Non-cooperative game theory

Non-cooperative game theory

In game-theory, a non-cooperative game is a game in which there are no external rules or binding agreements that enforce the cooperation of the players. A non-cooperative game is typically used to model a competitive environment. This is stated in various accounts most prominent being John Nash's 1951 paper in the journal Annals of Mathematics.

The difference between cooperative and non-cooperative game theory The terminology of cooperative and non-cooperative game theory does not imply that the players can only "cooperate" in one case and not another. This form of game theory pays close attention to the individuals involved and their rational decision making. There are winners and losers in each case, and yet agents may end up in Pareto-inferior outcomes, where every agent is worse off and there is a potential outcome for every agent to be better off. Agents will have the ability to predict what their opponents will do. Cooperative game theory models situations in which a binding agreement is possible. In other words, the cooperative game theory implies that agents cooperate to achieve a common goal and they are not necessarily referred to as a team because the correct term is the coalition. Each agent has its skills or contributions that provide strength to the coalition.

Further, it has been supposed that non-cooperative game theory is purported to analyse the effect of independent decisions on society as a whole. In comparison, cooperative game theory focuses only on the effects of participants in a certain coalition, when the coalition attempts to improve the collective welfare. The following assumptions are commonly made: # Perfect recall: each player remembers their decisions and known information. # [[complete-information]]: each player knows the preferences and strategies of the other players. This example is a two-person non-cooperative non-zero sum (TNNC) game with opposite payoffs or conflicting preferences.

The win condition for this game is different for both players. For simplicity in explanation, lets denote the players as Player 1 and Player 2. In order for Player 1 to win, the faces of the pennies must match (This means they must both be heads or tails). In order for Player 2 to win, the faces of the pennies must be different (This means that they must be in a combination of heads and tails). This framework often requires a detailed knowledge in the possible actions and the levels of information of each player.

Non-cooperative game theory provides a low-level approach as it models all the procedural details of the game, whereas cooperative game theory only describes the structure, strategies and payoffs of coalitions. Therefore, cooperative game theory is referred to as coalitional, and non-cooperative game theory is procedural.

Secondly, the assumption of self-interest and rationality could be argued. Arguments are made that being rational can result in the assumption of self-interest being invalidated and vice versa. One such example could be the reduction in profits and revenue in attempts to drive out competitors for a higher market share. This thus does not follow both of the assumptions as the player is concerned with the downfall of their opponent more than the maximisation of their profits. There is the argument to be made that although mathematically sound and feasible, it is not necessarily the best method of looking at real life economical problems that are more complex in nature.

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External links * [A brief introduction to non-cooperative game theory](https://web.archive.org/web/20100610071152/http://www.ewp.rpi.edu/hartford/~stoddj/BE/IntroGameT.htm)

it:Teoria dei giochi#Giochi non cooperativi