Game Theory- Assignment Aid
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Game theory is a multi-disciplinary technique used to study the behavior of humans whose key pioneers were John Nash and John von Neumann as well as famous economist Oskar Morgenstern and is commonly used in social sciences, economics, and mathematics. It is used as a tool to analyze the strategic interactions between two or more agents where actions of all agents are interdependent. It is a formal study of decision making where one agent has to make a choice that affects the interests of the other agent. The theory provides insight into different strategic choices by fundamentally and objectively analyzing the methodologies. It requires making models that provide a clearer picture and support in decision making. The theory has gained a lot of applications with game theory models for example finding applications by managers in making better decisions regarding price and output.
A cooperative game is also known as a coalition game and has two competitors only in case they both bind any possibility of external enforcement of cooperative behavior. In contrast to this, non-cooperative games are ones played by individuals alliance with self-enforcing. Self-enforcing are the restrictions or rules that are set by a party on itself.
Symmetric games are the ones in which the pay-off is dependent on the other strategies of the game rather than getting implied by other players. Unlike symmetric games, in asymmetric games, each individual is set by different strategies. No two players follow the same strategy except for some rare cases that you can know by seeking our experts’ help.
Zero-sum games is a mathematical representation of a situation where two players play a game. Now, the catch here is the utilities with which the players are playing the game are limited. That is the loss or gain of one player affects the loss or gain of others. In other words, suppose a player took a piece of cake. If it is a bigger piece than the fixed size, then there may be another player whose size of cake piece decreases automatically. This is known as a zero-sum game.
Simultaneous games are the ones in which players move simultaneously, and the other player would be aware of the earlier player’s actions. Divergent to this, in sequential games, the players move one step after the other in a sequence unaware of the previous step of the earlier player.
Other games include;
- Infinitely long games
- Discrete and continuous games
- Perfect/imperfect information
- Stochastic outcomes
- Pooling games
- Mean-field game theory
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The key to solving the game theory problem is the pure and mixed strategies where a mixed strategy is used when there is no pure strategy to take. Another concept in solving game theory problems is the payoff matrix which represents the set of decisions and their payoffs. To solve the game theory problem, a student must know how to form a payoff matrix and the value to be assigned to each decision. If a student correctly forms a payoff matrix, then they will be able to find the Nash equilibrium in the payoff table because as Nash equilibrium states, with a finite number of players there is at least a single Nash equilibrium. The Nash equilibrium provides the best optimal solution to the game theory problem, therefore understanding the concept of Nash equilibrium is very important in solving game theory problems.
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