Question

C. The local government is to decide whether to extend the Train \"Red\" line from Medway to Augusta. The values of the extension for people living in Medway and Augusta are $a$ and $b$ respectively. The cost of construction is $c > 0$. The govt. wants to go ahead with the construction if and only if $a+b \ge c$. The values $a$ and $b$ are known by the residents of Medway and Augusta but not by the Government; $c$ is known to everybody. To learn these values the Govt asks each neighbourhood (Medway and Augusta) to submit the value of the construction to the locality. Given the submitted valuations $v_a$ and $v_b$, which need to be non-negative, the government constructs the bridge if and only if $v_a + v_b \ge c$, and tax Medway and Augusta $t_a(v_a,v_b)$ and $t_b(v_a,v_b)$ respectively, where $t_a(v_a, v_b) = \begin{cases} c - v_b \text{if } v_a + v_b \ge c \text{ and } v_b < c, \ 0 \text{otherwise.} \end{cases}$ $t_b(v_a, v_b) = \begin{cases} c - v_a \text{if } v_a + v_b \ge c \text{ and } v_a < c, \ 0 \text{otherwise.} \end{cases}$ Does there exist a dominant strategy equilibrium (DSE) in this game? If so, find one.

          C. The local government is to decide whether to extend the Train \"Red\" line from
Medway to Augusta. The values of the extension for people living in Medway and
Augusta are $a$ and $b$ respectively. The cost of construction is $c > 0$. The govt. wants
to go ahead with the construction if and only if $a+b \ge c$. The values $a$ and $b$ are
known by the residents of Medway and Augusta but not by the Government; $c$ is
known to everybody. To learn these values the Govt asks each neighbourhood
(Medway and Augusta) to submit the value of the construction to the locality. Given
the submitted valuations $v_a$ and $v_b$, which need to be non-negative, the government
constructs the bridge if and only if $v_a + v_b \ge c$, and tax Medway and Augusta $t_a(v_a,v_b)$
and $t_b(v_a,v_b)$ respectively, where
$t_a(v_a, v_b) = \begin{cases} c - v_b \text{if } v_a + v_b \ge c \text{ and } v_b < c, \
0 \text{otherwise.} \end{cases}$
$t_b(v_a, v_b) = \begin{cases} c - v_a \text{if } v_a + v_b \ge c \text{ and } v_a < c, \
0 \text{otherwise.} \end{cases}$
Does there exist a dominant strategy equilibrium (DSE) in this game? If so, find one.

C. The local government is to decide whether to extend the Train R̈edl̈ine from
Medway to Augusta. The values of the extension for people living in Medway and
Augusta are a and b respectively. The cost of construction is c > 0. The govt. wants
to go ahead with the construction if and only if a+b ≥ c. The values a and b are
known by the residents of Medway and Augusta but not by the Government; c is
known to everybody. To learn these values the Govt asks each neighbourhood
(Medway and Augusta) to submit the value of the construction to the locality. Given
the submitted valuations va and vb, which need to be non-negative, the government
constructs the bridge if and only if va + vb ≥ c, and tax Medway and Augusta ta(va,vb)
and tb(va,vb) respectively, where
ta(va, vb) = c - vb if va + vb ≥ c and vb < c, 0 otherwise.
tb(va, vb) = c - va if va + vb ≥ c and va < c, 0 otherwise.
Does there exist a dominant strategy equilibrium (DSE) in this game? If so, find one.

Added by Tracy M.

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