Nicaea is a shared incentive game, but an unusual one. In most shared incentive games, you evaluate a potential move – a potential entanglement – based on a combination of board state and player positions. If I'm playing a train game, and a company has set itself up for a big payout, but is a few dollars short of building the track it needs to clinch the deal, there's an incentive, based on board state, for me to nab a share, pumping some extra moolah into its treasury and giving it the push it needs. But if another player stands to make two or three times as much as I do from the connection, I don't have an incentive to help them out. On the other hand, if that player is in dead last, and the little I make is enough to possibly give me the win, I might do it after all – those all being considerations based on player positions.
Parsing the board state helps us determine how valuable a thing is, and parsing the player positions helps us determine to whom it is valuable. What's different about what I sometimes cheekily refer to as the "stockholding element" of Nicaea is that there isn't a board state to parse, and that none of these things have any inherent value outside of how much the players desire it.
The game revolves around five doctrinal disputes, for which there are two positions. For example, one dispute is about the substance of Christ, with a homoousian and a homoiousian position, handily identified as "A" and "B" so we don't need to worry about trying to pronounce homoousian and homoiousian:
Players will "make an argument" (buy a card) for either the A side or the B side; when one side of the dispute buys its fourth card, its position is deemed orthodox and the opposing position heterodox. Each card for an orthodox position earns its owner a VP chit, which is randomly worth four, five, or six points. Heterodox positions are worth nothing. Players may "double down" on their argument, buying a second card for a position, for which they pay double the usual cost, but that's the limit; in order to get your position to score, you need the help of at least one other player. And this is where it gets tricky.
Let's say it's my turn to buy a card, and I'm going to buy my first red card – gonna throw my weight behind either the (A) homoousian or (B) homoiousian position. So, which side am I going to take?
If the only red card out is the first A, and Bob has it, I might buy the second A or I might buy the first B – might throw in my lot with Bob, or might oppose him, depending on how well he's doing and how well I'm doing. The side that is currently losing the argument – that has fewer cards in player hands – costs a little less, so there might be a slight incentive in that direction.
The incentive to go B is strengthened if there are two cards for A and one for B, because I'm not climbing out onto such a limb, and there's already a partner waiting for me on that side of the issue. Turn order will matter here though. If my would-be partner acts immediately after me, or after one of the A players, it's a safer bet to go B. If one A player comes immediately after the other in the turn order, it's more likely they'll be able to close the issue out before it gets back to me or my partner. It also depends of course on how much influence – the game's currency – those players have.
But let's say there are two cards out for A, and none for B. If one card is owned by Bob and one by Carol, I'm probably more likely to buy the third A than the first B, because I can see which way the wind is blowing. If both cards belong to Bob, however, I might buy the first B in the hopes that Carol will buy the second, and maybe Eustace will buy the third – all but certainly closing Bob out. Serves him right, doubling down that early.
Or I might buy that first B, and Carol will go A, and at that point, the easy move for Eustace is to buy the fourth A, closing the thing out – points are points, after all. Unless Eustace doesn't want points – or unless they think that I don't want points. Unless they think that I'm going for a schism.
How the endgame works is that the player with the most points wins, unless the player with the fewest points has the most influence. That player may not have won the most arguments, but they've got enough influence within the church, enough of a political power base, that they can reject the decisions of the council and breakaway, bringing a sizable number of bishops with them. Going for a schism, and pulling it off, is exciting but difficult. If the other players catch on to what you're doing – if they see for example that you don't have a lot of points but are building quite a bit of influence – they naturally have an incentive to prevent you from having the fewest points. And so some of us buy into your side of the dispute to ensure that it does score.
Some games are defined by dogpiling – a group of players working together to quickly close out an issue before the opposing viewpoint can build up any steam. In others, each issue is bitterly contested. Some games see a mix of the two behaviors, and sometimes folks buy cards not to score them, but to increase the cost of buying the next card, so that your new "partner" won't be able to double-down and clinch the deal, ensuring another player does score – thus preventing them from pulling off a schism victory.The flavor and character of these decisions, and the relative danger or success of staking out a contrary position, depend entirely on social dynamics. That's why, as much as I enjoy playing Nicaea, I like watching others play it even more. Naturally, this does make the game prone to "groupthink" or "local meta" – I fully expect to hear from folks where it's all dogpiling all the time, because "there's never any incentive to go against the grain", just as I fully expect to hear from folks where most issues aren't resolved until the very end. I wouldn't have it any other way.