2/3 of average game, Represent this game in Normal Form(matrix form) • There are

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2/3 of average game,  Represent this game in Normal Form(matrix form)

• There are two players.

• Each player names an integer between 1 and n.

• The player who names the integer closest to two thirds of the average integer gets a reward of 2, the other players get nothing.

• If there is a tie, each player gets reward of 1.

(a) Please Represent this game in Normal Form. You can select any n 5.

(b) Which pure strategy should each of the two rational players choose? Show your argument. (Hint: The selection of your strategy must be obtained by applying the concept of dominated strategies to rule out a succession of inferior strategies until only one choice remains.)

(c) Explain that the above strategy is indeed a Nash equilibrium.

Explanation / Answer

Game theorists use the Nash equilibrium concept to analyze the outcome of the strategic interaction of several decision makers. In other words, it provides a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the outcome depends on the decisions of the others. The simple insight underlying John Nash's idea is that one cannot predict the result of the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do, taking into account the decision-making of the others.

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