Game Theory, in a nutshell, is serious experimental mathematics applied to different sciences: Economics, Finance, Politics, Sociology, Evolutionary Biology, Military, etc., but can also be used as deceptive strategic technics. 

The most common types of game in Game Theory arethe following:

1. Ultimatum game - It is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. The first player proposes how to divide a sum of money with the second party. If the second player rejects this division, neither gets anything. If the second accepts, the first gets her demand and the second gets the rest.

The split dollar game has Sociological applications because it illustrates the human willingness to accept injustice and social inequality.

The extent to which people are willing to tolerate different distributions of the reward from "cooperative" ventures results in inequality that is, measurably, exponential across the strata of management within large corporations. (See also: Inequity Aversion within companies).

Some see the implications of the Ultimatum game as profoundly relevant to the relationship between society and the free market, with Prof. P.J. Hill, (Wheaton College) saying: "I see the ultimatum game as simply providing counter evidence to the general presumption that participation in a market economy (capitalism) makes a person more selfish." 

The possible variants are:

a.) In the "Competitive Ultimatum game" there are many proposers and the responder can accept at most one of their offers: With more than three (naive) proposers, the responder is usually offered almost the entire endowment (which would be the Nash Equilibrium assuming no collusion among proposers).

b.) The "Ultimatum Game with tipping" - If a tip is allowed, from responder back to proposer the game includes a feature of the trust game, and splits tend to be (net) more equitable.

c.) The "Reverse Ultimatum game" gives more power to the responder by giving the proposer the right to offer as many divisions of the endowment as they like. Now the game only ends when the responder accepts an offer or abandons the game, and therefore the proposer tends to receive slightly less than half of the initial endowment.

2. Dictator game - The first player - "the proposer" -  determines an allocation (split) of some endowment (such as a cash prize). The "responder" in this case simply receives the remainder of the endowment not allocated by the proposer to herself. The responder's role is entirely passive (she has no strategic input into the outcome of the game).

This game has been used to test the homo economicus model of individual behavior: If individuals were only concerned with their own economic well being, proposers would allocate the entire good to themselves and give nothing to the responder. However, Henrich et al (2004) discovered in a wide cross cultural study that proposers do allocate a non-zero share of the endowment to the responder. (This 2004 study was an extension of earlier developments[2] in the dictator and impunity games).

This result appears to demonstrate that either:

a.) Proposers fail to maximize their own expected utility, or 
b.) Proposer's utility functions include benefits received by others. 

However, other explanations have been offered, such as the anonymity hypothesis, which claim that the experiment is not correctly designed to test for "altruistic" behaviour, and that the presence of the experimenter causes the proposer to avoid the appearance of "greed".

The term "social preferences" refers to the concern (or lack thereof) that people have for each other's well-being, and it encompasses altruism, spitefulness, tastes for equality, and tastes for reciprocity. Experiments on social preferences generally study economic games including the dictator game, the ultimatum game, the trust game, the public goods game, and modifications to these canonical settings. As one example of results, ultimatum game experiments have shown that people are generally willing to sacrifice monetary rewards when offered unequal allocations, thus behaving inconsistently with simple models of self-interest. Interestingly, the direction and size of the bias varies between cultures. (More market-oriented societies tend to have higher inequity aversion.)

3. Prisoner's dilemma - Will two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? 

In game theory, the prisoner's dilemma is a type of non-zero-sum game in which two players try to get rewards from a banker by cooperating with or betraying the other player. In this game, as in many others, it is assumed that the primary concern of each individual player ("prisoner") is self-regarding; i.e., trying to maximize his own advantage with less concern for the well-being of the other players. 

In the prisoner's dilemma, cooperating is strictly dominated by defecting (i.e., betraying one's partner), so that the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect.

The unique equilibrium for this game does not lead to a Pareto-optimal solution - that is, two rational players will both play defect even though the total reward (the sum of the reward received by the two players) would be greater if they both played cooperate. In equilibrium, each prisoner chooses to defect even though both would be better off by cooperating, hence the dilemma.

In the iterated prisoner's dilemma the game is played repeatedly. Thus each player has an opportunity to "punish" the other player for previous non-cooperative play. Cooperation may then arise as an equilibrium outcome. The incentive to defect may then be overcome by the threat of punishment, leading to the possibility of a cooperative outcome. As the number of iterations approaches infinity, the Nash equilibrium tends to the Pareto optimum.

4. Game of chicken - Also referred to as playing chicken, it is a "game" in which two players engage in an activity that will result in serious harm unless one of them backs down. It is commonly applied to the use of motor vehicles whereby each drives a vehicle of some sort towards the other, and the first to swerve loses and is humiliated as the "chicken".

The principle of the game is to create pressure until one person backs down.

The phrase game of chicken may also be used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain, and only pride stops them from backing down. Bertrand Russell famously compared the game of chicken to nuclear brinkmanship, a method of negotiation in which each party delays making concessions until the deadline is imminent. The psychological pressure may force a negotiator to concede to avoid a negative outcome. It can be a very dangerous tactic; if neither party "swerves", a "crash" is certain to occur.

A formal version of the game of chicken has been the subject of serious research in game theory. Because the "loss" of swerving is so trivial compared to the crash that occurs if nobody swerves, the reasonable strategy would seem to be to swerve before a crash is likely. Yet, knowing this, if one believes one's opponent to be reasonable, one may well decide not to swerve at all, in the belief that he will be reasonable and decide to swerve, leaving the other player the winner. This unstable strategy can be formalized by saying there is more than one Nash equilibrium for the game, a Nash equilibrium being a pair of strategies for which neither player gains by changing his own strategy while the other stays the same. (In this case, the equilibria are the two situations wherein one player swerves while the other does not.)

One tactic in the game is for one party to signal their intentions convincingly before the game begins. For example, if one party were to ostentatiously disable their steering wheel just before the match, the other party would be compelled to swerve. This shows that, in some circumstances, reducing one's own options can be a good strategy. One real-world example is a protester who handcuffs himself to an object, so that no threat can be made which would compel him to move (since he cannot move).

In contrast to Prisoner's Dilemma, where one action is always best, in the game of chicken one wants to do the opposite of whatever the other player is doing.

In chicken, if your opponent cooperates (swerves), you are better off to defect (drive straight) - this is your best possible outcome. If your opponent defects, you are better off to cooperate. Mutual defection is the worst possible outcome (hence unstable), but in the prisoner's dilemma the worst possible outcome is cooperating while the other player defects, and mutual defection is stable. In both games, mutual cooperation is unstable

5. Stag hunt - A game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.

Formally, a Stag Hunt is a game with two pure strategy Nash equilibria - one that is risk dominant another that is payoff dominant.

6. Matching Pennies - A simple example game used in game theory. It is the two strategy equivalent of Rock, Paper, Scissors. Matching Pennies is used primarily to illustrate the concept of a mixed strategy and a mixed strategy Nash equilibrium.

The game is played between two players, Player A and Player B. Each player has a penny and must secretly turn the penny to Heads or Tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), Player A receives one dollar from Player B (+1 for A, -1 for B). If the pennies do not match (one heads and one tails), Player B receives one dollar from Player A (-1 for A, +1 for B). This is an example of a zero-sum game, where one player's gain is exactly equal to the other player's loss.

7. Minority Game - It is inspired by the El Farol bar problem which is a simple model that shows how (selfish) players cooperate with each other in the absence of communication. 

In the Minority Game, an odd number of players have to choose one of two choices independently at each turn. The players who end up on the minority side win.

8. Rock, Paper, Scissors - Rock, Paper, Scissors (also known by several other names) is a hand game most often played by children. 

It is often used as a selection method in a similar way to coin flipping, Odd or Even, throwing dice or drawing straws to randomly select a person for some purpose, though unlike truly random selections, it can be played with skill if the game extends over many sessions  because one can often recognize and exploit the non-random behavior of an opponent.

Strategy between human players obviously involves using psychology to attempt to predict or influence opponent behavior. It is considered acceptable to use deceptive speech ("Good old Rock, nothing beats that!", a quote from The Simpsons) to influence one's opponent.

The Common Side-blotched Lizard (Uta stansburiana) exhibits a Rock-Paper-Scissors pattern in its mating behaviour evolutionary strategy. Biologist Barry Sinervo (University of California, Santa Cruz) has discovered a Rock-Paper-Scissors evolutionary strategy in the mating behaviour of the side-blotched lizard species Uta stansburiana. 

Males have either orange, blue or yellow throats and each type follows a fixed, hereditable mating strategy:

a.) Orange-throated males are strongest but do not form strong pair bonds; instead, they fight orange-throated males for their females. Yellow-throated males, however, manage to snatch females away from them for mating.

 
b.) Blue-throated males are middle-sized and form strong pair bonds. While they are out-competed by orange-throated males, they can defend against yellow-throated ones. 

c.) Yellow-throated males are smallest, and their coloration mimics females. Under this disguise, they can approach orange-throated males but not the stronger-bonding blue-throated specimens and mate while the orange-throats are engaged in fights