each other in a penalty kick that will determine the outcome of the game. The kicker can kick the ball left or right, while the goalie can choose to jump left or right. Because of the speed of the kick, the decisions need to be made simultaneously. If the goalie jumps in the same direction as the kick, then the goalie wins and the kicker loses. If the goalie jumps in the opposite direction of the kick then the kicker wins and the goalie loses. Model this as a strategic form game and write down the matrix that represents the game you modeled. Find the Nash equilibrium.

5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:ˆA writes down either number 1 or number 2, and B must guess which one.ˆIf the number that A has written down is i and B has guessed correctly, B receives i units from A.ˆIf B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.ˆSuppose B guesses 1 with probability p and 2 with probability 1 −p.ˆLet X1 denote B’s gain (or loss) in a game where A has written down 1.ˆLet X2 denote B’s gain (or loss) in a game where A has written down 2.(a)  Find the pmf of X1 and X2(b)  Find B’s expected gain for these two cases, E[X1] and E[X2].(c)  What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player AˆSuppose that A writes down 1 with probability q and 2 with probability 1 −q.ˆLet Y1 be A’s loss (or gain) if B chooses number 1.ˆLet Y2 be A’s loss (or gain) if B…

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In a game theory payoff matrix. Your company (A) and a major competitor (B) havetwo potential strategies: to advertise or to not advertise during the Super Bowl. The payoffs in each cell represent the change in firm profits from advertising.   How would you create payoffs in each cell such that the Nash equilibrium is that both firms advertise despite having a higher profit if neither firm advertised

John and Jane usually vote against each other’s party in the SSC elections resulting to negating or offsetting their votes. If they vote for their party of choice, each of them gains four units of utility (and lose four units of utility from a vote against their party of choice). However, it costs each of them two units of utility for the hassle of actually voting during the SSC elections.                   A. Diagram a game in which John and Jane choose whether to vote or not to vote.                 B. Suppose John and Jane is in agreement not to vote during the election.                             1.) Would such an agreement improve utility? Justify your answer.                             2.) Would such an agreement be an equilibrium? Justify your answer.

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