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Ec101F10L7_8b_101028 - Economics 101 UCLA Fall 2010 Jernej...

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Economics 101, UCLA Fall 2010 Jernej Copic Lectures 7 and 8 10/19/10 and 10/21/10. Time: interest-rate and discounting; Bargaining: Ultimatum game, 2-stage alternating offers game (Stahl), infinite-stage alternating offers game (Rubinstein [1983]). One day, Jeremiah was meandering about the gilded walls of the oldest parts of downtown Los Angeles. As it turned out No1 was curious about the practicalities of bargaining and it so happened that just on that Tuesday, he set up a small bazaar for a piece of fashionable garment: a blue faux-silk handkerchief. He was anticipating Jeremiah’s arrival, and Jeremiah was a man of fashion; Alan was to run the shop. No1 being an experienced and wise man on the lore of bargaining instructed Alan on the protocol that he should observe: “Be the first to make an offer, and make sure to tell an elaborate story about the beauty and softness and all other special properties of the blue handkerchief. I mean, you and Jeremiah both know that the blue faux-silk handkerchief is worth exactly $ 1, but the question is really who gets what share of that dollar - how the surplus is allocated to you and Jeremiah.” Alan nodded, carefully listening to the instruction. “After you’ve made your offer, then,” continued No1, “you let the other respond to it with a counteroffer (unless he agrees). And I assure you that he will be no less elaborate about his reasoning as to why your offer was unreasonable. And then you will make another offer, and let him make a counteroffer and so on... Unless, of course, your were right on target the first time around, in which case, he won’t waste any of your time, or his own, for that matter, and just accept it the first time around, hehe,” No1 smiled with a mischievous spark in his eye. Alan looked it him in perplexedly and in awe:“but how on Earth will I do that?” “Ok, let me explain as my great grandmother explained to me that day, a very long time ago in our little backyard, cherries blossoming. Ah, may she rest in peace, the wonderful woman she was. My great grandmother was a very pedagogical and impressive lady – so let’s go step by step. 1
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Ultimatum game. First, just consider a very simple game, “the ultimatum game.” There are two players, 1 and 2: the first player, player 1, is the proposer, and he proposes the division of some surplus, let’s call it a pie, to the second player, player 2. The second player then either accepts or rejects the offer. If he accepts, then both players get their proposed shares, and otherwise they walk away with nothing. So this is as if you had made a take-it- or-leave-it proposal to Jeremiah when he came to negotiate the price of the handkerchief. In this first step there is no time, as everything unfolds in a moment. In the ultimatum game, we will call player who proposes the proposer , and player who accepts or rejects the decider .
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