Basic game theory examples

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Examination Results ISC K12 Toppers. Fibonacci Numbers. Graphs of Cubic Polynomials. Our Game Theory Tutorials- at a glance. Game Theory : An Introduction Game Theory helps us understand situations in which decision-makers interact. It encompasses a wide range of applications some of which are listed below: firms competing for business Arms race between the countries political candidates competing for votes animals fighting over prey bidders competing in an auction penalty kicks in a football game And the list goes on…..

Like other sciences, game theory consists of a collection of models. These models provide insights when interactions affect incentives. Theory of Rational Choice The theory of rational choice is a component of many models in game theory. By assuming a decision maker to be rational, according to this theory a decision-maker chooses the best action among all the actions available to her. In any given situation the decision-maker is faced with a subset of A, from which she must choose a single element.

If the decision-maker prefers the action a to the action b, and the action b to the action c, then she prefers the action a to the action c. Payoff function associates a number with each action in such a way that actions with higher numbers are preferred. A person is faced with the choice of three vacation packages, to Havana, Paris, and Venice.

She prefers the package to Havana to the other two, which she regards as equivalent. Her preferences between the three packages are represented by any payoff function that assigns the same number to both Paris and Venice and a higher number to Havana. It is a relative measure and just tells the order of preferences of actions in a set.

There is enough evidence to convict each of them of a minor offense, but not enough evidence to convict either of them of the major crime unless one of them acts as an informer against the other defects. If they both stay quiet, each will be convicted of the minor offense and spend one year in prison.

If one and only one of them defects, she will be freed and used as a witness against the other, who will spend four years in prison. If they both defect, each will spend three years in prison.

Players: The two suspects. All of the above data can be represented in tabular form. Example 2: Battle of Sexes There is a couple who want to go on a date, so they decide a place to meet either a movie or football game in our case. The husband prefers to go to a football match while the wife prefers movie. Problem is on the day of date both of them forget the place they have to meet. Now both of them would like to meet at the same place even though it might be the venue they prefer less.

Solution : The answer is yes. Product-based decisions related to launching a new product in the market or to exit the launch of the product are also executed using game theory by businesses. Similarly, the concept of game theory is also being used in deciding whether entering a new market or exiting it. The applications of game theory are also being used widely in deciding upon the pricing strategies of both consumers and retailers.

Retailers compete against each other to gain market share of customers and for this, they opt for different games or strategies, like offering attractive discounts on specific goods in order to increase sales of complementary products. For example, in the offseason, i. In this, retailers use the game theory approach where retailers and consumers are the main players. The focus of retailers is on using the best pricing strategy while the preference of consumers is to choose the best deal in terms of discount and variety.

Using game theory, decisions regarding buying and selling shares in the stock market can be taken wisely. The investors make different stock market decisions by using different strategies of investment and by considering different players or investors. Game theory helps in predicting the decisions of other players related to investments, and based on these decisions, they can decide upon the strategies for themselves which maximize profit.

So Beach-Beach is a dominant strategy equilibrium for this game. Because of this, Kim and Chris, if they are rational, do not need to cooperate make an agreement ahead of time.

Each can just pursue their own interest, and the best outcome will occur for both. Now consider Betty and John. John likes Betty, but Betty doesn't like John that much. Each knows this, and neither wants to call the other before deciding what to do this afternoon: stay at their respective homes or go to the neighborhood swimming pool. In this case, Betty's best strategy depends on what John does. But if she assumes John is rational, she will reason that he will not stay home, because going to the pool is a dominant strategy for him.

This is called iterated dominance. In this example, Betty gets higher utility than John because of their relative preferences, and John gets less utility than he would have if Betty wanted to be with him. An outcome is Pareto optimal or efficient if no agent can be made better off than that outcome without making another agent worse off.

The equilibrium outcomes in both this example and the previous one are Pareto optimal. Consider Stan and Leland, two prisoners who have each been offered a deal to turn state's witness defect against the other. They can't communicate. They had orginally agreed to remain in solidarity, i. If both remain in solidarity, then they will each only be convicted of a minor chage.

If only one defects, then the state will throw the book at the other and let the defector go. If they both defect, each will get convicted of a serious charge. The payoff matrix higher positive utility implies a better outcome is as follows: Leland Solidarity Defection Stan Solidarity 3,3 1,4 Defection 4,1 1,1.

In this game, the strategy of defection is weakly dominant for each player, meaning that whatever the other player does, defecting yields an outcome at least as good and possibly better than remaining in solidarity would.