What happens when two players play the same game at different difficulties?

Summarized results:

• Happiness is calculated based on individual player's difficulty.
• Bonus vs. Barbarians uses the lowest player's difficulty
• The AI starts use the lowest player's difficulty.
• Rewards from ruins are either based on individual player difficulty or lowest player's difficulty
• Culture costs are based on individual player difficulty.
• Not sure on City State Bonuses, will probably test those tonight. I assume they will use the lowest player's difficulty.
• Not sure on AI skill, I assume they will use the lower player's difficulty. I probably won't be able to test this due to the length of Civilization games.

Onto the proof, first the two testing parameters: vs.

Happiness works as expected:

I have a starting happiness of 6 after my first city on deity. Cartecs has a happiness of 15 on Settler.

vs.

I have a happiness of 15 on settler difficulty with cartec's playing on deity.

Interestingly, it looks like it uses the lowest player's difficulty for barbarian fights:

I'm playing on deity difficulty here with a settler difficulty human in the game:

vs.

I'm playing on settler difficulty here with a deity difficulty human in the game:

vs.

Lone human at deity difficulty:

AI Starts:

Turn 9 in both cases:

Playing on settler with another human on deity results in computer's using settler starts:

vs.

This is a game with just me playing on deity difficulty.

I saw further proof in both games. While playing the multiplayer Japan managed one city by turn ~14. In the deity game alone, Egypt managed two cities and multiple warriors. This is consistent with settler vs. deity starts.

As a settler difficulty player I was able to find settlers in ruins, and get a lot more upgrades quickly. As a deity player I did not notice a particular increase in ruin rewards. This doesn't really prove much beyond the fact it either uses the lowest difficulty bonus or uses the individual bonuses.

As a settler player it cost 10 culture to get the first policy. As the deity player it cost 25 culture to get the first policy. You can see this in the happiness screenshots.

Besides the great results that Rapida posted, it is also important to note that the difficulty a player is at determines the difficulty that the AI will be at if they player gets replaced by an AI (due to dropping out). So while having a player set to Deity will make it harder on that player, it will make it harder on the other players if that person drops out and is replaced by a Deity level AI (which gets lots of bonuses).