Suppose we’ve modelled a firm’s entry decision with a one-shot, simultaneous move game, determined payoffs and found the Nash equilibrium. Suppose with the payoffs we came up with, both firms have a clear dominant strategy such that there is a Nash equilibrium in which both firms play their dominant strategy. However, when we observe the actual actions of the firms, we see that they don’t choose the strategy wepredicted and the outcome of the game doesn’t match the Nash equilibrium. What are 4 reasons this might be? (Hint: The firms are rational.)

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Asked Jul 29, 2019
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Suppose we’ve modelled a firm’s entry decision with a one-shot, simultaneous move game, determined payoffs and found the Nash equilibrium. Suppose with the payoffs we came up with, both firms have a clear dominant strategy such that there is a Nash equilibrium in which both firms play their dominant strategy. However, when we observe the actual actions of the firms, we see that they don’t choose the strategy we
predicted and the outcome of the game doesn’t match the Nash equilibrium. What are 4 reasons this might be? (Hint: The firms are rational.)

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Step 1

The one-shot simultaneous move game is the game that determines the final decisions of two players (say two firms) only by looking at their first trial outcome. In this form of game, the final decision is taken by playing the game at once henceforth, the firms will make optimal decisions by looking at their final pay-offs.

Consider a game where Firm A is the existing firm in the market and Firm B wants to enter in the market but before entering in the market Firm B need to analyze that their entry in the market will be beneficial or not. Assume that both firms behave rationally and weight given to each outcome is same. Look at the game given below:

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Firm 2 Enter 2,2 4, 0 Not Enter 0,4 | 1, 1 Firm 1 Enter Not Enter

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Step 2

This situation can be modeled as a strategic game:

Players: Two firms

Actions: Each player’s set of actions is {Enter, Not Enter}

Here, in above game,

  1. When Firm 2 decides to enter in the market then the optimal strategy of Firm 1 is to leave the market as leaving the market will give a pay-off of 4 whereas staying in the market gives a pay-off of 2. Hence, if Firm 2 enters, Firm 1 should leave from the market.

 

  1. When Firm 2 decides not to enter in the market then the optimal strategy of Firm 1 is to leave the market as leaving the market will give a pay-off of 1 whereas staying in the market gives a pay-off of 0. Hence, if Firm 2 enters, Firm 1 should leave from the market.

 

Hence, the optional strategy of Firm 1 is to leave the market irrespective of Firm 2 decision.

 

  1. When Firm 1 decides to enter in the market then the optimal strategy of Firm 2 is to leave the market as leaving the market will give a pay-off of 4 whereas staying in the market gives a pay-off of 2. Hence, if Firm 1 enters, Firm 2 should leave from the market.

 

  1. When Firm 1 decides not to enter in the market then the optimal strategy of Firm 2 is to leave the market as staying the market will give a pay-off of 0 whereas leaving the market gives a pay-off of 1. Hence, if Firm 1 not enter, Firm 2 should leave from the market.

 

Hence, the optional strategy of Firm 1 is to leave the market irrespective of Firm 2 decision.

Step 3

Thus, the unique Nash equilibrium of this game, i.e., {Firm 1, Firm 2} is {Not Enter, Not Enter} in which the pay-off is {1, 1}.

Further, the dominant strategy is that strategy that always give a higher utility to a player irrespective of the other players strategy; hence for Firm 1, the dominant ...

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Introduction to Game theory

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