4. Some types of resource conflicts can be modeled using the following game. Two players would each like to capture a valuable resource, worth R. Each player must choose a strategy from {Amicable, Belligerent}. If one player chooses Belligerent while the other chooses Amicable, the first will walk away with the resource, leaving nothing for the other player. If they both choose Amicable, the resource will be split equally between them. If they both choose Belligerent, the resource will also be split equally between them, but they will each suffer a cost C. P2 Amicable Belligerent P1 Amicable Belligerent R/2, R/2 R, O 0, R R/2-C, R/2-C 4.1. What NEs in pure strategies will the game have for the case where a) R/2 > C, b) R/2 < C and c) R/2 = C? 4.2. Find a Nash equilibrium (NE) in fully (strictly) mixed strategies for this game using the indifference property. Assume that R and C are configured so that a fully mixed NE exists.

4. Some types of resource conflicts can be modeled using the following game. Two players would each like to capture a valuable resource, worth R. Each player must choose a strategy from {Amicable, Belligerent}. If one player chooses Belligerent while the other chooses Amicable, the first will walk away with the resource, leaving nothing for the other player. If they both choose Amicable, the resource will be split equally between them. If they both choose Belligerent, the resource will also be split equally between them, but they will each suffer a cost C. P2 Amicable Belligerent P1 Amicable Belligerent R/2, R/2 R, O 0, R R/2-C, R/2-C 4.1. What NEs in pure strategies will the game have for the case where a) R/2 > C, b) R/2 < C and c) R/2 = C? 4.2. Find a Nash equilibrium (NE) in fully (strictly) mixed strategies for this game using the indifference property. Assume that R and C are configured so that a fully mixed NE exists.

Principles of Economics (MindTap Course List)

8th Edition

ISBN:9781305585126

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5CQQ

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