Will and Grace have adjoining unfenced back yards, and each has just adopted a new puppy. Will values a fence between their yards at $$250$ and Grace values a fence between their yards at $$200.$ The cost of building the fence is $$300,$ which will be split equally if they both agree to build the fence. Therefore, their payoff matrix is as follows.

$\backslash$table$[[,,$Build,Will,$],[,,$Not build$],[,,$$$50$ for Grace,$-$$$100$ for Grace$],[,$Build,$$100$ for Will,$$250$ for Will$],[,,$$$200$ for Grace,$$0$ for Grace$],[$Grace$,$Not build,$-$$$50$ for Will,$$0$ for Will$]]$

In the Nash equilibrium of this game

Select one:

a$.$ Will will build the fence by himself.

b$.$ no fence will be built.

c$.$ Will and Grace will both build the fence and split the cost.

d$.$ the fence will be built, but it is uncertain who will build it$.$