 In studying the dynamics of cooperation and competition between actors, understanding the structure of the game that is being played is central to understanding the system of interest. In game theory, a primary distinction is made between those game structures that are cooperative and those that are non-cooperative. As we'll see, the fundamental dynamics surrounding the whole game are altered as we go from games whose structure is innately competitive to those games where cooperation is the default position. A cooperative game is one wherein the agents are able to resort to some institution or third party in order to enable cooperation and optimal results for all. A game is non-cooperative if players cannot form the structures required to enable cooperation. For example, we might think about two people wishing to make a commercial transaction online, given to anonymous people interacting without some institution to enable cooperation. There is no reason for either to think that the other will carry through with the transaction as promised. The seller is incentivized to take the money and not send the item, while the buyer is likewise incentivized to take the product without sending the money. In the absence of some cooperative structure that would enable each party to trust the other and thus cooperate, the game would naturally gravitate towards defection and the potentially valuable transaction would not take place. Thus we can see how in the absence of cooperative mechanisms each player may follow the course that renders them the best payoff without regard for what the other does or what is optimal for the overall system and this can result in sub-optimal outcomes for all. In non-cooperative games, each agent in the game is assumed to act in their self-interest and this self-interested agent is the primary unit of analysis within non-cooperative games precisely because there is no cooperative structure. This is in contrast to cooperative games that treats groups or sub-groups of agents as the unit of analysis and assumes they can achieve certain outcomes among themselves through binding cooperative agreements. Game theory historically has been very much focused on non-cooperative games and trying to find optimal strategies within such a context. This is likely because non-cooperative games are very much amenable to our standard mathematical framework and thus offer nice closed form solutions. However, it's important to note that the real world is made up of situations that are sometimes cooperative, sometimes non-cooperative and often involve elements of both. As previously mentioned, non-cooperative games arise due to a number of factors. Firstly, the game may be inherently zero-sum meaning what one wins the other loses and thus there is an inherent dynamic of competition. Many sports games are specifically designed to be zero-sum in their structure so as to create this dynamic of competition. In such a case, there is only one prize if someone else gets it then you won't. There is no incentive for cooperation and every incentive for competition and thus the best option is for the actor to focus on maximizing their payoff irrespective of all else and this is called a strictly competitive game. Likewise, a game may be non-cooperative due to the incapacity to create cooperative structures. Most people, when engaged in a game, will wish to not only optimize their own payoff but will wish also to optimize the overall outcome as well. In general, people do not like the idea of waste or of unfairness and we typically search for some optimal solution given both our own interests and some consideration for the overall organization. The real world of social interaction is full of all sorts of informal social and cultural institutions designed to enable trust, cooperation and the optimal outcomes for all that result from them. Almost as soon as two people start to interact, they will start to look for commonalities and shared interests that enable them to develop trust and cooperation. Thus non-cooperative games are typically those where the actors cannot interact and form the trust required for cooperation. Indeed, there will be certain games that we construct where we specifically want competition and we do that by not allowing the players to cooperate such as in a competitive market. Lastly, non-cooperative games can be a product of an incapacity to enforce binding contracts. If there is a third party involved to ensure optimal outcomes for the overall organization through sanctions and incentives, this can form a solid basis for cooperation in the way that a government does by enforcing laws. This is famously captured in Thomas Hobbes' conception of the state of nature where he pondered what was life like before civil society. He went on to write, During the time men live without a common power to keep them all in awe, they are in that condition which is called war and such a war as is of every man against every man. In this state, every person is seen to have a natural right or liberty to do anything one thinks necessary for preserving one's own life. Hobbes' ideas illustrate vividly how in the absence of a third party to enforce cooperation, competition and conflict can prevail. Non-cooperative games create a specific dynamic where we take the individual and their payoff as the basic unit of analysis. In such a circumstance, we do not need to consider what is best for all given some form of cooperation because there is no possibility for this within the context. We are then solely interested in how the individual will act, the question of how should they act to optimize their own payoff and given the assumption that both are performing this optimization what will be a stable solution to the game. Given these assumptions, both players should search for a strategy that optimizes their payoff and where these strategies of the players interact we should have a stable outcome to the game and we should also be able to predict this outcome. This stable outcome is what we call an equilibrium where equilibrium in the general sense means a state in which opposing forces are balanced thus creating a point of stability and status. When we see a ball at the bottom of a bowl there is a state of equilibrium because if we put it anywhere else in the bowl the force of gravity would act on it to put it back to this static point. This is the same for the actors in a non-corruptive game because they are both trying to optimize their payoff they will both naturally gravitate towards the strategy that gives them the highest payoff but because their payoff is dependent on what strategy the other chooses and because they cannot depend upon cooperation between them they have to choose the best strategy assuming that the other will work to optimize their payoff without cooperating. This point of equilibrium in a game is called the Nash Equilibrium so named after the famous mathematician John Nash. In game theory the Nash Equilibrium is a solution concept of a non-corruptive game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players and no player has anything to gain by changing only his or her own strategy. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged then the current set of strategy choices and the corresponding payoffs constitute a Nash Equilibrium. The idea of a Nash Equilibrium is one of the foundational concepts within classical game theory. The basic intuition of this Nash Equilibrium is in predicting what others will do given their self-interest only and then choosing your optimal strategy given that assumption. A Nash Equilibrium is a point where all players are doing their best given the absence of cooperative structures. A Nash Equilibrium is a law that no one would want to change in the absence of some effective overall structure for coordination. Nash Equilibrium is best illustrated through the Prisoner's Dilemma game. The Prisoner's Dilemma game is a classic two-player game that is often used to present the concept of Nash Equilibrium in a payoff matrix form. Conceive of two prisoners detained in separate cells interrogated simultaneously and offered deals in the form of lighter jail sentences for betraying the other criminal. They then have the option to cooperate with the other prisoner by not telling on them or defect by betraying the other. However, if both players defect then they will both serve a longer sentence than if neither said anything. Other jail sentences are here interpreted as higher payoffs. The Prisoner's Dilemma has a similar matrix as depicted for the coordination game. However, the maximum reward for each player is obtained only when the player's decisions are different and thus we can see the core dynamic of competition. Each player improves their own situation by switching from cooperating to defecting given the knowledge that the other player's best decision is also to defect. The Prisoner's Dilemma thus has a Nash Equilibrium where both players choose to defect. What has long made this game an interesting case to study is the fact that this Nash Equilibrium scenario is globally inferior to both cooperating. That is, both players would be better off if they both chose to cooperate instead of both choosing to defect. However, each player could improve their own situation by breaking that mutual cooperation no matter how the other player changes their position. The central aim of non-corruptive game theory then is in trying to predict people's actions within a game by finding the Nash Equilibrium and assuming they will play that because this is their best option given the structure of the game. It is then legitimate for us to ask does equilibrium analysis give us any predictive capacity over what happens in the real world? Often the outcome of experiments is not an equilibrium as predicted by the theory. This is mainly because people do not fully reason through the game in a full, logically consistent fashion. Equilibrium is a point where everyone has figured out what everyone else will do. Preferably, it often does not predict what people will do the first time they play the game. Equilibrium should more be interpreted as what will happen over a number of iterations within a non-corruptive game as players come to better understand the game and how to reason through it similar to putting a ball in a bowl it takes time before it arrives at an equilibrium and this is what is seen in game experiments they tend over time towards the equilibrium. For example, in a game people are asked to choose a number between 0 and 100 with the winner of the game being the person who is able to guess what will be two thirds of the average figure proposed by others so in this situation everyone is being asked to guess a bit below the average number proposed when this game is played only a small percentage choose the equilibrium point which is 0 and because other people interact rationally in this game they're wrong in their prediction in many ways then choosing this equilibrium as a prediction of what would happen in a real-world game is not a good option and this clearly diverges from what the theory of game equilibrium tells us. However, over time as the game is iterated upon the numbers chosen by people do move towards this equilibrium thus this method of equilibrium analysis tells us something about the statistical averages of the system but not very much about behavior in the real world on the first iteration of the game.