So I've had this game idea banging around in my head like a katamari, picking up more and more stuff over the past couple months, and it's kind of distracting me from some of my outstanding obligations and occupying valuable mental real estate that other projects should be using. You know who you are. Maybe if I put enough stuff about it here, I can move on without regrets... or at least, set it aside for now, and have notes to come back to when it's more appropriate.
You might call the core concept "competitive military recruiting and operational command". The game is simultaneous timed-turn-based for up to four players; single player games can or cannot use the timer, and they can be either normal competition mode or a more story-centric single-player campaign. You live in a heavily contested city-state in a fictitious dark age society, and several armies are converging in the area, so you decide to form your own militia to ensure your survival. In order for your organization to exist and be effective, you have to select 8 of 32 possible candidates to oversee the following projects.
1. Troop recruitment: figure out what kind of people make up your army and how many of them you can get.
2. Sponsorship: determine where your funding comes from, how often it comes, how big it is when it gets here, whether you have to pay it back, and whether it comes with any strings attached.
3. Provisioning: acquire food and gear and make sure it is where it needs to be; also affects your base.
4. Training: this determines what kinds of things your soldiers can do in the field and how effective they are at attempting to do them.
5. Field marshalry: governs the division of your army into units of different kinds, and the nature of those units' specialties.
6. Information gathering: learn what the enemy is up to and mislead him in his attempt to do the same to you.
7. Deployment: Set objectives for your units to achieve and put them to work achieving them.
8. Morale management: Find ways of keeping your soldiers happy, and keep tabs on when they're likely to stop, and what the consequences will be when they do.
The 32 characters who accomplish these functions have reputations for effectiveness: they each favor something at the expense of something else. They might favor power at the expense of cost, efficiency at the expense of speed, or flexibility at the expense of increased vulnerability. These reputations manifest in different ways depending on the position to which they're assigned. Using the "power at the expense of cost" guy as an example: if he's responsible for recruiting, you'll get mercenaries or other veterans as your troops, but they cost more to maintain. If he's responsible for training, trained troops' potential will be maximized, but training will be particularly expensive. If he's responsible for deployment, he'll devise particularly daring and dangerous attacks that will have a high rate of troop casualties.
The other major influence on the effectiveness of the eight arenas of development is the order in which you assign governors to them; each project has eight levels of effectiveness and one sub-level. (Each level of recruiting and sponsorship get you additional batches of recruits or funds; levels of field marshalry, training, provisioning, and deployment add both to the quality and to the kinds of squad, maneuvers, equipment, or missions you can use. Levels of information gathering and morale result in additional quality, kinds of information or morale boosting, and have other, more esoteric effects.) Every in-game day, you pick somebody to manage a project that hasn't got a manager yet, and every project with a manager will level up, until one of your projects is level 8, at which point leveling stops. Players reverse order of picks every day, so day 2 has player 4 make first choice of second recruit.
Players attack one another by committing units to missions available from their deployment projects, based on the information retrieved from information gathering. You commit the day before the attack, but you commit units to defense on the day of attacks; how much information you get about the attacking force is determined by the differential between your information gathering project and the enemy's. Actual combat is basically like pokemon, where your available moves are determined by training, the effectiveness of those moves is governed by morale, training, troop quality, the nature of your squad, etc.; the cost of attacks is determined by morale and provisioning, and your squads HP is the number of troops in it. A mission succeeds if the defending unit is destroyed or retreats, and fails in the opposite scenario; missions might vary from assassinating an enemy commander (reverting that player's relevant project to the sub-level) or raiding their provisions to seizing control of a base (which may be relevant to the demands of your sponsor, or theirs).
When players aren't doing anything because other people are making up their mind about recruitment or are indisposed in attacks, they can play something like Tetris in their base until the day ends; final Tetris ranks determine the ones digit of that player's final score, while completion of sponsorship objectives and overall survival/combat success determines the tens digit.