PLEASE CHECK THIS HOW TO SOLVE PLEASE TEACH EXPLAIN STEP BY STEP EXAMPLE 176.2 (A synergistic relationship) Consider a variant of the situation inExample 39.1, in which two individuals are involved in a synergistic relationship.Suppose that the players choose their effort levels sequentially, rather than simul-taneously. First individual 1 chooses her effort level a₁, then individual 2 choosesher effort level a2. An effort level is a nonnegative number, and individual i's pref-erences (for i = 1, 2) are represented by the payoff function a¡(c+a; − a;), where jis the other individual and c> 0 is a constant.To find the subgame perfect equilibria, we first consider the subgames of length1, in which individual 2 chooses a value of a2. Individual 2's optimal action afterthe history ay is her best response to a₁, which we found to be. (c + a₁) in Exam-ple 39.1. Thus individual 2's strategy in any subgame perfect equilibrium is thefunction that associates with each history a₁ the action (c+a₁).Now consider individual 1's action at the start of the game. Given individ-ual 2's strategy, individual 1's payoff if she chooses a₁ is a₁(c +(c + a₁) -a₁),or a₁ (3c-a₁). This function is a quadratic that is zero when a₁ = 0 and whena₁ = 3c, and reaches a maximum in between. Thus individual 1's optimal actionat the start of the game is a₁ = c.. We conclude that the game has a unique subgame perfect equilibrium, in whichindividual 1's strategy is a₁ = 3c and individual 2's strategy is the function thatassociates with each history at the action (c+a₁). The outcome of the equilibriumis thåt individual 1 chooses a₁ = 3c and individual 2 chooses a2 = c.

There are 2 playersPlayer 1 and player 2The game is a sequential game. It is not a simultaneous…

EXAMPLE 176.2 (A synergistic relationship) Consider a variant of the situation in Example 39.1, in which two individuals are involved in a synergistic relationship. Suppose that the players choose their effort levels sequentially, rather than simul- taneously. First individual 1 chooses her effort level a₁, then individual 2 chooses her effort level a2. An effort level is a nonnegative number, and individual i's pref- erences (for i= 1, 2) are represented by the payoff function a; (c +a; - a;), where j is the other individual and c> 0 is a constant. To find the subgame perfect equilibria, we first consider the subgames of length

EXAMPLE 176.2 (A synergistic relationship) Consider a variant of the situation in Example 39.1, in which two individuals are involved in a synergistic relationship. Suppose that the players choose their effort levels sequentially, rather than simul- taneously. First individual 1 chooses her effort level a₁, then individual 2 chooses her effort level a2. An effort level is a nonnegative number, and individual i's pref- erences (for i= 1, 2) are represented by the payoff function a; (c +a; - a;), where j is the other individual and c> 0 is a constant. To find the subgame perfect equilibria, we first consider the subgames of length

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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