Miguel Alberola Cano's (aka Miguelinileugim's) "Another random game theory essay nobody cares about":


	1. Basics

		1. Each party can offer a number of items of additive and subtractive value.
		2. Additive items (aka cooperation) are such that if given, will be of positive value to the other party.
		3. Subtractive items (aka the promise not to follow on a threat) are such that if not given, will be of negative value to the other party (due to following on the threat).
		4. Items have different values to each side.
		5. Agreeability: Value (to one side) divided by cost. Positive total agreeability means the deal is agreeable to both sides overall (even if its not guaranteed they will be better off because of subtractive items), although this doesn't guarantee it will be accepted (as one side might offer very agreeable stuff but get nothing in exchange). Negative total agreeability means the deal is not agreeable to both sides overall, this guarantees it will be rejected, albeit one side might still be willing to accept it (as one side might get very disagreeable stuff but have to give nothing in exchange).
		6. Trust: Certainty that of what the other side is going to offer
		7. Reputation cost:

			1. Additive: Impact of offering an additive item to the other party
			2. Subtractive: Impact of offering a subtractive item to the other party
			3. Neutral: Impact of offering an item on its own, regardless of its impact to the other party

	2. Trust, no reputation

		1. If the items on the opposite side of a party are more valuable to him than the items in his own side, he will accept. Otherwise he will refuse.
		2. The ideal strategy is to offer things in descending order of agreeability and request them in increased order of agreeability. Until the combined agreeability of what you offer and what they offer in exchange is negative.

	3. No trust, no reputation

		1. The items in any side are multiplied by the chance they will follow through. So a highly believable but low value item might be more significant than an unbeliable but high value item.
		2. The ideal strategy is divided in two depending on whether there's the expectation of repeated interaction or not

			1. No expected repeated interaction: Offer nothing, request everything.
			2. Expected repeated interaction: Consider the impact of what you offer on the probability of their future offers happening. Given one single offer from you and one single offer from them, if your offer being followed through will have no impact in the probability of their future offers happening, then don't offer it (as with no repeated interaction). If your offer being followed through will ensure 100% that their future ones will too, then the strategy is the same as with trust and no reputation (as trust is not a factor as there's certainty) while accounting for the one time benefits of not following through once (the possibility of recovering trust by following through, even if you expect them not to, should be accounted for) and the one time losses of the other side not following through once (with the similar possibility of them recovering your trust in the way already described). If the probability is neither (e.g 50%) then account for that and decide your ideal strategy based on the probabilities for each offer, their impact in the probabilities of other items, and their value to each side. If there's more than one item offered by each side, do the same, but you'll have to account to more things (not gonna figure out the decision tree involved here any further).
			3. Dubious repeated interaction: Figure out the probability of repeated interaction happening or not. If it is 50% likely for example, that'd mean half of your strategy should be based around no expected repeated interaction and 50% on expected repeated interaction.

	4. Reputation, trust

		1. There's a reputation cost for each item being offered
		2. The ideal strategy is the same as with trust, no reputation. But adding these reputation costs to each offer.

	5. No trust, reputation

		1. Reputation cost AND uncertainty of the other following throuh come into play.
		2. The ideal strategy is the same as with no trust no reputation. But adding these reputation costs to each offer.