2. Consider a game that game theory people refer to as the “ultimatum game.”We will refer to our two players as the “offerer” and the “decider”. How the gameworks is that the offerer proposes a way to split $1000 between the two players.While this could be done in a variety of ways, we will assume that the offerersonly has two possible proposals: Either a 50-50 split, or she offers the decider$50 and keeps the rest. The decider can either accept or reject the offer. If the offer is accepted, the money is split as proposed. If the offer is rejected, themoney spontaneously combusts and nobody gets anything. a) List the strategies for each player and write an extensive form version of thegame with payouts. b) List all the Nash equilibria of this game. c) Explain which, if any of the Nash equilibrium are not sub-game perfect. d) Write the game out in normal form and find the pure strategy Nashequilibrium. Explain how this matches with your answers to (b) and (c) . Alsoexplain why there is not a mixed strategy equilibrium.
2. Consider a game that
We will refer to our two players as the “offerer” and the “decider”. How the game
works is that the offerer proposes a way to split $1000 between the two players.
While this could be done in a variety of ways, we will assume that the offerers
only has two possible proposals: Either a 50-50 split, or she offers the decider
$50 and keeps the rest. The decider can either accept or reject the offer. If the offer is accepted, the money is split as proposed. If the offer is rejected, the
money spontaneously combusts and nobody gets anything.
a) List the strategies for each player and write an extensive form version of the
game with payouts.
b) List all the Nash equilibria of this game.
c) Explain which, if any of the Nash equilibrium are not sub-game perfect.
d) Write the game out in normal form and find the pure strategy Nash
equilibrium. Explain how this matches with your answers to (b) and (c) . Also
explain why there is not a mixed strategy equilibrium.
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