history and reverse a transaction, the optimal strategy for any miner is to mine on every chain, so that the miner gets their reward no matter which fork wins. Thus, assuming a large number of economically interested miners, an attacker may be able to send a transaction in exchange for some digital good (usually another cryptocurrency), receive the good, then start a fork of the blockchain from one block behind the transaction and send the money to themselves instead, and even with 1% of the total stake the attacker's fork would win because everyone else is mining on both.

Edit: I found this video, this is 4min and explains the issue quite well and with drawing : it makes things quite clear !