Alice and Bob negotiate over a deal which generates a surplus of 10 (payoffs inthousands of dollars). They negotiate as in the standard Rubinstein Stahlbargaining model from Chapter 11- Alice offers x, € [0,10] representing her shareof the surplus, Bob accepts or rejects, if Bob rejects then the roles reverse and Boboffers x2 € [0,10], and so on – with a twist: There is no time discount. Instead, thesize of the surplus remains the same (so, offers are always from 0 to 10), but forevery rejection, both players' payoffs are reduced by 1 to pay for lawyer fees. (Ex: ifthere are two rejections and then an acceptance of an offer of x3 = 5, then thepayoffs are 3 and 3).a. Solve the SPNE for the ultimatum game (T=1).Bob accepts any offer x, s 10. Alice sets x,= 10.b. Describe the SPNE outcome (does agreement occur, when, who offers, what isthe offer) for T=3.c. Describe the SPNE outcome for T=4.

A subgame Perfect Nash equilibrium (SPNE) is a concept in recreation principle that describes a…

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Business

Economics

SPNE

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Alice and Bob negotiate over a deal which generates a surplus of 10 (payoffs in
thousands of dollars). They negotiate as in the standard Rubinstein Stahl
bargaining model from Chapter 11- Alice offers x, € [0,10] representing her share
of the surplus, Bob accepts or rejects, if Bob rejects then the roles reverse and Bob
offers x2 € [0,10], and so on – with a twist: There is no time discount. Instead, the
size of the surplus remains the same (so, offers are always from 0 to 10), but for
every rejection, both players' payoffs are reduced by 1 to pay for lawyer fees. (Ex: if
there are two rejections and then an acceptance of an offer of x3 = 5, then the
payoffs are 3 and 3).
a. Solve the SPNE for the ultimatum game (T=1).
Bob accepts any offer x, s 10. Alice sets x,
= 10.
b. Describe the SPNE outcome (does agreement occur, when, who offers, what is
the offer) for T=3.
c. Describe the SPNE outcome for T=4.

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Step 1: Define subgame Perfect Nash equilibrium (SPNE)

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Step 2: Explain the SPNE for the ultimatum game (T=1).

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Step 3: Explain the SPNE outcome (does agreement occur, when, who offers, what is the offer) for T=3.

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Step 4: Explain the SPNE outcome for T=4.

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