Non-cooperative game theory

Our (non-cooperative game) theory, in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the others.”[4] Non-cooperative game theory models different situations in which agents are unable to reach a resolution to a conflict that enforces some action on one another.

[5][6] This form of game theory pays close attention to the individuals involved and their rational decision making.

[9] Further, it has been supposed that non-cooperative game theory is purported to analyse the effect of independent decisions on society as a whole.

As shown in the diagram, both players will receive a higher payoff in the form of a lower jail sentence if they both remain silent.

[14] This example is a two-person non-cooperative non-zero sum (TNNC) game with opposite payoffs or conflicting preferences.

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).

Cooperative game theory does not analyse the strategic bargaining that occurs within each coalition and affects the distribution of the collective payoff between the members.

It is also more general, as cooperative games can be analysed using the terms of non-cooperative game theory where arbitration is available to enforce an agreement, that agreement falls outside the scope of non-cooperative theory: but it may be possible to state sufficient assumptions to encompass all the possible strategies players may adopt, in relation to arbitration.

Alternatively, it may be possible to describe the arbitrator as a party to the agreement and model the relevant processes and payoffs suitably.

As already mentioned, there are many scenarios where perfect symmetry of information is not possible which therefore results in the decision making process to be flawed.

One such example could be the reduction in profits and revenue in attempts to drive out competitors for a higher market share.

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.

Most solutions used in non-cooperative game are refinements developed from Nash equilibrium, including the minimax mixed-strategy proved by John von Neumann.