Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Resource Allocation for Political Campaigns   In an election campaign, candidates must decide how to optimally allocate
their efforts/resources optimally among the regions of a country. As a result,
the outcome of the election will depend on the players' strategies and the
voters' preferences. In this work, we present a zero-sum game where two
candidates decide how to invest a fixed resource in a set of regions, while
considering their sizes and biases. We explore the Majority System (MS) as well
as the Electoral College (EC) voting systems. We prove equilibrium existence
and uniqueness under MS in a deterministic model; in addition, their closed
form expressions are provided when fixing the subset of regions and relaxing
the non-negative investing constraint. For the stochastic case, we use Monte
Carlo simulations to compute the players' payoffs, together with its gradient
and hessian. For the EC, given the lack of Equilibrium in pure strategies, we
propose an iterative algorithm to find Equilibrium in mixed strategies in a
subset of the simplex lattice. We illustrate numerical instances under both
election systems, and contrast players' equilibrium strategies. Finally, we
show that polarization induces candidates to focus on larger regions with
negative biases under MS, whereas candidates concentrate on swing states under
EC.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio