Non Cooperative Game Theory Essay

Game theory models strategic interaction between self-interested agents. It is mostly used in economics, psychology, politics, and computer science. The game is formed by three main parameters, which are players, actions, and payoff.

Players could be represented by people, companies, or governments. They are self-interested, where each player or agent has his/her own description of states of the world that he/she likes. Actions are taken by players such actions can either be voting or bidding in an auction. The third parameter is the payoff, which motivates the players such as the profit. The rational approach states that each agent acts to maximize the expected utility.

3.2. Forms of games

3.2.1. Normal Form

A normal form game is the basic

However, the players are not assumed to be altruistic, they only join a coalition if this helps them increase their individual payoff. Indeed, competition plays an important role in cooperative games, as the agents have to divide the fruits of their collective labor.

Non-Cooperative game theory

In non-cooperative game theory, players choose their actions individually, selfishly seeking to reach their own goals and to maximize their own payoff. While this does not mean that players are necessarily opponents to other players, they are not interested in other players welfare.

Inspection games form an applied field of game theory. An inspection game is a mathematical model of a situation where an inspector verifies that another party, called inspectee, adheres to certain legal rules. The inspectee has a potential interest in violating these rules. Typically, the inspector’s resources are limited so that verification can only be partial. A mathematical analysis should help in designing an optimal inspection scheme, where it must be assumed that an illegal action is executed strategically. This defines a game-theoretic problem, usually with two players, inspector and inspectee. In some cases, several inspectees are considered as individual players.

3.2-Solution of Games

3.2.1- Pure