- #1
matth123
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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?
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?