Reaction functions, differentiation question _ Game theory economics

In summary, in a joint project where value depends on the effort expended by both individuals, Robert and Stuart each receive a value of V(x,y) = 5(x+y) + xy. However, they also incur a cost of effort, with Robert's cost being 3(x^2) and Stuart's being 4(y^2). Assuming they have complete freedom over their effort choices and make them simultaneously, the Nash equilibrium can be determined by deducing the reaction functions of each player. An appropriate diagram can be used to illustrate the equilibrium. The players' equilibrium payoffs can then be determined.
  • #1
matth123
1
0
Consider a scenario where two individuals—Robert and Stuart—are under-
taking a joint project, where the value generated from the project depends
on the effort expended by both individuals. Let x be Robert’s level of effort
and y the level of effort of Stuart; the value of the project for each individual
is given by V (x, y) = 5(x + y) + xy. Each individual receives the value from
the joint project, but incurs a cost of effort, which is given by 3 (x^2) for Robert
and 4 (y^2) for Stuart.

^2 =squared

suppose that both Robert and Stuart have complete freedom
over their effort choices (i.e. effort is a continuous strategy), which are
again chosen simultaneously. After deducing the reaction function of
each player determine what the Nash equilibrium is. Illustrate using
an appropriate diagram. What are the players’ equilibrium payoffs?
 
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  • #2
Hello and welcome to MHB, matth123! :D

Can you show us what you have tried so far, so our helpers know where you are stuck or where you may be going wrong and can then offer better assistance?
 

FAQ: Reaction functions, differentiation question _ Game theory economics

What are reaction functions in game theory economics?

Reaction functions are mathematical equations that describe how players in a game will respond to different strategies chosen by their opponents. In economics, they are used to model the behavior of firms or individuals in a competitive market.

How do you differentiate a reaction function?

To differentiate a reaction function, you would take the derivative of the equation with respect to the variable of interest. This can help determine how the player's response changes as the opponent's strategy changes.

What is the purpose of using reaction functions in game theory economics?

The purpose of using reaction functions is to predict the behavior of players in a game and understand how they will respond to different strategies. This can help in analyzing the outcomes of a game and making strategic decisions.

Can reaction functions be used in non-competitive situations?

Yes, reaction functions can also be used in non-competitive situations, such as in negotiations or decision-making processes. They can help model how different parties will respond to each other's actions and inform optimal strategies.

Are there any limitations to using reaction functions in game theory economics?

One limitation of using reaction functions is that they assume players are rational and have perfect information. In reality, this may not always be the case. Additionally, the accuracy of reaction functions relies on the accuracy of the assumptions and inputs used in the model.

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