Rosencrantz and Guildenstern play a game in which they simultaneously put down some number of coins with either a head or a tail showing on each coin. Rosencrantz puts down one coin and Guildenstern puts down two coins. Rosencrantz pays Guildenstern one dollar for each coin that shows the side that Rosencrantz played; for example, if Rosencrantz played a head and Guildenstern played a head and a tail, Rosencrantz would pay Guildenstern two dollars, since two heads were displayed among the three coins. a. Formulate a strategic game that represents this situation. b. Find all Nash equilibria of this game (including any mixed strategy equilibria). c. For each of the Nash equilibria in (b), give Guildenstern’s expected payoff.
Rosencrantz and Guildenstern play a game in which they simultaneously put down some number of coins with either a head or a tail showing on each coin. Rosencrantz puts down one coin and Guildenstern puts down two coins. Rosencrantz pays Guildenstern one dollar for each coin that shows the side that Rosencrantz played; for example, if Rosencrantz played a head and Guildenstern played a head and a tail, Rosencrantz would pay Guildenstern two dollars, since two heads were displayed among the three coins.
a. Formulate a strategic game that represents this situation.
b. Find all Nash equilibria of this game (including any mixed strategy equilibria).
c. For each of the Nash equilibria in (b), give Guildenstern’s expected payoff.
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