Here we shall briefly discuss how the game theory can be used to study the economic behaviour in oligopolistic markets. The Payoff Matrix of a Game: Strategic interaction may involve many players and many strategies, but here we shall consider only two-person games with a finite number of strategies. This will enable us to present the game easily in a payoff matrix.
Payoff matrix for the game of Matching Pennies Row wins if the two coins do not match, whereas Column wins if the two coins match. While it is true that every noncooperative game in which players may use mixed strategies has a Nash equilibrium, some have questioned the significance of this for real agents.
If it seems appropriate to require rational agents to adopt only pure strategies perhaps because the cost of implementing a mixed strategy runs too highthen the game theorist must admit that certain games lack solutions.
A more significant problem with invoking the Nash equilibrium as the appropriate solution concept arises because games exist which have multiple Nash equilibria see the section on Solution Concepts and Equilibriain the entry on game theory.
Unfortunately, so many refinements of the notion of a Nash equilibrium have been developed that, in many games which have multiple Nash equilibria, each equilibrium could be justified by some refinement present in the literature.
The problem has thus shifted from choosing among multiple Nash equilibria to choosing among the various refinements. Some see SamuelsonEvolutionary Games and Equilibrium Selection hope that further development of evolutionary game theory can be of service in addressing this issue.
This requirement originates in the development of the theory of utility which provides game theory's underpinnings see Luce for an introduction.
Since the number of different lotteries over outcomes is uncountably infinite, this requires each agent to have a well-defined, consistent set of uncountably infinitely many preferences. Numerous results from experimental economics have shown that these strong rationality assumptions do not describe the behavior of real human subjects.
Humans are rarely if ever the hyperrational agents described by traditional game theory. For example, it is not uncommon for people, in experimental situations, to indicate that they prefer A to B, B to C, and C to A.
The hope, then, is that evolutionary game theory may meet with greater success in describing and predicting the choices of human subjects, since it is better equipped to handle the appropriate weaker rationality assumptions. We repeat most emphatically that our theory is thoroughly static. A dynamic theory would unquestionably be more complete and therefore preferable.
But there is ample evidence from other branches of science that it is futile to try to build one as long as the static side is not thoroughly understood.
Von Neumann and Morgenstern,p. Since the traditional theory of games lacks an explicit treatment of the dynamics of rational deliberation, evolutionary game theory can be seen, in part, as filling an important lacuna of traditional game theory.
One may seek to capture some of the dynamics of the decision-making process in traditional game theory by modeling the game in its extensive form, rather than its normal form.
However, for most games of reasonable complexity and hence interestthe extensive form of the game quickly becomes unmanageable. Moreover, even in the extensive form of a game, traditional game theory represents an individual's strategy as a specification of what choice that individual would make at each information set in the game.
A selection of strategy, then, corresponds to a selection, prior to game play, of what that individual will do at any possible stage of the game. This representation of strategy selection clearly presupposes hyperrational players and fails to represent the process by which one player observes his opponent's behavior, learns from these observations, and makes the best move in response to what he has learned as one might expect, for there is no need to model learning in hyperrational individuals.
The inability to model the dynamical element of game play in traditional game theory, and the extent to which evolutionary game theory naturally incorporates dynamical considerations, reveals an important virtue of evolutionary game theory.
Applications of Evolutionary Game Theory Evolutionary game theory has been used to explain a number of aspects of human behavior. A small sampling of topics which have been analysed from the evolutionary perspective include: The following subsections provide a brief illustration of the use of evolutionary game theoretic models to explain two areas of human behavior.
The first concerns the tendency of people to share equally in perfectly symmetric situations.Utility is the amount of happiness an agent (player) gets from a particular outcome, or payoff. In order to create a game matrix, we first need to work out the utility values.
We assign the payoffs that are least attractive to a player low values and payoffs that are attractive to the player high payoffs. A payoff matrix is a tool that is used to simplify all of the possible outcomes of a strategic decision. It is a visual representation of all the possible strategies and all of the possible outcomes.
In the prisoner's dilemma, Alice and Bob each choose a strategy, defect or cooperate, for a total of four possible combinations, each of which corresponds to an outcome, or payoff. One can thus draw the following payoff matrix, which illustrates the payoff for each combination of strategies.
Changes to the payoff matrix have been studied in a number of contexts, including one-shot two-player games, payoff evolution without strategy evolution (30, 31), under environmental “shocks” to the payoff matrix (32 ⇓ –34), and using continuous games (22, 23, 35).
Here we adopt a different approach, and we explicitly study the. a) Assuming this to be a zero-sum game, construct the reward matrix (payoff table). b) Find and eliminate all dominated strategies. c) We are given that an optimal strategy for the soldier is to hide 1/3 of the time in foxholes 1, 3, and 5.
Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff.