# expected payoff

H T

H -1,1 1,-1

T 1,-1 -1,1

1. What is the MSNE of the matching pennies game above?

2. Make a graph of the best-responses.

3. Suppose this game were repeated 15 times. What would be the SPNE of the repeated game?

Suppose that someone decided to hold the World Series of Matching Pennies in Las Vegas, Nevada. The contest is only open to two players, both of whom get an invitation beforehand. If an invited player chooses to participate the player must pay fee of c<15 to the casino. If only one player chooses to enter, then he gets a reward of 15, paid for by the Association of Matching Pennies Players (not the casino).. If both players enter then they play 15 rounds of matching pennies and each player keeps his winnings.

4. Consider the SPNE of the World Series of Matching Pennies game. What is the probability that an invited player will choose to enter?

5. What is the casino revenue when the entry fee is c?

6. BONUS: What value of c maximizes the casino's revenue? Feel free to use a calculator or computer in solving this question (although it isn't necessary).

Reminder:

1) If the chance of something happening is p, then in two trials the probability that it happens twice is , the probability it happens once is , the probability it doesn't happen at all is .

2) The expected payoff is the sum of the possible payoffs multiplied by the chance that the payoff occurs.

See attached file for full problem description.

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#### Solution Summary

The expected payoff is examined.