Consider the ultimatum game: The proposer offers a split of $10 between himself and the respondent. The proposer can choose any split (x, 10 − x), where x ∈ [0, 10] is the amount the respondent gets (i.e. continuous strategies). Observing the proposer’s offer, the respondent accepts or rejects. If he accepts, the proposed split is implemented. If he rejects, both players get nothing.

Note that the respondent’s strategy is an acceptance rule specifying which offers he will accept. Assume each player maximizes his own monetary payoff.

a. Identify all pure-strategy Nash equilibria of this game. (4 marks)
b. What is the outcome of the subgame perfect equilibrium of the game? (3 marks)

c. Using your results in parts (a) and (b), briefly explain the difference between Nash equilibrium and subgame perfect equilibrium. (1 mark)

d. Explain how threats to reject ‘unfair’ offers could be made credible.

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a The purestrategy Nash equilibria of the ultimatum game occur when both players are making their be... View the full answer