Imagine a 3 member legislature that must decide how to allocate an asset of unit value. There are three rounds to the game and in each round a randomly assigned proposer must make an offer to each of his fellow legislators. If an oer is accepted by two of the three legislators then the proposed distribution is made and the game ends. If however no agreement is reached by the end of three rounds then each legislator receives zero. Legislators payoffs are given by the share of the asset that they obtain. Assume that for each legislator the current value of a share of the output received in the next round is discounted by 0 < \delta < 1. Find the subgame-perfect Nash equilibrium of this game.
2026-04-18 17:56:51.1776535011
Multiplayer finitely ultimatum game
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In the third round, the proposer should offer some small $x$ to one of the others and keep $1-x$. The value of this to each one is $\delta^2/3$ so in round $2$....