Rules of the Game | Game Theory | Decision Making | Economics

Game should be systematic and every game has certain rules. The action of the individual agents is the subject matter of game theory. The decision theory helps one person to arrive at particular decision. The decision theory may help to get the right decision under uncertainty. The general model of action seems to be the heart of game theory. For instance, it could apply to any type of player and not just individual.

So long as the state or the working class has a consistent set of objectives/preferences, then we could assume that it (or they) also acts instrumentally so as to achieve these ends. Likewise it does not matter what ends a person pressures, they can be selfish, weird, altruistic or whatever, so along as they consistently motivate then people can still act so as to satisfy them best.

Game theory takes help of the decision theory. But it goes beyond classical explanation. In decision theory, there are no players and actions. But in game theory, there are different players and actions, payoffs and information. In simple formula it is called as PAPI. It is referred as the rule of the game and they try to maximize their payoffs. In the game theory, the players formulate the plans which are known as strategies. Such alternative strategies, actions are depending on the information received by the individual player. Each player’s action is different from each other.

It is depending on the information received at different levels and time. The strategies and actions played by each player achieve different equilibriums at different points. The experts of the game theory explain the strategies and game played and payoff of different players. Such common strategies are useful to formulate the policies at micro and macro level.

In game theory, the players of any game are the individuals and firms. The goal of the individual player is to maximize his utility. For maximizing the utility, the players choose alternative actions. The firm chooses particular strategy to get more profit out of various alternative strategies.

Games are the way of modeling strategic interactions that is situations in which the consequences of individual’s actions depend on the actions taken by others and this mutual interdependence is recognized by those involved. Game theory is the study of games, also called strategic situations. These are decision problems with multiple decision makers, whose decisions impact one another.

It is divided into two branches:

1. Non-cooperative game theory and

2. Co-operative game theory.

The actors in non-cooperative game theory are individual players, who may reach agreements only if they are self-enforcing. The non-cooperative approach provides a rich language and develops useful tools to analyze games.

One clear advantage of the approach is that it is able to model how specific details of the interaction among individual players may impact the final outcome. One limitation, however, is that its predictions may be highly sensitive to those details. For this reason it is worth also analyzing more abstract approaches that attempt to obtain conclusions that are independent of such details. The cooperative approach is one such attempt and it is the subject of this article.

The actors in cooperative game theory are coalitions that are group of players. For the most part, two facts, that a coalition has formed and that it has a feasible set of payoffs available to its members, are taken and given. Given the coalitions and their sets of feasible payoffs as primitives, the question tackled is the identification of final payoffs awarded to each player. 

In the game theory, an action by any individual player is simply denoted as a_i The numbers of actions are taken in the action set Ai = {a}. The set is consists of action taken by individual player at i. Actions of an individual player is the combination of ordered set a = {a_i} where (I = 1…n). It is an action for each of the n players in the game. All players in the game maximize their utility. The player i receives the return π1(S_i……….. S_n) after play of a game.

The two important points are raised here:

1. The utility of player i receive after all players. The nature has picked their strategies and the game has been played out by two or multiple players. It can be explained alternatively as follows,

2. A player expects some gain after play of any game.

It means expected utility is a function of the strategies chosen by individual and other players ∏_i (S_s, S_o). Here, s is denoted as self and o is denoted as other player. The profit is for i^th player.

Any game has an interesting outcome. It means the values can be given for actions, payoffs and other variables after the game is played. Such actions, payoffs are useful for development of microeconomic models. Micro economists are keen to understand who is playing what game and for what benefit. Sometimes, the actions and payoffs are useful for development of model. Most of the actions and payoffs are used for decision theory. Such decisions and actions and payoffs are presented in graphical way.

Such geographical actions depict the order of play of players. They are very useful for prohibiting certain risky behaviors, illegal transaction, market failure etc. Particular laws can be made to prohibit such risky actions. The aim behind any law is to increase the welfare of individuals and work the system efficiently without failure. Game theory studies the actions by other players. At the same time, it practices the game by assuming himself in everybody’s position. Individual player i has particular strategies and there are certain rules which explain to choose a particular action based on given information set.

The player i with particular strategies at particular time are the set of strategies available to him. Such strategies are S = (S_i). Such strategy combination is S = (S_i……S_n). It consists of one strategy for each of the n players in the game. An equilibrium S* = (S*1,……S*n) strategy combination is consisting of a best strategy for each of the n individual players in the game. Most of the equilibrium strategies are visible because players pick the strategies to maximize their own payoffs.