I need its solution within one hour 1Sober-Wilson Model – Kin-Based Altruism and Direct ReciprocityLet's analyze the Sober-Wilson model in more detail and use it to derive some rules about kin-basedaltruism and direct reciprocity. Start with the same game as in Sober and Wilson with baseline fitness x,benefit to recipient b, and cost to altruist c. The payoff matrix can be written as:Person 211, 12ASA x+ bC, x+ bс, х+Personb1х+b,x сх, хDefine the payoff for Person 1 as 1 and the payoff for Person 2 as ↑2.1. Numerical example: Assume that x = 3, b = 5, and c = 2. Write down the payoff matrix and solve forthe Nash equilibrium.2. Imagine that the two players are kin with genetic relatedness r. When kin play the game together, wecan define the inclusive fitness of Person 1 to be 1+ ri2 and the inclusive fitness of Person 2 to be12 + r1. Using this information, please recreate this payoff matrix using inclusive fitness as thepayoffs. (In other words, calculate 1+ riz and î2+ ri for each cell and put these expressions into thepayoff matrix.)

Given,The payoff matrix associated with the Sober-Wilson model:Person 2Person 1ASAS Here,

1 Sober-Wilson Model - Kin-Based Altruism and Direct Reciprocity Let's analyze the Sober-Wilson model in more detail and use it to derive some rules about kin-based altruism and direct reciprocity. Start with the same game as in Sober and Wilson with baseline fitness x, benefit to recipient b, and cost to altruist c. The payoff matrix can be written as: Person 2 Person 1 11, 12 A x+b A c, x + b X с S C, X+ b X, X S x+b, x Define the payoff for Person 1 as and the payoff for Person 2 as 12. 1. Numerical example: Assume that x = 3, b = 5, and c = 2. Write down the payoff matrix and solve for the Nash equilibrium. 2. Imagine that the two players are kin with genetic relatedness r. When kin play the game together, we can define the inclusive fitness of Person 1 to be 1 + r12 and the inclusive fitness of Person 2 to be 12+ r1. Using this information, please recreate this payoff matrix using inclusive fitness as the payoffs. (In other words, calculate 11+ r12 and 12+ rt for each cell and put these expressions into the payoff matrix.)

1 Sober-Wilson Model - Kin-Based Altruism and Direct Reciprocity Let's analyze the Sober-Wilson model in more detail and use it to derive some rules about kin-based altruism and direct reciprocity. Start with the same game as in Sober and Wilson with baseline fitness x, benefit to recipient b, and cost to altruist c. The payoff matrix can be written as: Person 2 Person 1 11, 12 A x+b A c, x + b X с S C, X+ b X, X S x+b, x Define the payoff for Person 1 as and the payoff for Person 2 as 12. 1. Numerical example: Assume that x = 3, b = 5, and c = 2. Write down the payoff matrix and solve for the Nash equilibrium. 2. Imagine that the two players are kin with genetic relatedness r. When kin play the game together, we can define the inclusive fitness of Person 1 to be 1 + r12 and the inclusive fitness of Person 2 to be 12+ r1. Using this information, please recreate this payoff matrix using inclusive fitness as the payoffs. (In other words, calculate 11+ r12 and 12+ rt for each cell and put these expressions into the payoff matrix.)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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